tothemeanhttp://tothemean.com/2021-07-31T00:00:00Z2021 NBA Draft Analyticshttp://tothemean.com/2021/07/31/nba-draft-2021.html2021-07-31T00:00:00Z2021-07-31T15:22:53-07:00Jesse Fischer<script>
var player_header = {
"cade-cunningham-2021-oklahoma": "Cade Cunningham",
"jalen-green-2021-ign": "Jalen Green",
"evan-mobley-2021-usc": "Evan Mobley",
"scott-barnes-2021-florida-": "Scott Barnes",
"jalen-suggs-2021-gonzaga": "Jalen Suggs",
"josh-giddey-2021-adelaide": "Josh Giddey",
"jonathan-kuminga-2021-ign": "Jonathan Kuminga",
"franz-wagner-2021-michigan": "Franz Wagner",
"davion-mitchell-2021-baylor": "Davion Mitchell",
"ziaire-williams-2021-stanford": "Ziaire Williams",
"james-bouknight-2021-connecti": "James Bouknight",
"joshua-primo-2021-alabama": "Joshua Primo",
"chris-duarte-2021-oregon": "Chris Duarte",
"moses-moody-2021-arkansas": "Moses Moody",
"corey-kispert-2021-gonzaga": "Corey Kispert",
"alperen-sengun-2021-besiktas": "Alperen Sengun",
"trey-murphy-iii-2021-virginia": "Trey Murphy III",
"tre-mann-2021-florida": "Tre Mann",
"kai-jones-2021-texas": "Kai Jones",
"jalen-johnson-2021-duke": "Jalen Johnson",
"keon-johnson-2021-tennesse": "Keon Johnson",
"isaiah-jackson-2021-kentucky": "Isaiah Jackson",
"usman-garuba-2021-real-mad": "Usman Garuba",
"josh-christopher-2021-arizona-": "Josh Christopher",
"quentin-grimes-2021-houston": "Quentin Grimes",
"bones-hyland-2021-vcu": "Bones Hyland",
"cam-thomas-2021-lsu": "Cam Thomas",
"jaden-springer-2021-tennesse": "Jaden Springer",
"dayron-sharpe-2021-north-ca": "Day'Ron Sharpe",
"santiago-aldama-2021-loyola-(": "Santiago Aldama",
"isaiah-todd-2021-ign": "Isaiah Todd",
"jeremiah-robinson-earl-2021-villanov": "Jeremiah Robinson-Earl",
"jason-preston-2021-ohio": "Jason Preston",
"rokas-jokubaitis-2021-zalgiris": "Rokas Jokubaitis",
"herb-jones-2021-alabama": "Herb Jones",
"miles-mcbride-2021-west-vir": "Miles McBride",
"jt-thor-2021-auburn": "J.T. Thor",
"ayo-dosunmu-2021-illinois": "Ayo Dosunmu",
"neemias-queta-2021-utah-sta": "Neemias Queta",
"jared-butler-2021-baylor": "Jared Butler",
"joe-wieskamp-2021-iowa": "Joe Wieskamp",
"isaiah-livers-2021-michigan": "Isaiah Livers",
"greg-brown-iii-2021-texas": "Greg Brown III",
"kessler-edwards-2021-pepperdi": "Kessler Edwards",
"juhann-begarin-2021-paris-ba": "Juhann Begarin",
"dalano-banton-2021-nebraska": "Dalano Banton",
"david-johnson-2021-louisvil": "David Johnson",
"sharife-cooper-2021-auburn": "Sharife Cooper",
"marcus-zegarowski-2021-creighto": "Marcus Zegarowski",
"filip-petrusev-2021-kk-mega-": "Filip Petrusev",
"bj-boston,-jr-2021-kentucky": "B.J. Boston, Jr.",
"luka-garza-2021-iowa": "Luka Garza",
"charles-bassey-2021-western-": "Charles Bassey",
"sandro-mamukelashvili-2021-seton-ha": "Sandro Mamukelashvili",
"aaron-wiggins-2021-maryland": "Aaron Wiggins",
"scottie-lewis-2021-florida": "Scottie Lewis",
"balsa-koprivica-2021-florida-": "Balsa Koprivica",
"jericho-sims-2021-texas": "Jericho Sims",
"raiquan-gray-2021-florida-": "Raiquan Gray",
"georgios-kalaitzakis-2021-panathin": "Georgios Kalaitzakis",
"justin-champagnie-2021-pittsbur": "Justin Champagnie",
"cameron-krutwig-2021-loyola-(": "Cameron Krutwig",
"mckinley-wright-2021-colorado": "McKinley Wright",
"trendon-watford-2021-lsu": "Trendon Watford",
"jay-huff-2021-virginia": "Jay Huff",
"null": null
};
var player_info = {
"cade-cunningham-2021-oklahoma": "Oklahoma State | FR | SF | 6-8 | 215 | 19.6 | wingspan: 7-0 | rsci: 1 | <a href='https://basketball.realgm.com/player/Cade-Cunningham/Summary/124839'>realgm</a>",
"jalen-green-2021-ign": "IGN | G LEAGUE | SG | 6-5 | 170 | 19.2 | wingspan: 6-8 | rsci: 3 | <a href='https://basketball.realgm.com/player/Jalen-Green/Summary/117342'>realgm</a>",
"evan-mobley-2021-usc": "USC | FR | PF | 7-0 | 200 | 19.9 | wingspan: 7-4 | rsci: 2 | <a href='https://basketball.realgm.com/player/Evan-Mobley/Summary/117327'>realgm</a>",
"scott-barnes-2021-florida-": "Florida State | FR | SF | 6-9 | 225 | 19.8 | wingspan: 7-3 | rsci: 7 | <a href='https://basketball.realgm.com/player/Scott-Barnes/Summary/119506'>realgm</a>",
"jalen-suggs-2021-gonzaga": "Gonzaga | FR | SG | 6-4 | 200 | 19.9 | wingspan: 6-6 | rsci: 11 | <a href='https://basketball.realgm.com/player/Jalen-Suggs/Summary/117344'>realgm</a>",
"josh-giddey-2021-adelaide": "Adelaide | INTL | G | 6-8 | 190 | 18.6 | wingspan: 6-8 | <a href='https://basketball.realgm.com/player/Josh-Giddey/Summary/150528'>realgm</a>",
"jonathan-kuminga-2021-ign": "IGN | G LEAGUE | F | 6-8 | 200 | 18.6 | wingspan: 6-11 | <a href='https://basketball.realgm.com/player/Jonathan-Kuminga/Summary/127826'>realgm</a>",
"franz-wagner-2021-michigan": "Michigan | SO | SF | 6-9 | 215 | 19.7 | wingspan: 7-0 | <a href='https://basketball.realgm.com/player/Franz-Wagner/Summary/108861'>realgm</a>",
"davion-mitchell-2021-baylor": "Baylor | JR | PG | 6-2 | 200 | 22.7 | wingspan: 6-4 | rsci: 57 | <a href='https://basketball.realgm.com/player/Davion-Mitchell/Summary/89964'>realgm</a>",
"ziaire-williams-2021-stanford": "Stanford | FR | F | 6-8 | 190 | 19.6 | wingspan: 6-10 | rsci: 6 | <a href='https://basketball.realgm.com/player/Ziaire-Williams/Summary/137400'>realgm</a>",
"james-bouknight-2021-connecti": "Connecticut | SO | G | 6-5 | 190 | 20.6 | wingspan: 6-8 | rsci: 64 | <a href='https://basketball.realgm.com/player/James-Bouknight/Summary/128317'>realgm</a>",
"joshua-primo-2021-alabama": "Alabama | FR | G | 6-6 | 190 | 18.4 | wingspan: 6-9 | <a href='https://basketball.realgm.com/player/Joshua-Primo/Summary/134341'>realgm</a>",
"chris-duarte-2021-oregon": "Oregon | SR | PG | 6-6 | 180 | 23.9 | wingspan: 6-7 | rsci: 194 | <a href='https://basketball.realgm.com/player/Chris-Duarte/Summary/105378'>realgm</a>",
"moses-moody-2021-arkansas": "Arkansas | FR | SG | 6-6 | 210 | 18.9 | wingspan: 7-1 | rsci: 36 | <a href='https://basketball.realgm.com/player/Moses-Moody/Summary/132632'>realgm</a>",
"corey-kispert-2021-gonzaga": "Gonzaga | SR | SF | 6-7 | 225 | 22.2 | wingspan: 6-7 | rsci: 104 | <a href='https://basketball.realgm.com/player/Corey-Kispert/Summary/105831'>realgm</a>",
"alperen-sengun-2021-besiktas": "Besiktas Sompo Japan | INTL | C | 6-9 | 235 | 18.8 | wingspan: 7-0 | <a href='https://basketball.realgm.com/player/Alperen-Sengun/Summary/137853'>realgm</a>",
"trey-murphy-iii-2021-virginia": "Virginia | JR | G | 6-9 | 205 | 20.9 | wingspan: 7-0 | <a href='https://basketball.realgm.com/player/Trey-Murphy-III/Summary/139788'>realgm</a>",
"tre-mann-2021-florida": "Florida | SO | PG | 6-4 | 180 | 20.2 | wingspan: 6-4 | rsci: 25 | <a href='https://basketball.realgm.com/player/Tre-Mann/Summary/117467'>realgm</a>",
"kai-jones-2021-texas": "Texas | SO | PF | 6-11 | 220 | 20.3 | wingspan: 7-2 | rsci: 52 | <a href='https://basketball.realgm.com/player/Kai-Jones/Summary/120102'>realgm</a>",
"jalen-johnson-2021-duke": "Duke | FR | PF | 6-9 | 210 | 19.4 | wingspan: 7-0 | rsci: 10 | <a href='https://basketball.realgm.com/player/Jalen-Johnson/Summary/117333'>realgm</a>",
"keon-johnson-2021-tennesse": "Tennessee | FR | PG | 6-4 | 185 | 19.2 | wingspan: 6-7 | rsci: 23 | <a href='https://basketball.realgm.com/player/Keon-Johnson/Summary/117372'>realgm</a>",
"isaiah-jackson-2021-kentucky": "Kentucky | FR | PF | 6-10 | 200 | 19.3 | wingspan: 7-2 | rsci: 25 | <a href='https://basketball.realgm.com/player/Isaiah-Jackson/Summary/132627'>realgm</a>",
"usman-garuba-2021-real-mad": "Real Madrid | INTL | C | 6-8 | 215 | 19.2 | wingspan: 7-2 | <a href='https://basketball.realgm.com/player/Usman-Garuba/Summary/108741'>realgm</a>",
"josh-christopher-2021-arizona-": "Arizona State | FR | G | 6-5 | 215 | 19.4 | wingspan: 6-9 | rsci: 12 | <a href='https://basketball.realgm.com/player/Josh-Christopher/Summary/120138'>realgm</a>",
"quentin-grimes-2021-houston": "Houston | JR | SG | 6-5 | 205 | 21.0 | wingspan: 6-8 | rsci: 8 | <a href='https://basketball.realgm.com/player/Quentin-Grimes/Summary/107566'>realgm</a>",
"bones-hyland-2021-vcu": "VCU | SO | G | 6-3 | 170 | 20.6 | wingspan: 6-9 | rsci: 160 | <a href='https://basketball.realgm.com/player/Bones-Hyland/Summary/120125'>realgm</a>",
"cam-thomas-2021-lsu": "LSU | FR | PG | 6-3 | 205 | 19.6 | wingspan: 6-8 | rsci: 26 | <a href='https://basketball.realgm.com/player/Cam-Thomas/Summary/132633'>realgm</a>",
"jaden-springer-2021-tennesse": "Tennessee | FR | SG | 6-4 | 200 | 18.6 | wingspan: 6-8 | rsci: 18 | <a href='https://basketball.realgm.com/player/Jaden-Springer/Summary/117325'>realgm</a>",
"dayron-sharpe-2021-north-ca": "North Carolina | FR | PF | 6-11 | 240 | 19.5 | wingspan: 7-0 | rsci: 24 | <a href='https://basketball.realgm.com/player/DayRon-Sharpe/Summary/135668'>realgm</a>",
"santiago-aldama-2021-loyola-(": "Loyola (MD) | SO | C | 6-11 | 210 | 20.3 | wingspan: | <a href='https://basketball.realgm.com/player/Santiago-Aldama/Summary/119596'>realgm</a>",
"isaiah-todd-2021-ign": "IGN | G LEAGUE | PF | 6-10 | 220 | 19.6 | wingspan: 7-1 | rsci: 17 | <a href='https://basketball.realgm.com/player/Isaiah-Todd/Summary/117340'>realgm</a>",
"jeremiah-robinson-earl-2021-villanov": "Villanova | SO | PF | 6-9 | 240 | 20.5 | wingspan: 6-10 | rsci: 15 | <a href='https://basketball.realgm.com/player/Jeremiah-Robinson-Earl/Summary/103951'>realgm</a>",
"jason-preston-2021-ohio": "Ohio | JR | G | 6-4 | 180 | 22.1 | wingspan: 6-8 | <a href='https://basketball.realgm.com/player/Jason-Preston/Summary/139852'>realgm</a>",
"rokas-jokubaitis-2021-zalgiris": "Zalgiris | INTL | PG | 6-4 | 180 | 20.5 | wingspan: 6-9 | <a href='https://basketball.realgm.com/player/Rokas-Jokubaitis/Summary/108679'>realgm</a>",
"herb-jones-2021-alabama": "Alabama | SR | SF | 6-8 | 205 | 22.6 | wingspan: 7-0 | rsci: 94 | <a href='https://basketball.realgm.com/player/Herb-Jones/Summary/105363'>realgm</a>",
"miles-mcbride-2021-west-vir": "West Virginia | SO | G | 6-2 | 195 | 20.7 | wingspan: 6-9 | rsci: 187 | <a href='https://basketball.realgm.com/player/Miles-McBride/Summary/132462'>realgm</a>",
"jt-thor-2021-auburn": "Auburn | FR | PF | 6-10 | 205 | 18.7 | wingspan: 7-3 | rsci: 47 | <a href='https://basketball.realgm.com/player/JT-Thor/Summary/143359'>realgm</a>",
"ayo-dosunmu-2021-illinois": "Illinois | JR | PG | 6-5 | 195 | 21.3 | wingspan: 6-10 | rsci: 31 | <a href='https://basketball.realgm.com/player/Ayo-Dosunmu/Summary/107970'>realgm</a>",
"neemias-queta-2021-utah-sta": "Utah State | JR | C | 7-0 | 250 | 21.8 | wingspan: 7-4 | <a href='https://basketball.realgm.com/player/Neemias-Queta/Summary/120369'>realgm</a>",
"jared-butler-2021-baylor": "Baylor | JR | PG | 6-3 | 195 | 20.7 | wingspan: 6-4 | rsci: 113 | <a href='https://basketball.realgm.com/player/Jared-Butler/Summary/127262'>realgm</a>",
"joe-wieskamp-2021-iowa": "Iowa | JR | SF | 6-6 | 205 | 21.7 | wingspan: 6-11 | rsci: 50 | <a href='https://basketball.realgm.com/player/Joe-Wieskamp/Summary/89520'>realgm</a>",
"isaiah-livers-2021-michigan": "Michigan | SR | PF | 6-7 | 230 | 22.8 | wingspan: 6-9 | rsci: 153 | <a href='https://basketball.realgm.com/player/Isaiah-Livers/Summary/107423'>realgm</a>",
"greg-brown-iii-2021-texas": "Texas | FR | SF | 6-9 | 205 | 19.7 | wingspan: 7-0 | rsci: 8 | <a href='https://basketball.realgm.com/player/Greg-Brown-III/Summary/117334'>realgm</a>",
"kessler-edwards-2021-pepperdi": "Pepperdine | JR | SG | 6-8 | 205 | 20.7 | wingspan: 6-11 | rsci: 233 | <a href='https://basketball.realgm.com/player/Kessler-Edwards/Summary/88952'>realgm</a>",
"juhann-begarin-2021-paris-ba": "Paris Basketball | INTL | SG | 6-5 | 190 | 18.8 | wingspan: 6-12 | <a href='https://basketball.realgm.com/player/Juhann-Begarin/Summary/123854'>realgm</a>",
"dalano-banton-2021-nebraska": "Nebraska | SO | PG | 6-9 | 195 | 21.5 | wingspan: | rsci: 100 | <a href='https://basketball.realgm.com/player/Dalano-Banton/Summary/132170'>realgm</a>",
"david-johnson-2021-louisvil": "Louisville | SO | SG | 6-5 | 205 | 20.2 | wingspan: 6-10 | rsci: 75 | <a href='https://basketball.realgm.com/player/David-Johnson/Summary/132437'>realgm</a>",
"sharife-cooper-2021-auburn": "Auburn | FR | PG | 6-1 | 160 | 19.9 | wingspan: 7-3 | rsci: 20 | <a href='https://basketball.realgm.com/player/Sharife-Cooper/Summary/117356'>realgm</a>",
"marcus-zegarowski-2021-creighto": "Creighton | JR | PG | 6-2 | 180 | 22.8 | wingspan: 6-3 | rsci: 145 | <a href='https://basketball.realgm.com/player/Marcus-Zegarowski/Summary/108211'>realgm</a>",
"filip-petrusev-2021-kk-mega-": "KK Mega Bemax | INTL | FC | 6-11 | 220 | 21.1 | wingspan: 7-3 | rsci: 82 | <a href='https://basketball.realgm.com/player/Filip-Petrusev/Summary/75786'>realgm</a>",
"bj-boston,-jr-2021-kentucky": "Kentucky | FR | SG | 6-7 | 190 | 19.4 | wingspan: 6-11 | rsci: 5 | <a href='https://basketball.realgm.com/player/BJ-Boston-Jr/Summary/126853'>realgm</a>",
"luka-garza-2021-iowa": "Iowa | SR | C | 6-11 | 245 | 22.4 | wingspan: 7-2 | rsci: 110 | <a href='https://basketball.realgm.com/player/Luka-Garza/Summary/105352'>realgm</a>",
"charles-bassey-2021-western-": "Western Kentucky | JR | PF | 6-11 | 230 | 20.5 | wingspan: 7-3 | rsci: 9 | <a href='https://basketball.realgm.com/player/Charles-Bassey/Summary/88593'>realgm</a>",
"sandro-mamukelashvili-2021-seton-ha": "Seton Hall | SR | F | 6-11 | 240 | 22.0 | wingspan: 7-1 | rsci: 151 | <a href='https://basketball.realgm.com/player/Sandro-Mamukelashvili/Summary/103506'>realgm</a>",
"aaron-wiggins-2021-maryland": "Maryland | JR | F | 6-6 | 190 | 22.3 | wingspan: 6-10 | rsci: 51 | <a href='https://basketball.realgm.com/player/Aaron-Wiggins/Summary/120275'>realgm</a>",
"scottie-lewis-2021-florida": "Florida | SO | SF | 6-5 | 190 | 21.1 | wingspan: 7-0 | rsci: 7 | <a href='https://basketball.realgm.com/player/Scottie-Lewis/Summary/107987'>realgm</a>",
"balsa-koprivica-2021-florida-": "Florida State | SO | C | 7-1 | 255 | 21.0 | wingspan: | rsci: 57 | <a href='https://basketball.realgm.com/player/Balsa-Koprivica/Summary/104912'>realgm</a>",
"jericho-sims-2021-texas": "Texas | SR | C | 6-10 | 250 | 22.6 | wingspan: 7-3 | rsci: 53 | <a href='https://basketball.realgm.com/player/Jericho-Sims/Summary/105383'>realgm</a>",
"raiquan-gray-2021-florida-": "Florida State | JR | PF | 6-8 | 270 | 22.1 | wingspan: 6-11 | rsci: 136 | <a href='https://basketball.realgm.com/player/Raiquan-Gray/Summary/104922'>realgm</a>",
"georgios-kalaitzakis-2021-panathin": "Panathinaikos | INTL | F | 6-7 | 200 | 22.3 | wingspan: | <a href='https://basketball.realgm.com/player/Georgios-Kalaitzakis/Summary/94544'>realgm</a>",
"justin-champagnie-2021-pittsbur": "Pittsburgh | SO | F | 6-6 | 205 | 19.9 | wingspan: 6-10 | <a href='https://basketball.realgm.com/player/Justin-Champagnie/Summary/135180'>realgm</a>",
"cameron-krutwig-2021-loyola-(": "Loyola (IL) | SR | PF | 6-9 | 220 | 22.4 | wingspan: | <a href='https://basketball.realgm.com/player/Cameron-Krutwig/Summary/89392'>realgm</a>",
"mckinley-wright-2021-colorado": "Colorado | SR | PG | 6-0 | 190 | 22.5 | wingspan: 6-5 | rsci: 179 | <a href='https://basketball.realgm.com/player/McKinley-Wright/Summary/118870'>realgm</a>",
"trendon-watford-2021-lsu": "LSU | SO | SF | 6-9 | 235 | 20.5 | wingspan: 7-2 | rsci: 14 | <a href='https://basketball.realgm.com/player/Trendon-Watford/Summary/104914'>realgm</a>",
"jay-huff-2021-virginia": "Virginia | SR | C | 7-1 | 240 | 22.7 | wingspan: | rsci: 60 | <a href='https://basketball.realgm.com/player/Jay-Huff/Summary/106525'>realgm</a>",
"null": null
};
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};
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};
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"bj-boston,-jr-2021-kentucky": "/images/nba_draft/2021/players/bj-boston,-jr-2021-kentucky_comps-bd615e32.png",
"corey-kispert-2021-gonzaga": "/images/nba_draft/2021/players/corey-kispert-2021-gonzaga_comps-1acbdb96.png",
"trey-murphy-iii-2021-virginia": "/images/nba_draft/2021/players/trey-murphy-iii-2021-virginia_comps-b5e6502c.png",
"sandro-mamukelashvili-2021-seton-ha": "/images/nba_draft/2021/players/sandro-mamukelashvili-2021-seton-ha_comps-b2ae0420.png",
"dalano-banton-2021-nebraska": "/images/nba_draft/2021/players/dalano-banton-2021-nebraska_comps-f39dc18d.png",
"marcus-zegarowski-2021-creighto": "/images/nba_draft/2021/players/marcus-zegarowski-2021-creighto_comps-b9c4befd.png",
"kai-jones-2021-texas": "/images/nba_draft/2021/players/kai-jones-2021-texas_comps-0b3874d2.png",
"joe-wieskamp-2021-iowa": "/images/nba_draft/2021/players/joe-wieskamp-2021-iowa_comps-67640e69.png",
"greg-brown-iii-2021-texas": "/images/nba_draft/2021/players/greg-brown-iii-2021-texas_comps-5074301d.png",
"david-johnson-2021-louisvil": "/images/nba_draft/2021/players/david-johnson-2021-louisvil_comps-76b5680c.png",
"davion-mitchell-2021-baylor": "/images/nba_draft/2021/players/davion-mitchell-2021-baylor_comps-b41d13b3.png",
"aaron-wiggins-2021-maryland": "/images/nba_draft/2021/players/aaron-wiggins-2021-maryland_comps-27612045.png",
"jericho-sims-2021-texas": "/images/nba_draft/2021/players/jericho-sims-2021-texas_comps-3fdc824c.png",
"raiquan-gray-2021-florida-": "/images/nba_draft/2021/players/raiquan-gray-2021-florida-_comps-f28ebe7a.png",
"herb-jones-2021-alabama": "/images/nba_draft/2021/players/herb-jones-2021-alabama_comps-64b850bc.png",
"scottie-lewis-2021-florida": "/images/nba_draft/2021/players/scottie-lewis-2021-florida_comps-793fb150.png",
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"joshua-primo-2021-alabama": "/images/nba_draft/2021/players/joshua-primo-2021-alabama_comps-f6aac1e0.png",
"georgios-kalaitzakis-2021-panathin": "/images/nba_draft/2021/players/georgios-kalaitzakis-2021-panathin_comps-986e81ff.png",
"null": null
};
</script>
<p><em>Anyone who has analyzed historical NBA draft picks should know that translating success to the NBA is never a sure thing. No matter how good the scout, GM, or draft model, there is still a high level of uncertainty involved in predicting NBA success.</em></p>
<p><em>My goal is to highlight this uncertainty. By putting less emphasis on a single number, and more emphasis on a probabilistic range of outcomes, our evaluation of players can be more representative of the roll of the dice that NBA teams face.</em></p>
<hr />
<h3 id="a-namemodelnba-draft-modela"><a name="model">NBA Draft Model</a></h3>
<p>If you want to learn more about the machine learning behind these projections - check out <a href="/2020/11/14/nba-draft-2020.html">last year's post</a> as well as this <a href="https://twitter.com/jessefischer33/status/1419934289773273090">Twitter thread</a> which went over model changes for this year. You might also be interested in this <a href="https://twitter.com/jessefischer33/status/1420901438352334849">Twitter thread</a> where I shared real-time insight on players as they were drafted.</p>
<p><em>Follow me on <a href="https://twitter.com/jessefischer33">Twitter</a> if you find this interesting!</em></p>
<hr />
<h3 id="a-namerankings2021-resultsa"><a name="rankings">2021 Results</a></h3>
<p><a href="/images/nba_draft/2021/top_2021-a9b4f9ed.png"><img alt="Top 2021" src="/images/nba_draft/2021/top_2021-a9b4f9ed.png" /></a></p>
<hr />
<h3 id="a-namerankings2021-draft-picksa"><a name="rankings">2021 Draft Picks</a></h3>
<p><a href="/images/nba_draft/2021/pk_2021-585c80ae.png"><img alt="Picks 2021" src="/images/nba_draft/2021/pk_2021-585c80ae.png" /></a></p>
<p><em>Here you can find historical (out of sample) projections for the last several draft classes: <a href="/images/nba_draft/2021/historical_2018-84cebe62.png">2018</a> | <a href="/images/nba_draft/2021/historical_2019-88cc18ed.png">2019</a> | <a href="/images/nba_draft/2021/historical_2020-a2ccabe0.png">2020</a></em></p>
<hr />
<h3 id="a-nameprofilesplayer-profilesa"><a name="profiles">Player Profiles</a></h3>
<p>Select a player to see a player draft profile including:</p>
<ul>
<li><strong>Statistical Profile</strong> - visualize the strengths, weaknesses, and growth trajectory of individual players over their college careers</li>
<li><strong>Playing Style Comps</strong> - find the <a href="/2018/06/10/nba-draft-2018.html#comps">most similar player seasons</a> compared to the potential draftees most recent season, which can keep you honest on a players expected outcome</li>
</ul>
<hr />
<center><select id="player_name" onchange="document.getElementById('player_header').innerHTML = player_header[this.value]; document.getElementById('player_info').innerHTML = player_info[this.value]; document.getElementById('player_growth').src = player_growth[this.value]; document.getElementById('player_growth_a').href = player_growth[this.value]; document.getElementById('player_stats').src = player_stats[this.value]; document.getElementById('player_stats_a').href = player_stats[this.value]; document.getElementById('player_comps').src = player_comps[this.value]; document.getElementById('player_comps_a').href = player_comps[this.value]; ">
<option value="alperen-sengun-2021-besiktas">1. Alperen Sengun - Besiktas Sompo Japan</option>
<option value="evan-mobley-2021-usc">2. Evan Mobley - USC</option>
<option value="dayron-sharpe-2021-north-ca">3. Day'Ron Sharpe - North Carolina</option>
<option value="cade-cunningham-2021-oklahoma">4. Cade Cunningham - Oklahoma State</option>
<option value="jaden-springer-2021-tennesse">5. Jaden Springer - Tennessee</option>
<option value="franz-wagner-2021-michigan">6. Franz Wagner - Michigan</option>
<option value="justin-champagnie-2021-pittsbur">7. Justin Champagnie - Pittsburgh</option>
<option value="jalen-green-2021-ign">8. Jalen Green - IGN</option>
<option value="santiago-aldama-2021-loyola-(">9. Santiago Aldama - Loyola (MD)</option>
<option value="jalen-johnson-2021-duke">10. Jalen Johnson - Duke</option>
<option value="cameron-krutwig-2021-loyola-(">11. Cameron Krutwig - Loyola (IL)</option>
<option value="scott-barnes-2021-florida-">12. Scott Barnes - Florida State</option>
<option value="neemias-queta-2021-utah-sta">13. Neemias Queta - Utah State</option>
<option value="jt-thor-2021-auburn">14. J.T. Thor - Auburn</option>
<option value="jared-butler-2021-baylor">15. Jared Butler - Baylor</option>
<option value="jalen-suggs-2021-gonzaga">16. Jalen Suggs - Gonzaga</option>
<option value="jeremiah-robinson-earl-2021-villanov">17. Jeremiah Robinson-Earl - Villanova</option>
<option value="charles-bassey-2021-western-">18. Charles Bassey - Western Kentucky</option>
<option value="isaiah-jackson-2021-kentucky">19. Isaiah Jackson - Kentucky</option>
<option value="mckinley-wright-2021-colorado">20. McKinley Wright - Colorado</option>
<option value="filip-petrusev-2021-kk-mega-">21. Filip Petrusev - KK Mega Bemax</option>
<option value="jonathan-kuminga-2021-ign">22. Jonathan Kuminga - IGN</option>
<option value="josh-giddey-2021-adelaide">23. Josh Giddey - Adelaide</option>
<option value="sharife-cooper-2021-auburn">24. Sharife Cooper - Auburn</option>
<option value="trendon-watford-2021-lsu">25. Trendon Watford - LSU</option>
<option value="ayo-dosunmu-2021-illinois">26. Ayo Dosunmu - Illinois</option>
<option value="luka-garza-2021-iowa">27. Luka Garza - Iowa</option>
<option value="jay-huff-2021-virginia">28. Jay Huff - Virginia</option>
<option value="moses-moody-2021-arkansas">29. Moses Moody - Arkansas</option>
<option value="usman-garuba-2021-real-mad">30. Usman Garuba - Real Madrid</option>
<option value="keon-johnson-2021-tennesse">31. Keon Johnson - Tennessee</option>
<option value="tre-mann-2021-florida">32. Tre Mann - Florida</option>
<option value="josh-christopher-2021-arizona-">33. Josh Christopher - Arizona State</option>
<option value="jason-preston-2021-ohio">34. Jason Preston - Ohio</option>
<option value="juhann-begarin-2021-paris-ba">35. Juhann Begarin - Paris Basketball</option>
<option value="cam-thomas-2021-lsu">36. Cam Thomas - LSU</option>
<option value="kessler-edwards-2021-pepperdi">37. Kessler Edwards - Pepperdine</option>
<option value="chris-duarte-2021-oregon">38. Chris Duarte - Oregon</option>
<option value="miles-mcbride-2021-west-vir">39. Miles McBride - West Virginia</option>
<option value="bones-hyland-2021-vcu">40. Bones Hyland - VCU</option>
<option value="james-bouknight-2021-connecti">41. James Bouknight - Connecticut</option>
<option value="quentin-grimes-2021-houston">42. Quentin Grimes - Houston</option>
<option value="balsa-koprivica-2021-florida-">43. Balsa Koprivica - Florida State</option>
<option value="ziaire-williams-2021-stanford">44. Ziaire Williams - Stanford</option>
<option value="isaiah-todd-2021-ign">45. Isaiah Todd - IGN</option>
<option value="rokas-jokubaitis-2021-zalgiris">46. Rokas Jokubaitis - Zalgiris</option>
<option value="bj-boston,-jr-2021-kentucky">47. B.J. Boston, Jr. - Kentucky</option>
<option value="corey-kispert-2021-gonzaga">48. Corey Kispert - Gonzaga</option>
<option value="trey-murphy-iii-2021-virginia">49. Trey Murphy III - Virginia</option>
<option value="sandro-mamukelashvili-2021-seton-ha">50. Sandro Mamukelashvili - Seton Hall</option>
<option value="dalano-banton-2021-nebraska">51. Dalano Banton - Nebraska</option>
<option value="marcus-zegarowski-2021-creighto">52. Marcus Zegarowski - Creighton</option>
<option value="kai-jones-2021-texas">53. Kai Jones - Texas</option>
<option value="joe-wieskamp-2021-iowa">54. Joe Wieskamp - Iowa</option>
<option value="greg-brown-iii-2021-texas">55. Greg Brown III - Texas</option>
<option value="david-johnson-2021-louisvil">56. David Johnson - Louisville</option>
<option value="davion-mitchell-2021-baylor">57. Davion Mitchell - Baylor</option>
<option value="aaron-wiggins-2021-maryland">58. Aaron Wiggins - Maryland</option>
<option value="jericho-sims-2021-texas">59. Jericho Sims - Texas</option>
<option value="raiquan-gray-2021-florida-">60. Raiquan Gray - Florida State</option>
<option value="herb-jones-2021-alabama">61. Herb Jones - Alabama</option>
<option value="scottie-lewis-2021-florida">62. Scottie Lewis - Florida</option>
<option value="isaiah-livers-2021-michigan">63. Isaiah Livers - Michigan</option>
<option value="joshua-primo-2021-alabama">64. Joshua Primo - Alabama</option>
<option value="georgios-kalaitzakis-2021-panathin">65. Georgios Kalaitzakis - Panathinaikos</option>
</select></center>
<h3 id="a-idplayerheaderalperen-senguna"><strong><a id="player_header">Alperen Sengun</a></strong></h3>
<text id="player_info">Besiktas Sompo Japan | INTL | C | 6-9 | 235 | 18.8 | wingspan: 7-0 | <a href="https://basketball.realgm.com/player/Alperen-Sengun/Summary/137853">realgm</a></text>
<p><a href="/images/nba_draft/2021/players/alperen-sengun-2021-besiktas_growth.png" id="player_growth_a"><img src="/images/nba_draft/2021/players/alperen-sengun-2021-besiktas_growth.png" id="player_growth" /></a></p>
<h4 id="statistical-profile">Statistical Profile</h4>
<p><a href="/images/nba_draft/2021/players/alperen-sengun-2021-besiktas_stats.png" id="player_stats_a"><img src="/images/nba_draft/2021/players/alperen-sengun-2021-besiktas_stats.png" id="player_stats" /></a></p>
<h4 id="playing-style-comps">Playing Style Comps</h4>
<p><a href="/images/nba_draft/2021/players/alperen-sengun-2021-besiktas_comps.png" id="player_comps_a"><img src="/images/nba_draft/2021/players/alperen-sengun-2021-besiktas_comps.png" id="player_comps" /></a></p>
<hr />
<h3 id="a-namemodelsdraft-model-comparisona"><a name="models">Draft Model Comparison</a></h3>
<p><em>See <a href="https://twitter.com/jessefischer33/status/1420571311265357825">here</a> for links to the various models.</em></p>
<p><a href="/images/nba_draft/2021/models_2021-08e44044.png"><img alt="Models" src="/images/nba_draft/2021/models_2021-08e44044.png" /></a></p>
2021 WNBA Draft Analyticshttp://tothemean.com/2021/04/18/wnba-draft-2021.html2021-04-18T00:00:00Z2021-04-18T17:56:08-07:00Jesse Fischer
<ul>
<li><a href="#plum">PLUM Draft Model</a></li>
<li><a href="#top">2021 PLUM Rankings</a>
<ul>
<li><a href="#top">Top 36</a></li>
<li><a href="#guards">Guards</a></li>
<li><a href="#bigs">Bigs</a></li>
</ul>
</li>
<li><a href="#actual">Actual</a></li>
</ul>
<hr />
<h3 id="a-nameplumplum-draft-modela"><a name="plum">PLUM Draft Model</a></h3>
<p>The <strong>PLUM</strong> draft model (<a href="/2017/04/13/plum-draft-model.html">named after Kelsey Plum</a>) utilizes machine learning to objectively predict which players will succeed in the WNBA.</p>
<p>The model incorporates advanced statistics derived from college play-by-play data which are not available anywhere else (<a href="/2019/05/03/ncaaw-rapm.html">Bayesian RAPM</a>, <a href="/2019/06/01/rapm-stats.html">"Adjusted" box score stats</a>, rate stats, etc.). These statistics isolate the impact and efficiency of a single player by controlling for playing time, pace, other players on the court (opponents, teammates), etc. The model also uses player characteristics (year in school, height) and <a href="http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/">espnW 100 HoopGurlz</a> high school recruit rank.</p>
<p>If you want to read more about modeling details, check out analysis from prior years such as <a href="/2018/04/11/wnba-draft-2018.html">2018</a>, <a href="/2019/04/20/wnba-draft-2019.html">2019</a>, <a href="/2020/04/12/wnba-draft-2020.html">2020</a> or reach out to me on <a href="https://twitter.com/jessefischer33">Twitter</a>.</p>
<hr />
<h3 id="a-nametop2021-plum-rankingsa"><a name="top">2021 PLUM Rankings</a></h3>
<p>Below are the Top 36 players as ranked by the draft model:</p>
<p><a href="/images/wnba_draft/2021/top_2021-5307ca92.png"><img alt="Plum 2021" src="/images/wnba_draft/2021/top_2021-5307ca92.png" /></a></p>
<hr />
<h3 id="a-nameguardstop-guardsa"><a name="guards">Top Guards</a></h3>
<p><a href="/images/wnba_draft/2021/top_2021_guards_stats-6b9110cc.png"><img alt="Guards" src="/images/wnba_draft/2021/top_2021_guards_stats-6b9110cc.png" /></a></p>
<hr />
<h3 id="a-namebigstop-bigsa"><a name="bigs">Top Bigs</a></h3>
<p><a href="/images/wnba_draft/2021/top_2021_bigs_stats-f9c1a640.png"><img alt="Bigs" src="/images/wnba_draft/2021/top_2021_bigs_stats-f9c1a640.png" /></a></p>
<hr />
<h3 id="a-nameactualactuala"><a name="actual">Actual</a></h3>
<p><a href="/images/wnba_draft/2021/actual_2021-2fcfbf48.png"><img alt="Actual" src="/images/wnba_draft/2021/actual_2021-2fcfbf48.png" /></a></p>
NFL Big Data Bowl - Ghost Defenderhttp://tothemean.com/2021/02/21/nfl-ghost-defenders.html2021-02-21T00:00:00Z2021-02-28T11:10:58-08:00Jesse Fischer<p><em>A previous post introduced <a href="/2021/02/07/nfl-pass-cnn.html">Pass CNN</a> which is a Convolutional Neural Network that predicts pass play outcomes in real-time. In this post I will show one (of many) practical applications of such work - using tracking data to learn optimal pass coverage movement and positioning.</em></p>
<p><em>This work was inspired by an article showing how one NBA team <a href="https://grantland.com/features/the-toronto-raptors-sportvu-cameras-nba-analytical-revolution/">uses tracking data to teach optimal defender positioning</a>.</em></p>
<h2 id="what-is-optimal">What is optimal?</h2>
<p>It would be misguided to think that anyone outside of coaches and players will ever know the exact play call or corresponding defensive assignments on a given play. Thus, I won't pretend to believe that my definition of "optimal" will necessarily align with those who are sitting in film study or on the sidelines. However, that doesn't mean we can't try!</p>
<p>What I do know is that we can use historical data to get an estimate of how successful a play will be based purely on <a href="/2021/02/07/nfl-pass-cnn.html">player tracking data at each instant of a play</a>. This is a powerful tool - as we are able to evaluate "what-if" scenarios.</p>
<p><em>What if the safety was a yard deeper at the time of throw?</em></p>
<p><em>What if the cornerback started moving towards the sideline a tenth of second sooner?</em></p>
<p>By holding constant the positioning and movement of all other players on the field (both offensive and defensive), we can evaluate a number of different scenarios and effectively reverse-engineer what optimal coverage might have looked like for a specific defender.</p>
<p>To determine defender positioning that is most optimal, I will be using my <a href="/2021/02/07/nfl-pass-cnn.html">Pass CNN</a> model can which estimates EPA based on a single "frame" of player movement data. The most optimal coverage is defined as the positioning and movement that <strong>minimizes EPA</strong>. If successful, this work has the potential to be a valuable learning tool for defenders - allowing players to see how they defended a play vs. what the model considered as optimal.</p>
<p>To visualize optimal vs. actual, I generate play animations with a <strong>Ghost Defender</strong> that shows where a player ideally would have been located throughout the play. You can see in the animations below how much any differences in positioning actually mattered, by comparing the real-time EPA (actual coverage) vs. Ghost EPA (hypothetical coverage). Note that Ghost EPA is the predicted EPA if the defender was removed and replaced with the Ghost Defender.</p>
<h2 id="what-about-the-coverage">What about the coverage?</h2>
<p>Since I don't have data on defensive coverage (i.e. Cover 1, Cover 2, etc.), I will be focusing on the optimal coverage limited to one or two defenders per play. By making the assumption that the rest of the defensive unit is generally doing what they should be, we can let the model somewhat infer a player's role based on the location of all other players. However, it is feasible to extend this work and learn optimal coverage for the entire defensive unit depending on the defensive play call (e.g. by training a different model for each defensive coverage type).</p>
<h2 id="what-movement-is-feasible">What movement is feasible?</h2>
<p>One challenge with this work was making sure that optimal defender movement is feasible. For example, it isn't reasonable to expect players to be able to go from a standstill to top speed in a tenth of a second. One simple approach used was restricting ghost player locations to be within X yards of the players actual location. In the example below we can see what optimal positioning would have been with the Ghost Defender restricted to be within a 3-yard radius of the actual defender location.</p>
<p><a href="/images/nfl/ghost_defender_relative-fb3c432f.gif"><img alt="Relative Ghost Defender" src="/images/nfl/ghost_defender_relative-fb3c432f.gif" /></a></p>
<p><br />Wow! It is interesting to see the optimal defender location jump around as time advances. One benefit of this approach is that it avoids ghost defenders trying to play an entirely different role from the actual defender. This was a constant challenge, as I found that Ghost Defenders tend to be very aggressive on the blitz when near the line of scrimmage (even if it means leaving a receiver wide open).</p>
<p>However, this still doesn't ensure that player movement is realistic - a player can't teleport from covering one receiver to another instantaneously. Another downside is that this forces Ghost Defenders to behave fairly similarly to the actual player - which is especially limiting when evaluating a blown coverage.</p>
<p>To give Ghost Defenders complete freedom of movement, the ideal approach is to model physics in some capacity. Since I am not well versed on video game physics engines, I decided to use historical data to learn what type of movement is reasonable. Using a players speed in the X and Y direction from one frame, we can estimate an expected range of speed outcomes for that player in the next frame i.e. if at time T1 a player is moving S yards/sec, then at time T2 we can expect the player to be moving S +/- D (where D depends on how fast players can accelerate/decelerate).</p>
<p>Using this approach results in more fluid and realistic Ghost Defender movement. Note that there is an opportunity to personalize Ghost Defenders by incorporating player-specific capabilities (i.e. different players have different maximum acceleration, speed, sharpness of cuts).</p>
<p>Here is the exact same play but with the more realistic modeling of physics. Relative to the Ghost Defender, we can see how the cornerback overcommitted to the middle which allowed the receiver to get just enough space on the outside for a completion.</p>
<p><a href="/images/nfl/ghost_defender_physics-970d3ba4.gif"><img alt="Ghost Defender X" src="/images/nfl/ghost_defender_physics-970d3ba4.gif" /></a></p>
<p>Before looking at other examples, one last methodology note is that I found it useful to let the play develop slightly before allowing the Ghost Defender to be able to diverge greatly from the actual defender location.</p>
<h2 id="highlighted-plays">Highlighted Plays</h2>
<h3 id="blown-coverage">Blown Coverage</h3>
<p>Here is an example that resulted in 29-yard Touchdown pass by Russell Wilson to a wide-open Tyler Lockett. On this 3rd and short play, both Budda Baker (#36) and Patrick Peterson (#21) played the first down line more than any receiver. Both of these players have strong instincts and were likely anticipating quick hitters in that situation. This allowed Lockett to sneak behind for an easy score. While it is hard for me to say who blew their assignment, I thought this would be an interesting play to see how Ghost Defenders would have defended.</p>
<p>It turns out that the Ghost Defenders also aggressively played the first down marker, however the hypothetical Budda Baker dropped back just far enough to still be able to react and give himself a chance to make a play on the ball (even if it still would have resulted in a Touchdown).</p>
<p><a href="/images/nfl/ghost_defender_blown_coverage-73173b13.gif"><img alt="Ghost Defender X" src="/images/nfl/ghost_defender_blown_coverage-73173b13.gif" /></a></p>
<p>Here is the actual video (redirect to Twitter):</p>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Flipping our way to a touchdown!<a href="https://twitter.com/hashtag/AZvsSEA?src=hash&ref_src=twsrc%5Etfw">#AZvsSEA</a> <a href="https://t.co/pxoHuFBRUg">pic.twitter.com/pxoHuFBRUg</a></p>— Seattle Seahawks (@Seahawks) <a href="https://twitter.com/Seahawks/status/1079497756652199936?ref_src=twsrc%5Etfw">December 30, 2018</a></blockquote>
<script async="" src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<h3 id="slow-on-crossing-route">Slow on crossing route</h3>
<p>On this play we can see Mahomes complete an easy pass to Kelce for a third down conversion. This was due to the defender (#31) leaning towards the far side of the field more than he probably should have been.</p>
<p>On the other hand, the Ghost Defender recognized the cross route happening and was able to jump the pass, possibly resulting in a breakup if not interception. It is worth mentioning that with the tighter coverage Mahomes might have checked down to Tyreek Hill (#10) who was open in space, although Mahomes was facing pressure.</p>
<p><a href="/images/nfl/ghost_defender_kelce-640c12b7.gif"><img alt="Ghost Defender X" src="/images/nfl/ghost_defender_kelce-640c12b7.gif" /></a></p>
<h3 id="safety-caught-napping">Safety caught napping</h3>
<p>In this last example, we look at a 37-yard completion on a play-action rollout by Matt Ryan. Julio Jones got a step on the corner after running an out route and help from the safety (#39) arrived too late. Even with most of the action moving towards the far side of the field (top of animation) the safety was slow to react. This is a good example of how play-action can help the pass, as it likely contributed to the safety freezing briefly.</p>
<p>Meanwhile, the Ghost Defender made a good read as the play developed and put himself in a position to challenge Julio at the ball. The positioning of the Ghost Defender turned the predicted EPA from a large positive value to a slightly negative (at the time of ball arrival).</p>
<p><a href="/images/nfl/ghost_defender_safety-31007904.gif"><img alt="Ghost Defender X" src="/images/nfl/ghost_defender_safety-31007904.gif" /></a></p>
<p><em>Feel free to follow me on <a href="https://twitter.com/jessefischer33">Twitter</a> if you liked this post!</em></p>
NFL Big Data Bowl - PassNethttp://tothemean.com/2021/02/07/nfl-pass-cnn.html2021-02-07T00:00:00Z2021-02-28T11:26:49-08:00Jesse Fischer<p><em>After submitting an entry to the <a href="https://www.kaggle.com/c/nfl-big-data-bowl-2021">2021 Big Data Bowl</a> in which I evaluated new <a href="https://www.kaggle.com/jessefis/nfl-big-data-bowl-2021-next-gen-stats">Next Gen Stats for pass defense</a> (<a href="https://twitter.com/StatsbyLopez/status/1357719092543819781">honorable mention!</a> <a href="https://operations.nfl.com/gameday/analytics/big-data-bowl/2018-19-big-data-bowl/">again…</a>), I decided to play around with an entirely different idea. This work was inspired by the <a href="https://www.kaggle.com/c/nfl-big-data-bowl-2020/discussion/119400">2020 Big Data Bowl winning solution</a> which used Convolutional Neural Networks (CNN) to predict expected rush yards at the time of handoff.</em></p>
<h2 id="goal">Goal</h2>
<p>My objective was to build a <a href="https://en.wikipedia.org/wiki/Convolutional_neural_network">CNN model</a> using NFL tracking data to predict expected pass play outcomes at every frame of a play (i.e. every tenth of a second).</p>
<p>Not only would it be fun to see how the expected pass outcome changes in real-time as plays develop (analytics broadcast anyone!?) - I have an <a href="/2021/02/21/nfl-ghost-defenders.html">even cooler application that I'll share soon!</a></p>
<h2 id="evaluating-pass-play-outcomes-in-real-time">Evaluating pass play outcomes in real-time</h2>
<p>In the example below we can see how various outcomes (i.e. EPA, Success Rate, TD Probability) change in real-time as the play progresses.</p>
<p>In this particular example, a perfect Patrick Mahomes throw turns a negative expectation play (at time of throw) into an 89-yard touchdown. After the receiver catches the throw in stride and the defender falls down, the TD probability jumps from near zero to almost certain in a matter of a few tenths of a second.</p>
<p><a href="/images/nfl/mahomes_long_pass-1203c67e.gif"><img alt="Mahomes" src="/images/nfl/mahomes_long_pass-1203c67e.gif" /></a></p>
<p><br />Below is an actual video of the play:</p>
<video controls="" width="100%">
<source src="/videos/nfl/mahomes_long_pass.mp4" type="video/mp4" />
</video>
<p><br /><em>If you don't care about nitty gritty model details, skip down to see <a href="#plays">more sample plays</a>.</em></p>
<h2 id="approach">Approach</h2>
<p>Similar to the 2020 Big Data Bowl winning solution for "expected rush yards", I found that a highly predictive CNN model can be built using only the location and speed of players (and football) at a single instant of the play. The basic intuition behind my approach is that there are two groups of players: (1) offensive players - who are trying to advance the football downfield via a pass and (2) defensive players - who are trying to interact with offensive players to prevent a successful pass.</p>
<p>The structure of the model follows this same intuition - one convolution for offensive players using location and speed relative to the football and a second convolution for defensive players relative to each offensive player.</p>
<h3 id="data">Data</h3>
<p>To train the CNN models I used the <a href="https://www.kaggle.com/c/nfl-big-data-bowl-2021/data">2021 Big Data Bowl</a> dataset which includes NFL tracking data across all 19,239 pass plays from the 2018 regular season. With the typical passing play lasting ~5.5 seconds and tracking data existing for each tenth of a second, there are on average around 55 "frames" of movement data per play. On each play the tracking data captures player movement data for all non-lineman offensive players (typically 6) and defensive players (typically 7+).</p>
<p>I filtered out pre-snap data and various small-sample edge cases (i.e. offensive players < 6, defensive players < 7, no football tracking data). I also excluded plays with a penalty to avoid noise being fed into the model when player movement doesn't necessarily align with pass play outcome (the EPA outcome in particular).</p>
<h3 id="data-processing">Data processing</h3>
<p>Tracking data was normalized from left to right (in terms of field direction). To improve CNN performance, each play was replicated with an inverted Y axis in training data (i.e. augmentation) under the assumption that mirrored plays will have identical outcomes. Data for model features was standardized.</p>
<p>To deal with variability in terms of number of defensive players with tracking data across plays (i.e. most commonly there is data for 7 defensive players, but it will vary anywhere from 7 to 11 depending on the play), I filtered to the 7 players furthest from the original line of scrimmage at the time of pass (or sack) as I assume those players are most responsible for pass coverage. I made this decision (instead of populating with zeros for example) to avoid introducing sampling bias if plays with tracking data for >7 defensive players happened to correlate with play outcome.</p>
<h3 id="models">Models</h3>
<ol>
<li><strong>EPA</strong> - Expected points added</li>
<li><strong>SR</strong> - Expected offensive success rate (as determined by whether a play had positive EPA)</li>
<li><strong>COMP</strong> - Expected probability of pass completion</li>
<li><strong>TD</strong> - Expected probability of touchdown</li>
<li><strong>INT</strong> - Expected probability of interception</li>
</ol>
<h3 id="model-structure">Model Structure</h3>
<p>The structure of my CNN follows the success from the 2020 Big Data Bowl winning solution (<a href="https://www.kaggle.com/jccampos/nfl-2020-winner-solution-the-zoo">which someone kindly replicated here</a>). Each "image" (i.e. row of data) fed to the CNN represents a single "frame" from a given passing play. In total, the models were trained on ~2 million unique "images". Each image is transformed into the following vector features (6 offensive players x 7 defensive players x N features):</p>
<ul>
<li>off x,y - football x,y</li>
<li>off sx,sy - football sx,sy</li>
<li>off sx,sy</li>
<li>def x,y - off x,y</li>
<li>def sx,sy - off sx,sy</li>
</ul>
<p>While not required to have a solid model, I also explored adding the following features to improve performance, particularly for the EPA/SR models where it is useful to have more situational context:</p>
<ul>
<li>off x - los x (relative to line of scrimmage)</li>
<li>off x - first x (relative to first down marker)</li>
<li>off x (relative to end zone)</li>
<li>down of play (1,2,3,4)</li>
</ul>
<h3 id="training">Training</h3>
<p>Models were trained on week's 1->16 with week 17 used as hold out data (for evaluation and analysis). Bagging was used to improve model performance with predictions averaged.</p>
<h3 id="evaluation">Evaluation</h3>
<p>As noted, evaluation metrics are based on week 17 holdout data.</p>
<style type="text/css">
table {
border-collapse: collapse;
width: 100%;
}
table th, table td {
padding: 4px;
border-bottom: 1px solid #ddd;
}
tr:hover {background-color: #ddd;}
</style>
<table>
<thead>
<tr>
<th>Model</th>
<th>Correlation</th>
<th style="text-align: center">MAE</th>
<th style="text-align: center">AUC</th>
<th style="text-align: center">Accuracy</th>
</tr>
</thead>
<tbody>
<tr>
<td>EPA</td>
<td>0.538</td>
<td style="text-align: center">0.97</td>
<td style="text-align: center">n/a</td>
<td style="text-align: center">n/a</td>
</tr>
<tr>
<td>SR</td>
<td>0.488</td>
<td style="text-align: center">n/a</td>
<td style="text-align: center">0.77</td>
<td style="text-align: center">0.682</td>
</tr>
<tr>
<td>COMP</td>
<td>0.533</td>
<td style="text-align: center">n/a</td>
<td style="text-align: center">0.814</td>
<td style="text-align: center">0.694</td>
</tr>
<tr>
<td>TD</td>
<td>0.476</td>
<td style="text-align: center">n/a</td>
<td style="text-align: center">0.897</td>
<td style="text-align: center">0.914</td>
</tr>
<tr>
<td>INT</td>
<td>0.386</td>
<td style="text-align: center">n/a</td>
<td style="text-align: center">0.79</td>
<td style="text-align: center">0.94</td>
</tr>
</tbody>
</table>
<p><br />The INT model could be better (interceptions have a lot of randomness to them) but otherwise performance is not bad!</p>
<p>Note that these statistics are equally weighting each frame, which means plays that last longer represent a higher proportion of the total data. We can ensure longer plays aren't biasing our results by looking at performance at specific events (e.g. at snap, at time of throw) or across frame numbers (i.e. frame 1, frame 2, etc.) - the latter is done below.</p>
<p>As a play progress, we expect that the play outcome becomes more obvious (i.e. towards the end of a play, the ball location and closest player is very telling of the outcome). As expected, we can see model accuracy improves as time advances.</p>
<p><a href="/images/nfl/nfl_passnet_accuracy-b92383f1.png"><img alt="Accuracy" src="/images/nfl/nfl_passnet_accuracy-b92383f1.png" /></a></p>
<p><a href="/images/nfl/nfl_passnet_auc-d8eaf69b.png"><img alt="AUC" src="/images/nfl/nfl_passnet_auc-d8eaf69b.png" /></a></p>
<p><a href="/images/nfl/nfl_passnet_mae-7bca811f.png"><img alt="MAE" src="/images/nfl/nfl_passnet_mae-7bca811f.png" /></a></p>
<h2 id="a-nameplayshighlighted-playsa"><a name="plays">Highlighted Plays</a></h2>
<p>Below are various top plays from Week 17, which showcase how expected outcomes change in real-time as a play evolves.</p>
<h3 id="russ-to-lockett-pass">Russ to Lockett Pass</h3>
<p>In this play Russell Wilson steps outside of the pocket and throws a 37-yard dime to Lockett. After the ball is thrown the real-time EPA increases as the intended WR becomes known. Interestingly, the EPA drops for a few frames as the pass is going over the head of the Cardinals defender (#41) which is because the model doesn't know how high in the air the ball is (adding z-axis football coordinates can improve!). The plays ends with a predicted EPA of ~2.5 which is close to the actual EPA of 1.8 (<a href="https://youtu.be/w1CiYo5Pd8c?t=0">watch the video</a>).</p>
<p><a href="/images/nfl/russ_lockett_pass-74a9f749.gif"><img alt="Russ" src="/images/nfl/russ_lockett_pass-74a9f749.gif" /></a></p>
<h3 id="dj-moore-great-catch">D.J. Moore Great Catch</h3>
<p>On this 3rd down play we can see D.J. Moore is well covered by Marshon Lattimore all throughout, which translated to a low completion probability until the very end when Moore makes an amazing catch (<a href="https://youtu.be/w1CiYo5Pd8c?t=12">watch the video</a>).</p>
<p><a href="/images/nfl/moore_catch-a1dd5e48.gif"><img alt="Moore" src="/images/nfl/moore_catch-a1dd5e48.gif" /></a></p>
<h3 id="big-ben-interception">Big Ben Interception</h3>
<p>After Ben throws the ball into coverage we can see the interception probability quickly increase and then spike up after the ball is caught. After the interception starts to be returned for a TD, the model sees that the football and most players are moving towards the Bengals endzone, which bumps the interception probability up even more (<a href="https://youtu.be/w1CiYo5Pd8c?t=23">watch the video</a>).</p>
<p><a href="/images/nfl/big_ben_int-7ab1fff5.gif"><img alt="Ben" src="/images/nfl/big_ben_int-7ab1fff5.gif" /></a></p>
<h3 id="baker-pass-under-pressure">Baker Pass Under Pressure</h3>
<p>Baker buys just enough time for Higgins to free up and then makes a strong throw under pressure to flip the success rate probability in the Brown's favor (<a href="https://youtu.be/w1CiYo5Pd8c?t=121">watch the video</a>).</p>
<p><a href="/images/nfl/baker_pass-bdbdb955.gif"><img alt="Luck" src="/images/nfl/baker_pass-bdbdb955.gif" /></a></p>
<p><em>Follow me on <a href="https://twitter.com/jessefischer33">Twitter</a> and I might share some more interesting plays.</em></p>
2020 NBA Draft Analyticshttp://tothemean.com/2020/11/14/nba-draft-2020.html2020-11-14T00:00:00Z2020-11-17T23:53:44-08:00Jesse Fischer<script>
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"patrick-williams-2020-florida-": "Patrick Williams",
"aleksej-pokusevski-2020-olympiac": "Aleksej Pokusevski",
"isaiah-stewart-ii-2020-washingt": "Isaiah Stewart II",
"onyeka-okongwu-2020-usc": "Onyeka Okongwu",
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"abdoulaye-ndoye-2020-cholet-b": "Abdoulaye N'Doye",
"karim-mane-2019-canada": "Karim Mane",
"null": null
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"james-wiseman-2020-memphis": "Memphis | FR | C | 7-1 | 235 | 19.1 | wingspan: 7-6 | rsci: 1 | <a href='https://basketball.realgm.com/player/James-Wiseman/Summary/107990'>realgm</a>",
"vernon-carey,-jr-2020-duke": "Duke | FR | PF | 6-10 | 265 | 19.2 | wingspan: 7-0 | rsci: 4 | <a href='https://basketball.realgm.com/player/Vernon-Carey-Jr/Summary/107983'>realgm</a>",
"patrick-williams-2020-florida-": "Florida State | FR | G | 6-8 | 210 | 18.7 | wingspan: 6-11 | rsci: 40 | <a href='https://basketball.realgm.com/player/Patrick-Williams/Summary/132443'>realgm</a>",
"aleksej-pokusevski-2020-olympiac": "Olympiacos B | INTL | C | 7-0 | 200 | 18.4 | wingspan: 7-3 | <a href='https://basketball.realgm.com/player/Aleksej-Pokusevski/Summary/130811'>realgm</a>",
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"reggie-perry-2020-mississi": "Mississippi State | SO | F | 6-10 | 250 | 20.1 | wingspan: 7-0 | rsci: 30 | <a href='https://basketball.realgm.com/player/Reggie-Perry/Summary/81695'>realgm</a>",
"devin-vassell-2020-florida-": "Florida State | SO | SG | 6-6 | 180 | 19.7 | wingspan: 6-10 | rsci: 184 | <a href='https://basketball.realgm.com/player/Devin-Vassell/Summary/132173'>realgm</a>",
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"tyrell-terry-2020-stanford": "Stanford | FR | PG | 6-1 | 170 | 19.6 | wingspan: 6-2 | rsci: 91 | <a href='https://basketball.realgm.com/player/Tyrell-Terry/Summary/117533'>realgm</a>",
"filip-petrusev-2021-kk-mega-": "KK Mega Bemax | INTL | FC | 6-11 | 230 | 21.1 | wingspan: 6-10 | rsci: 82 | <a href='https://basketball.realgm.com/player/Filip-Petrusev/Summary/75786'>realgm</a>",
"jahmius-ramsey-2020-texas-te": "Texas Tech | FR | PG | 6-4 | 195 | 18.9 | wingspan: 6-6 | rsci: 31 | <a href='https://basketball.realgm.com/player/Jahmius-Ramsey/Summary/120272'>realgm</a>",
"xavier-tillman-2020-michigan": "Michigan State | JR | PF | 6-8 | 265 | 21.3 | wingspan: 7-2 | rsci: 85 | <a href='https://basketball.realgm.com/player/Xavier-Tillman/Summary/88905'>realgm</a>",
"kaleb-wesson-2020-ohio-sta": "Ohio State | JR | C | 6-9 | 255 | 20.8 | wingspan: 7-4 | rsci: 82 | <a href='https://basketball.realgm.com/player/Kaleb-Wesson/Summary/88920'>realgm</a>",
"tyrese-haliburton-2020-iowa-sta": "Iowa State | SO | PG | 6-5 | 170 | 20.2 | wingspan: 6-8 | rsci: 196 | <a href='https://basketball.realgm.com/player/Tyrese-Haliburton/Summary/132168'>realgm</a>",
"deni-avdija-2020-maccabi-": "Maccabi FOX Tel Aviv | INTL | SG | 6-8 | 205 | 19.3 | wingspan: 6-9 | <a href='https://basketball.realgm.com/player/Deni-Avdija/Summary/116938'>realgm</a>",
"udoka-azubuike-2020-kansas": "Kansas | SR | C | 7-0 | 260 | 20.6 | wingspan: 7-7 | rsci: 29 | <a href='https://basketball.realgm.com/player/Udoka-Azubuike/Summary/71574'>realgm</a>",
"nico-mannion-2020-arizona": "Arizona | FR | PG | 6-3 | 175 | 19.1 | wingspan: 6-2 | rsci: 9 | <a href='https://basketball.realgm.com/player/Nico-Mannion/Summary/117373'>realgm</a>",
"anthony-edwards-2020-georgia": "Georgia | FR | SG | 6-5 | 220 | 18.8 | wingspan: 6-9 | rsci: 2 | <a href='https://basketball.realgm.com/player/Anthony-Edwards/Summary/117444'>realgm</a>",
"devon-dotson-2020-kansas": "Kansas | SO | PG | 6-2 | 185 | 20.8 | wingspan: 6-3 | rsci: 23 | <a href='https://basketball.realgm.com/player/Devon-Dotson/Summary/104371'>realgm</a>",
"jordan-ford-2020-saint-ma": "Saint Mary's | SR | PG | 6-1 | 175 | 21.9 | wingspan: | rsci: 142 | <a href='https://basketball.realgm.com/player/Jordan-Ford/Summary/85675'>realgm</a>",
"markus-howard-2020-marquett": "Marquette | SR | SG | 5-11 | 170 | 21.2 | wingspan: 6-0 | rsci: 87 | <a href='https://basketball.realgm.com/player/Markus-Howard/Summary/81690'>realgm</a>",
"malachi-flynn-2020-san-dieg": "San Diego State | JR | PG | 6-1 | 180 | 22.0 | wingspan: 6-3 | <a href='https://basketball.realgm.com/player/Malachi-Flynn/Summary/89432'>realgm</a>",
"anthony-lamb-2020-vermont": "Vermont | SR | PF | 6-6 | 225 | 22.3 | wingspan: | <a href='https://basketball.realgm.com/player/Anthony-Lamb/Summary/87247'>realgm</a>",
"lamelo-ball-2020-illawarr": "Illawarra | INTL | G | 6-5 | 180 | 18.7 | wingspan: 6-10 | rsci: 21 | <a href='https://basketball.realgm.com/player/LaMelo-Ball/Summary/103892'>realgm</a>",
"killian-tillie-2020-gonzaga": "Gonzaga | SR | C | 6-10 | 220 | 22.2 | wingspan: 6-8 | <a href='https://basketball.realgm.com/player/Killian-Tillie/Summary/77639'>realgm</a>",
"jalen-harris-2020-nevada": "Nevada | JR | SG | 6-5 | 195 | 21.7 | wingspan: 6-7 | <a href='https://basketball.realgm.com/player/Jalen-Harris/Summary/107049'>realgm</a>",
"yoeli-childs-2020-brigham-": "Brigham Young | SR | PF | 6-8 | 225 | 22.3 | wingspan: 7-0 | rsci: 112 | <a href='https://basketball.realgm.com/player/Yoeli-Childs/Summary/85755'>realgm</a>",
"grant-riller-2020-charlest": "Charleston | SR | SG | 6-3 | 180 | 23.2 | wingspan: 6-5 | <a href='https://basketball.realgm.com/player/Grant-Riller/Summary/85385'>realgm</a>",
"theo-maledon-2020-asvel-ba": "ASVEL Basket | INTL | PG | 6-3 | 185 | 18.9 | wingspan: 6-9 | <a href='https://basketball.realgm.com/player/Theo-Maledon/Summary/105847'>realgm</a>",
"christian-keeling-2020-north-ca": "North Carolina | SR | SG | 6-3 | 180 | 21.9 | wingspan: | <a href='https://basketball.realgm.com/player/Christian-Keeling/Summary/107076'>realgm</a>",
"rj-hampton-2020-new-zeal": "New Zealand | INTL | G | 6-5 | 185 | 19.2 | wingspan: 6-7 | rsci: 5 | <a href='https://basketball.realgm.com/player/RJ-Hampton/Summary/117366'>realgm</a>",
"paul-reed-2020-depaul": "DePaul | JR | F | 6-9 | 220 | 20.9 | wingspan: 7-2 | rsci: 234 | <a href='https://basketball.realgm.com/player/Paul-Reed/Summary/121485'>realgm</a>",
"tyler-bey-2020-colorado": "Colorado | JR | PF | 6-7 | 215 | 22.2 | wingspan: 7-1 | rsci: 124 | <a href='https://basketball.realgm.com/player/Tyler-Bey/Summary/85695'>realgm</a>",
"cole-anthony-2020-north-ca": "North Carolina | FR | PG | 6-3 | 190 | 20.0 | wingspan: 6-4 | rsci: 3 | <a href='https://basketball.realgm.com/player/Cole-Anthony/Summary/105342'>realgm</a>",
"obi-toppin-2020-dayton": "Dayton | SO | F | 6-9 | 215 | 22.2 | wingspan: 6-11 | <a href='https://basketball.realgm.com/player/Obi-Toppin/Summary/121580'>realgm</a>",
"nate-hinton-2020-houston": "Houston | SO | SF | 6-5 | 205 | 20.9 | wingspan: | rsci: 130 | <a href='https://basketball.realgm.com/player/Nate-Hinton/Summary/127263'>realgm</a>",
"desmond-bane-2020-texas-ch": "Texas Christian | SR | SG | 6-5 | 210 | 21.9 | wingspan: 6-5 | <a href='https://basketball.realgm.com/player/Desmond-Bane/Summary/107663'>realgm</a>",
"cj-elleby-2020-washingt": "Washington State | SO | SF | 6-6 | 200 | 19.9 | wingspan: 6-7 | <a href='https://basketball.realgm.com/player/CJ-Elleby/Summary/132313'>realgm</a>",
"jordan-nwora-2020-louisvil": "Louisville | JR | F | 6-7 | 225 | 21.7 | wingspan: 6-10 | rsci: 74 | <a href='https://basketball.realgm.com/player/Jordan-Nwora/Summary/76982'>realgm</a>",
"trent-forrest-2020-florida-": "Florida State | SR | SG | 6-4 | 205 | 21.9 | wingspan: 6-8 | rsci: 68 | <a href='https://basketball.realgm.com/player/Trent-Forrest/Summary/85602'>realgm</a>",
"cassius-winston-2020-michigan": "Michigan State | SR | PG | 6-1 | 195 | 23.2 | wingspan: 6-6 | rsci: 32 | <a href='https://basketball.realgm.com/player/Cassius-Winston/Summary/74073'>realgm</a>",
"jerrick-harding-2020-weber-st": "Weber State | SR | PG | 6-1 | 180 | 22.1 | wingspan: | <a href='https://basketball.realgm.com/player/Jerrick-Harding/Summary/106805'>realgm</a>",
"ty-shon-alexander-2020-creighto": "Creighton | JR | SG | 6-5 | 200 | 21.8 | wingspan: 6-8 | rsci: 86 | <a href='https://basketball.realgm.com/player/Ty-Shon-Alexander/Summary/88782'>realgm</a>",
"isaac-okoro-2020-auburn": "Auburn | FR | SG | 6-6 | 210 | 19.3 | wingspan: 6-9 | rsci: 33 | <a href='https://basketball.realgm.com/player/Isaac-Okoro/Summary/117420'>realgm</a>",
"tyrese-maxey-2020-kentucky": "Kentucky | FR | PG | 6-3 | 195 | 19.5 | wingspan: 6-6 | rsci: 10 | <a href='https://basketball.realgm.com/player/Tyrese-Maxey/Summary/108178'>realgm</a>",
"josh-green-2020-arizona": "Arizona | FR | SG | 6-6 | 215 | 19.5 | wingspan: 6-10 | rsci: 13 | <a href='https://basketball.realgm.com/player/Josh-Green/Summary/107565'>realgm</a>",
"saddiq-bey-2020-villanov": "Villanova | SO | F | 6-8 | 215 | 21.1 | wingspan: 6-10 | rsci: 125 | <a href='https://basketball.realgm.com/player/Saddiq-Bey/Summary/120280'>realgm</a>",
"borisa-simanic-2020-kk-crven": "KK Crvena Zvezda | INTL | F | 6-11 | 215 | 22.1 | wingspan: | <a href='https://basketball.realgm.com/player/Borisa-Simanic/Summary/54450'>realgm</a>",
"tre-jones-2020-duke": "Duke | SO | PG | 6-3 | 185 | 20.3 | wingspan: 6-4 | rsci: 11 | <a href='https://basketball.realgm.com/player/Tre-Jones/Summary/92235'>realgm</a>",
"taylor-maughan-2020-brigham-": "Brigham Young | SR | G | 6-4 | 200 | nan | wingspan: | <a href='https://basketball.realgm.com/player/Taylor-Maughan/Summary/48268'>realgm</a>",
"omer-yurtseven-2020-georgeto": "Georgetown | JR | C | 7-0 | 250 | 21.9 | wingspan: 7-1 | <a href='https://basketball.realgm.com/player/Omer-Yurtseven/Summary/53794'>realgm</a>",
"payton-pritchard-2020-oregon": "Oregon | SR | PG | 6-2 | 200 | 22.3 | wingspan: 6-4 | rsci: 51 | <a href='https://basketball.realgm.com/player/Payton-Pritchard/Summary/59506'>realgm</a>",
"marko-simonovic-2021-kk-mega-": "KK Mega Bemax | INTL | C | 6-10 | 205 | 21.6 | wingspan: | <a href='https://basketball.realgm.com/player/Marko-Simonovic/Summary/95242'>realgm</a>",
"precious-achiuwa-2020-memphis": "Memphis | FR | SF | 6-9 | 235 | 20.6 | wingspan: 7-1 | rsci: 12 | <a href='https://basketball.realgm.com/player/Precious-Achiuwa/Summary/107977'>realgm</a>",
"daniel-oturu-2020-minnesot": "Minnesota | SO | FC | 6-10 | 220 | 20.6 | wingspan: 7-2 | rsci: 52 | <a href='https://basketball.realgm.com/player/Daniel-Oturu/Summary/121152'>realgm</a>",
"shamarkus-kennedy-2020-mcneese-": "McNeese State | SR | F | 6-8 | 215 | 21.9 | wingspan: | <a href='https://basketball.realgm.com/player/Shamarkus-Kennedy/Summary/118415'>realgm</a>",
"elijah-hughes-2020-syracuse": "Syracuse | JR | SF | 6-6 | 230 | 22.2 | wingspan: 6-8 | rsci: 198 | <a href='https://basketball.realgm.com/player/Elijah-Hughes/Summary/95914'>realgm</a>",
"kj-martin-2019-oakland-": "Oakland Soldiers | AAU | F | 6-6 | 215 | nan | wingspan: 6-7 | rsci: 183 | <a href='https://basketball.realgm.com/player/KJ-Martin/Summary/129710'>realgm</a>",
"justinian-jessup-2020-boise-st": "Boise State | SR | SF | 6-6 | 200 | 22.0 | wingspan: | <a href='https://basketball.realgm.com/player/Justinian-Jessup/Summary/86984'>realgm</a>",
"leandro-bolmaro-2021-barca": "Barca | INTL | F | 6-7 | 175 | 20.6 | wingspan: 6-8 | <a href='https://basketball.realgm.com/player/Leandro-Bolmaro/Summary/120098'>realgm</a>",
"jaden-mcdaniels-2020-washingt": "Washington | FR | F | 6-9 | 200 | 19.6 | wingspan: 6-11 | rsci: 23 | <a href='https://basketball.realgm.com/player/Jaden-McDaniels/Summary/132425'>realgm</a>",
"isaiah-joe-2020-arkansas": "Arkansas | SO | SG | 6-5 | 170 | 20.9 | wingspan: 6-8 | rsci: 187 | <a href='https://basketball.realgm.com/player/Isaiah-Joe/Summary/132164'>realgm</a>",
"sam-merrill-2020-utah-sta": "Utah State | SR | G | 6-5 | 200 | 24.0 | wingspan: | <a href='https://basketball.realgm.com/player/Sam-Merrill/Summary/109478'>realgm</a>",
"immanuel-quickley-2020-kentucky": "Kentucky | SO | PG | 6-3 | 185 | 20.9 | wingspan: 6-8 | rsci: 18 | <a href='https://basketball.realgm.com/player/Immanuel-Quickley/Summary/104825'>realgm</a>",
"yam-madar-2021-hapoel-t": "Hapoel Tel Aviv | INTL | G | 6-2 | 185 | 20.4 | wingspan: | <a href='https://basketball.realgm.com/player/Yam-Madar/Summary/133147'>realgm</a>",
"skylar-mays-2020-lsu": "LSU | SR | PG | 6-4 | 205 | 22.7 | wingspan: 6-6 | rsci: 103 | <a href='https://basketball.realgm.com/player/Skylar-Mays/Summary/85943'>realgm</a>",
"robert-woodard-2020-mississi": "Mississippi State | SO | G | 6-7 | 230 | 20.6 | wingspan: 7-2 | rsci: 46 | <a href='https://basketball.realgm.com/player/Robert-Woodard/Summary/81706'>realgm</a>",
"aaron-nesmith-2020-vanderbi": "Vanderbilt | SO | SF | 6-6 | 210 | 20.6 | wingspan: 6-10 | rsci: 54 | <a href='https://basketball.realgm.com/player/Aaron-Nesmith/Summary/132149'>realgm</a>",
"cassius-stanley-2020-duke": "Duke | FR | G | 6-6 | 200 | 20.7 | wingspan: 6-7 | rsci: 29 | <a href='https://basketball.realgm.com/player/Cassius-Stanley/Summary/81701'>realgm</a>",
"abdoulaye-ndoye-2020-cholet-b": "Cholet Basket | INTL | PG | 6-7 | 180 | 22.2 | wingspan: | <a href='https://basketball.realgm.com/player/Abdoulaye-NDoye/Summary/77641'>realgm</a>",
"karim-mane-2019-canada": "Canada | FIBA | PG | 6-4 | 195 | 19.0 | wingspan: 6-11 | <a href='https://basketball.realgm.com/player/Karim-Mane/Summary/134530'>realgm</a>",
"null": null
};
var model_insight = {
"killian-hayes-2020-ratiopha": ["2p%","ft%","ast%","blk%","drb%","tov%"],
"james-wiseman-2020-memphis": ["blk%","usg%","efg%","ast%","stl%","3p%"],
"vernon-carey,-jr-2020-duke": ["usg%","drb%","blk%","stl%","ft%","ast%"],
"patrick-williams-2020-florida-": ["blk%","usg%","ft%","efg%","tov%","3p%"],
"aleksej-pokusevski-2020-olympiac": ["drb%","blk%","ft%","pf%","2p%","orb%"],
"isaiah-stewart-ii-2020-washingt": ["blk%","usg%","efg%","ast%","3p%","stl%"],
"onyeka-okongwu-2020-usc": ["2p%","blk%","usg%","ast%","3p%","ft%"],
"reggie-perry-2020-mississi": ["blk%","usg%","drb%","3p%","stl%","tov%"],
"devin-vassell-2020-florida-": ["tov%","3p%","blk%","usg%","ftr","drb%"],
"kira-lewis-2020-alabama": ["ast%","usg%","efg%","blk%","drb%","tov%"],
"jalen-smith-2020-maryland": ["drb%","blk%","2p%","ast%","stl%","orb%"],
"zeke-nnaji-2020-arizona": ["usg%","efg%","2p%","ast%","blk%","3p%"],
"tyrell-terry-2020-stanford": ["ft%","usg%","3p%","blk%","2p%","ftr"],
"filip-petrusev-2021-kk-mega-": ["blk%","usg%","2p%","ast%","drb%","stl%"],
"jahmius-ramsey-2020-texas-te": ["usg%","efg%","3p%","blk%","2p%","ft%"],
"xavier-tillman-2020-michigan": ["blk%","ast%","2p%","3p%","usg%","tov%"],
"kaleb-wesson-2020-ohio-sta": ["drb%","3p%","usg%","2p%","stl%","tov%"],
"tyrese-haliburton-2020-iowa-sta": ["ast%","stl%","2p%","blk%","pf%","usg%"],
"deni-avdija-2020-maccabi-": ["2p%","3p%","drb%","pf%","stl%","ft%"],
"udoka-azubuike-2020-kansas": ["2p%","drb%","blk%","orb%","usg%","stl%"],
"nico-mannion-2020-arizona": ["usg%","ast%","ft%","blk%","efg%","2p%"],
"anthony-edwards-2020-georgia": ["usg%","tov%","ft%","blk%","efg%","drb%"],
"devon-dotson-2020-kansas": ["usg%","ft%","stl%","blk%","drb%","orb%"],
"jordan-ford-2020-saint-ma": ["usg%","efg%","tov%","blk%","drb%","ftr"],
"markus-howard-2020-marquett": ["usg%","3p%","ft%","drb%","blk%","2p%"],
"malachi-flynn-2020-san-dieg": ["ast%","usg%","ft%","blk%","2p%","efg%"],
"anthony-lamb-2020-vermont": ["blk%","usg%","drb%","efg%","2p%","3p%"],
"lamelo-ball-2020-illawarr": ["usg%","ast%","tov%","blk%","pf%","efg%"],
"killian-tillie-2020-gonzaga": ["2p%","3p%","tov%","usg%","ast%","drb%"],
"jalen-harris-2020-nevada": ["usg%","ft%","tov%","blk%","2p%","efg%"],
"yoeli-childs-2020-brigham-": ["usg%","drb%","3p%","stl%","ft%","tov%"],
"grant-riller-2020-charlest": ["usg%","efg%","stl%","blk%","3p%","tov%"],
"theo-maledon-2020-asvel-ba": ["ast%","usg%","2p%","blk%","stl%","ft%"],
"christian-keeling-2020-north-ca": ["orb%","efg%","pf%","usg%","blk%","2p%"],
"rj-hampton-2020-new-zeal": ["usg%","tov%","stl%","blk%","2p%","pf%"],
"paul-reed-2020-depaul": ["blk%","drb%","stl%","tov%","3p%","ft%"],
"tyler-bey-2020-colorado": ["drb%","blk%","stl%","tov%","usg%","ft%"],
"cole-anthony-2020-north-ca": ["usg%","stl%","ast%","efg%","blk%","2p%"],
"obi-toppin-2020-dayton": ["2p%","efg%","blk%","ast%","stl%","ft%"],
"nate-hinton-2020-houston": ["3p%","drb%","tov%","usg%","blk%","2p%"],
"desmond-bane-2020-texas-ch": ["3p%","stl%","efg%","blk%","2p%","tov%"],
"cj-elleby-2020-washingt": ["usg%","drb%","ft%","efg%","blk%","2p%"],
"jordan-nwora-2020-louisvil": ["usg%","3p%","drb%","2p%","blk%","ast%"],
"trent-forrest-2020-florida-": ["stl%","ast%","ft%","usg%","blk%","2p%"],
"cassius-winston-2020-michigan": ["ast%","usg%","ft%","blk%","2p%","drb%"],
"jerrick-harding-2020-weber-st": ["usg%","efg%","ft%","blk%","stl%","tov%"],
"ty-shon-alexander-2020-creighto": ["tov%","3p%","ft%","usg%","blk%","2p%"],
"isaac-okoro-2020-auburn": ["2p%","blk%","ast%","usg%","drb%","stl%"],
"tyrese-maxey-2020-kentucky": ["ft%","tov%","pf%","blk%","2p%","stl%"],
"josh-green-2020-arizona": ["ft%","tov%","stl%","blk%","2p%","drb%"],
"saddiq-bey-2020-villanov": ["3p%","tov%","efg%","blk%","2p%","drb%"],
"borisa-simanic-2020-kk-crven": ["blk%","3p%","2p%","usg%","drb%","stl%"],
"tre-jones-2020-duke": ["ast%","usg%","stl%","blk%","2p%","efg%"],
"taylor-maughan-2020-brigham-": ["stl%","blk%","orb%","usg%","2p%","tov%"],
"omer-yurtseven-2020-georgeto": ["usg%","blk%","drb%","3p%","ast%","orb%"],
"payton-pritchard-2020-oregon": ["usg%","ast%","efg%","blk%","drb%","tov%"],
"marko-simonovic-2021-kk-mega-": ["drb%","ft%","3p%","usg%","stl%","ast%"],
"precious-achiuwa-2020-memphis": ["blk%","usg%","drb%","tov%","ast%","3p%"],
"daniel-oturu-2020-minnesot": ["blk%","usg%","efg%","ast%","3p%","stl%"],
"shamarkus-kennedy-2020-mcneese-": ["efg%","2p%","blk%","usg%","ast%","3p%"],
"elijah-hughes-2020-syracuse": ["usg%","blk%","tov%","2p%","efg%","drb%"],
"kj-martin-2019-oakland-": ["2p%","drb%","blk%","usg%","ast%","stl%"],
"justinian-jessup-2020-boise-st": ["ft%","tov%","3p%","usg%","blk%","ftr"],
"leandro-bolmaro-2021-barca": ["ft%","ftr","stl%","usg%","blk%","2p%"],
"jaden-mcdaniels-2020-washingt": ["blk%","usg%","ft%","efg%","2p%","stl%"],
"isaiah-joe-2020-arkansas": ["ft%","usg%","tov%","blk%","2p%","efg%"],
"sam-merrill-2020-utah-sta": ["ft%","3p%","tov%","blk%","2p%","stl%"],
"immanuel-quickley-2020-kentucky": ["ft%","3p%","tov%","blk%","2p%","ftr"],
"yam-madar-2021-hapoel-t": ["ast%","ft%","tov%","pf%","blk%","2p%"],
"skylar-mays-2020-lsu": ["3p%","ft%","efg%","usg%","blk%","tov%"],
"robert-woodard-2020-mississi": ["3p%","pf%","efg%","usg%","ast%","2p%"],
"aaron-nesmith-2020-vanderbi": ["efg%","usg%","3p%","2p%","ast%","drb%"],
"cassius-stanley-2020-duke": ["orb%","pf%","blk%","usg%","ast%","drb%"],
"abdoulaye-ndoye-2020-cholet-b": ["3p%","stl%","efg%","usg%","blk%","tov%"],
"karim-mane-2019-canada": ["usg%","ast%","orb%","blk%","2p%","efg%"],
"null": ['','','','','','']
};
var player_growth = {
"killian-hayes-2020-ratiopha": "/images/nba_draft/2020/players/killian-hayes-2020-ratiopha_growth-07ad5d52.png",
"james-wiseman-2020-memphis": "/images/nba_draft/2020/players/james-wiseman-2020-memphis_growth-caaeb46f.png",
"vernon-carey,-jr-2020-duke": "/images/nba_draft/2020/players/vernon-carey,-jr-2020-duke_growth-7a267e6f.png",
"patrick-williams-2020-florida-": "/images/nba_draft/2020/players/patrick-williams-2020-florida-_growth-c471c0ff.png",
"aleksej-pokusevski-2020-olympiac": "/images/nba_draft/2020/players/aleksej-pokusevski-2020-olympiac_growth-5d0567e2.png",
"isaiah-stewart-ii-2020-washingt": "/images/nba_draft/2020/players/isaiah-stewart-ii-2020-washingt_growth-a7d190e1.png",
"onyeka-okongwu-2020-usc": "/images/nba_draft/2020/players/onyeka-okongwu-2020-usc_growth-24989f70.png",
"reggie-perry-2020-mississi": "/images/nba_draft/2020/players/reggie-perry-2020-mississi_growth-d54b2c08.png",
"devin-vassell-2020-florida-": "/images/nba_draft/2020/players/devin-vassell-2020-florida-_growth-0f3316c2.png",
"kira-lewis-2020-alabama": "/images/nba_draft/2020/players/kira-lewis-2020-alabama_growth-30cb4858.png",
"jalen-smith-2020-maryland": "/images/nba_draft/2020/players/jalen-smith-2020-maryland_growth-b5369464.png",
"zeke-nnaji-2020-arizona": "/images/nba_draft/2020/players/zeke-nnaji-2020-arizona_growth-5c26ae1b.png",
"tyrell-terry-2020-stanford": "/images/nba_draft/2020/players/tyrell-terry-2020-stanford_growth-70f8c06d.png",
"filip-petrusev-2021-kk-mega-": "/images/nba_draft/2020/players/filip-petrusev-2021-kk-mega-_growth-b166ec9b.png",
"jahmius-ramsey-2020-texas-te": "/images/nba_draft/2020/players/jahmius-ramsey-2020-texas-te_growth-ec2354ab.png",
"xavier-tillman-2020-michigan": "/images/nba_draft/2020/players/xavier-tillman-2020-michigan_growth-5cdd76f3.png",
"kaleb-wesson-2020-ohio-sta": "/images/nba_draft/2020/players/kaleb-wesson-2020-ohio-sta_growth-9fe8f121.png",
"tyrese-haliburton-2020-iowa-sta": "/images/nba_draft/2020/players/tyrese-haliburton-2020-iowa-sta_growth-2b0ccd9e.png",
"deni-avdija-2020-maccabi-": "/images/nba_draft/2020/players/deni-avdija-2020-maccabi-_growth-9ab855e3.png",
"udoka-azubuike-2020-kansas": "/images/nba_draft/2020/players/udoka-azubuike-2020-kansas_growth-62804488.png",
"nico-mannion-2020-arizona": "/images/nba_draft/2020/players/nico-mannion-2020-arizona_growth-491fefcb.png",
"anthony-edwards-2020-georgia": "/images/nba_draft/2020/players/anthony-edwards-2020-georgia_growth-526129ad.png",
"devon-dotson-2020-kansas": "/images/nba_draft/2020/players/devon-dotson-2020-kansas_growth-4d519a08.png",
"jordan-ford-2020-saint-ma": "/images/nba_draft/2020/players/jordan-ford-2020-saint-ma_growth-7585b346.png",
"markus-howard-2020-marquett": "/images/nba_draft/2020/players/markus-howard-2020-marquett_growth-f48b62da.png",
"malachi-flynn-2020-san-dieg": "/images/nba_draft/2020/players/malachi-flynn-2020-san-dieg_growth-d9bc03b1.png",
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<p><em>Anyone who has analyzed historical NBA draft picks should know that translating success to the NBA is never a sure thing. No matter how good the scout, GM, or draft model, there is still a high level of uncertainty involved in predicting NBA success.</em></p>
<p><em>My goal is to highlight this uncertainty. By putting less emphasis on a single number, and more emphasis on a probabilistic range of outcomes, our evaluation of players can be more representative of the roll of the dice that NBA teams face.</em></p>
<hr />
<h3 id="a-namemodelnba-draft-modela"><a name="model">NBA Draft Model</a></h3>
<p>This is my seventh year using machine learning to project NBA draftees. Each year brings an opportunity to reflect on previous results, revisit methodology, and experiment with new technology - all in hopes of having fun, learning, and most importantly improving projections! While my general approach is similar to previous years (such as <a href="/2018/06/10/nba-draft-2018.html">2018</a> or <a href="/2019/06/16/nba-draft-2019.html">2019</a>), the biggest change I made this year was revamping my process in terms of how to factor in the context of player statistics.</p>
<p>Since many top prospects had limited data to base our evaluations on, properly <a href="/2020/09/06/empirical-bayes.html">dealing with small sample performances</a> and incorporating non-NCAA data (i.e. HS, AAU, International) was essential this year. Additionally, as more players are choosing to play outside of the NCAA, streamlining my process for how to normalize statistics across different leagues was an area I set out to improve. This will pay off for years to come given the upcoming change to the minimum draft age, the new option for high schoolers to jump to the G League, and the continual rise of international players dominating the NBA - being able to gain insight from non-NCAA statistics is now more important than ever!</p>
<p>Without getting into all the details, you can think of my "contextualizing process" as a sequence of steps, where each step neutralizes a player's statistics to control for a specific factor that impacts player statistics (e.g. sample size, quality of opposition, three-point line distance). In the past I had fed raw statistics into a black box model alongside other pieces of data (e.g. minutes, pace, age, league), in hopes of implicitly controlling for different pieces of context. Instead, I am explicitly neutralizing individual contextual components one by one. This offers other benefits too - like being able to gain insight into interesting questions (<em>What international league is the most difficult to rack up blocks? How does aging impact a player's usage?</em>).</p>
<p>Data translation steps:</p>
<ol>
<li>Regress towards the mean (see my post on <a href="/2020/09/06/empirical-bayes.html">Empirical Bayes-ketball</a>!)</li>
<li>Normalize by era</li>
<li>Normalize by age (upcoming post on aging curves!)</li>
<li>Normalize by league (upcoming post on league factors!)</li>
</ol>
<p>This approach allows us to compare all player performances on the same scale. I perform all of these translations on the data before feeding into a machine learning model that is trained to project future NBA success.</p>
<p>Projections are performed for each segment of data (i.e. player + year + league) - this is useful because you can easily observe how a player's draft potential changes across different seasons and situations. To get a final player projection, results are aggregated (weighted by minutes) across all historical data segments for a given player.</p>
<p>This year I'm withholding results from my <a href="/2018/06/10/nba-draft-2018.html#quant">Quant model</a> to avoid unnecessary confusion when there are subtle differences on various players (will revisit this in the future). Therefore, I am only sharing results from my <a href="/2018/06/10/nba-draft-2018.html#star">Star model</a> - which predicts the probability of being an All Star (star), Starter (start), Role Player (role), or Bust (bust).</p>
<p>Other notable call outs this year:</p>
<ul>
<li>Model is "stats-only," which means it doesn't include high school rank, projected draft pick, or combine stats. The positive here is that it is not biased by narratives, isn't overly correlated with analyst projection, and provides a diverse data point from scouting. The downside is that some results may seem "off" relative to the consensus (i.e. <em>Why are Ball and Edwards so low!?</em>).<sup id="fnref:1"><a href="#fn:1" class="footnote">1</a></sup></li>
<li>Probabilities are not well calibrated (i.e. they are directionally predictive but the star/starter percentages are muted relative to reality). While there is always room for improvement, this is partially due to a couple of intentional modeling decisions. First, because the model is "stats-only," it is more difficult to get a strong signal on higher end outcomes - since it doesn't have the help of draft projections to hone in on potential stars. Secondly, to avoid selection bias<sup id="fnref:2"><a href="#fn:2" class="footnote">2</a></sup> the model is trained on data spanning ALL players (including International, JC, D3, etc.) which makes "stars" even more rare in the underlying data (but also more meaningful when the model says there is a chance!).</li>
</ul>
<p>While I recommend focusing on the full spectrum of projected outcomes, I realize there are times when a single number is unavoidable (i.e. draft board rank). Therefore, for my "ranking" I apply a custom heuristic which sorts players based on how teams generally behave (i.e. top picks ordered by star potential, next tier by starter+star potential, and the rest by role+starter+star, in all cases placing a higher weighting on upside potential).</p>
<p><em>Feel free to reach out to me on <a href="https://twitter.com/jessefischer33">Twitter</a> to discuss anything here.</em></p>
<hr />
<h3 id="a-namerankings2020-resultsa"><a name="rankings">2020 Results</a></h3>
<p><a href="/images/nba_draft/2020/top_2020-c610506a.png"><img alt="Top 2020" src="/images/nba_draft/2020/top_2020-c610506a.png" /></a></p>
<hr />
<h3 id="a-nameguardstop-guardsa"><a name="guards">Top Guards</a></h3>
<p><a href="/images/nba_draft/2020/top_2020_guards-9d8c5069.png"><img alt="Guards" src="/images/nba_draft/2020/top_2020_guards-9d8c5069.png" /></a></p>
<hr />
<h3 id="a-namebigstop-bigsa"><a name="bigs">Top Bigs</a></h3>
<p><a href="/images/nba_draft/2020/top_2020_bigs-091de976.png"><img alt="Bigs" src="/images/nba_draft/2020/top_2020_bigs-091de976.png" /></a></p>
<hr />
<h3 id="a-nameprofilesplayer-profilesa"><a name="profiles">Player Profiles</a></h3>
<p>Select a player to see a player draft profile including:</p>
<ul>
<li><strong>Statistical Profile</strong> - visualize the strengths, weaknesses, and growth trajectory of individual players over their college careers</li>
<li><strong>Playing Style Comps</strong> - find the <a href="/2018/06/10/nba-draft-2018.html#comps">most similar player seasons</a> compared to the potential draftees most recent season, which can keep you honest on a players expected outcome</li>
<li><strong>Draft Model Insight</strong> - better understand what statisitical factors are most impacting a player projection (based on most recent/highest minute season)</li>
</ul>
<hr />
<center><select id="player_name" onchange="document.getElementById('player_header').innerHTML = player_header[this.value]; document.getElementById('player_info').innerHTML = player_info[this.value]; document.getElementById('player_growth').src = player_growth[this.value]; document.getElementById('player_growth_a').href = player_growth[this.value]; document.getElementById('player_stats').src = player_stats[this.value]; document.getElementById('player_stats_a').href = player_stats[this.value]; document.getElementById('player_comps').src = player_comps[this.value]; document.getElementById('player_comps_a').href = player_comps[this.value]; document.getElementById('insight1').innerHTML = model_insight[this.value][0]; document.getElementById('insight2').innerHTML = model_insight[this.value][1]; document.getElementById('insight3').innerHTML = model_insight[this.value][2]; document.getElementById('insight4').innerHTML = model_insight[this.value][3]; document.getElementById('insight5').innerHTML = model_insight[this.value][4]; document.getElementById('insight6').innerHTML = model_insight[this.value][5]; ">
<option value="killian-hayes-2020-ratiopha">1. Killian Hayes - Ratiopharm Ulm</option>
<option value="james-wiseman-2020-memphis">2. James Wiseman - Memphis</option>
<option value="vernon-carey,-jr-2020-duke">3. Vernon Carey, Jr. - Duke</option>
<option value="patrick-williams-2020-florida-">4. Patrick Williams - Florida State</option>
<option value="aleksej-pokusevski-2020-olympiac">5. Aleksej Pokusevski - Olympiacos B</option>
<option value="isaiah-stewart-ii-2020-washingt">6. Isaiah Stewart II - Washington</option>
<option value="onyeka-okongwu-2020-usc">7. Onyeka Okongwu - USC</option>
<option value="reggie-perry-2020-mississi">8. Reggie Perry - Mississippi State</option>
<option value="devin-vassell-2020-florida-">9. Devin Vassell - Florida State</option>
<option value="kira-lewis-2020-alabama">10. Kira Lewis - Alabama</option>
<option value="jalen-smith-2020-maryland">11. Jalen Smith - Maryland</option>
<option value="zeke-nnaji-2020-arizona">12. Zeke Nnaji - Arizona</option>
<option value="tyrell-terry-2020-stanford">13. Tyrell Terry - Stanford</option>
<option value="filip-petrusev-2021-kk-mega-">14. Filip Petrusev - KK Mega Bemax</option>
<option value="jahmius-ramsey-2020-texas-te">15. Jahmi'us Ramsey - Texas Tech</option>
<option value="xavier-tillman-2020-michigan">16. Xavier Tillman - Michigan State</option>
<option value="kaleb-wesson-2020-ohio-sta">17. Kaleb Wesson - Ohio State</option>
<option value="tyrese-haliburton-2020-iowa-sta">18. Tyrese Haliburton - Iowa State</option>
<option value="deni-avdija-2020-maccabi-">19. Deni Avdija - Maccabi FOX Tel Aviv</option>
<option value="udoka-azubuike-2020-kansas">20. Udoka Azubuike - Kansas</option>
<option value="nico-mannion-2020-arizona">21. Nico Mannion - Arizona</option>
<option value="anthony-edwards-2020-georgia">22. Anthony Edwards - Georgia</option>
<option value="devon-dotson-2020-kansas">23. Devon Dotson - Kansas</option>
<option value="jordan-ford-2020-saint-ma">24. Jordan Ford - Saint Mary's</option>
<option value="markus-howard-2020-marquett">25. Markus Howard - Marquette</option>
<option value="malachi-flynn-2020-san-dieg">26. Malachi Flynn - San Diego State</option>
<option value="anthony-lamb-2020-vermont">27. Anthony Lamb - Vermont</option>
<option value="lamelo-ball-2020-illawarr">28. LaMelo Ball - Illawarra</option>
<option value="killian-tillie-2020-gonzaga">29. Killian Tillie - Gonzaga</option>
<option value="jalen-harris-2020-nevada">30. Jalen Harris - Nevada</option>
<option value="yoeli-childs-2020-brigham-">31. Yoeli Childs - Brigham Young</option>
<option value="grant-riller-2020-charlest">32. Grant Riller - Charleston</option>
<option value="theo-maledon-2020-asvel-ba">33. Theo Maledon - ASVEL Basket</option>
<option value="christian-keeling-2020-north-ca">34. Christian Keeling - North Carolina</option>
<option value="rj-hampton-2020-new-zeal">35. R.J. Hampton - New Zealand</option>
<option value="paul-reed-2020-depaul">36. Paul Reed - DePaul</option>
<option value="tyler-bey-2020-colorado">37. Tyler Bey - Colorado</option>
<option value="cole-anthony-2020-north-ca">38. Cole Anthony - North Carolina</option>
<option value="obi-toppin-2020-dayton">39. Obi Toppin - Dayton</option>
<option value="nate-hinton-2020-houston">40. Nate Hinton - Houston</option>
<option value="desmond-bane-2020-texas-ch">41. Desmond Bane - Texas Christian</option>
<option value="cj-elleby-2020-washingt">42. C.J. Elleby - Washington State</option>
<option value="jordan-nwora-2020-louisvil">43. Jordan Nwora - Louisville</option>
<option value="trent-forrest-2020-florida-">44. Trent Forrest - Florida State</option>
<option value="cassius-winston-2020-michigan">45. Cassius Winston - Michigan State</option>
<option value="jerrick-harding-2020-weber-st">46. Jerrick Harding - Weber State</option>
<option value="ty-shon-alexander-2020-creighto">47. Ty-Shon Alexander - Creighton</option>
<option value="isaac-okoro-2020-auburn">48. Isaac Okoro - Auburn</option>
<option value="tyrese-maxey-2020-kentucky">49. Tyrese Maxey - Kentucky</option>
<option value="josh-green-2020-arizona">50. Josh Green - Arizona</option>
<option value="saddiq-bey-2020-villanov">51. Saddiq Bey - Villanova</option>
<option value="borisa-simanic-2020-kk-crven">52. Borisa Simanic - KK Crvena Zvezda</option>
<option value="tre-jones-2020-duke">53. Tre Jones - Duke</option>
<option value="taylor-maughan-2020-brigham-">54. Taylor Maughan - Brigham Young</option>
<option value="omer-yurtseven-2020-georgeto">55. Omer Yurtseven - Georgetown</option>
<option value="payton-pritchard-2020-oregon">56. Payton Pritchard - Oregon</option>
<option value="marko-simonovic-2021-kk-mega-">57. Marko Simonovic - KK Mega Bemax</option>
<option value="precious-achiuwa-2020-memphis">58. Precious Achiuwa - Memphis</option>
<option value="daniel-oturu-2020-minnesot">59. Daniel Oturu - Minnesota</option>
<option value="shamarkus-kennedy-2020-mcneese-">60. Shamarkus Kennedy - McNeese State</option>
<option value="elijah-hughes-2020-syracuse">62. Elijah Hughes - Syracuse</option>
<option value="kj-martin-2019-oakland-">64. K.J. Martin - Oakland Soldiers</option>
<option value="justinian-jessup-2020-boise-st">65. Justinian Jessup - Boise State</option>
<option value="leandro-bolmaro-2021-barca">67. Leandro Bolmaro - Barca</option>
<option value="jaden-mcdaniels-2020-washingt">82. Jaden McDaniels - Washington</option>
<option value="isaiah-joe-2020-arkansas">92. Isaiah Joe - Arkansas</option>
<option value="sam-merrill-2020-utah-sta">99. Sam Merrill - Utah State</option>
<option value="immanuel-quickley-2020-kentucky">108. Immanuel Quickley - Kentucky</option>
<option value="yam-madar-2021-hapoel-t">119. Yam Madar - Hapoel Tel Aviv</option>
<option value="skylar-mays-2020-lsu">132. Skylar Mays - LSU</option>
<option value="robert-woodard-2020-mississi">137. Robert Woodard - Mississippi State</option>
<option value="aaron-nesmith-2020-vanderbi">194. Aaron Nesmith - Vanderbilt</option>
<option value="cassius-stanley-2020-duke">211. Cassius Stanley - Duke</option>
<option value="abdoulaye-ndoye-2020-cholet-b">298. Abdoulaye N'Doye - Cholet Basket</option>
<option value="karim-mane-2019-canada">319. Karim Mane - Canada</option>
</select></center>
<h3 id="a-idplayerheaderkillian-hayesa"><strong><a id="player_header">Killian Hayes</a></strong></h3>
<text id="player_info">Ratiopharm Ulm | INTL | G | 6-5 | 210 | 18.8 | wingspan: 6-8 | <a href="https://basketball.realgm.com/player/Killian-Hayes/Summary/108654">realgm</a></text>
<p><a href="/images/nba_draft/2020/players/killian-hayes-2020-ratiopha_growth.png" id="player_growth_a"><img src="/images/nba_draft/2020/players/killian-hayes-2020-ratiopha_growth.png" id="player_growth" /></a></p>
<h4 id="statistical-profile">Statistical Profile</h4>
<p><a href="/images/nba_draft/2020/players/killian-hayes-2020-ratiopha_stats.png" id="player_stats_a"><img src="/images/nba_draft/2020/players/killian-hayes-2020-ratiopha_stats.png" id="player_stats" /></a></p>
<h4 id="playing-style-comps">Playing Style Comps</h4>
<p><a href="/images/nba_draft/2020/players/killian-hayes-2020-ratiopha_comps.png" id="player_comps_a"><img src="/images/nba_draft/2020/players/killian-hayes-2020-ratiopha_comps.png" id="player_comps" /></a></p>
<h4 id="draft-model-insight">Draft Model Insight</h4>
<p><span class="fa fa-plus" style="color:green"></span> <text id="insight1">2p%</text>, <text id="insight2">ft%</text>, <text id="insight3">ast%</text><br />
<span class="fa fa-minus" style="color:red"></span> <text id="insight4">blk%</text>, <text id="insight5">drb%</text>, <text id="insight6">tov%</text><br /></p>
<hr />
<h3 id="a-namemodelsdraft-model-comparisona"><a name="models">Draft Model Comparison</a></h3>
<p><a href="/images/nba_draft/2020/models_2020-90a68762.png"><img alt="Models" src="/images/nba_draft/2020/models_2020-90a68762.png" /></a></p>
<div class="footnotes">
<ol>
<li id="fn:1">
<p>This year, I went in this direction because improvements made the "stats-only" model results more reasonable than in the past, so I wanted keep the model "pure". I have gone back and forth on this over time - both are interesting, so I'll probably bring back both in the future. <a href="#fnref:1" class="reversefootnote">↩</a></p>
</li>
<li id="fn:2">
<p>As an example, if you only train a model on players who were drafted, then your model might learn that being under 6-feet is predictive of success based on a few data points of players who have overcome this roadblock. Training on all players allows the model to have stronger projections on fringe NBA players (Ethan Happ anyone!?) and/or to find diamonds in the rough. <a href="#fnref:2" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>
Bayesian Hierarchical Modelinghttp://tothemean.com/2020/09/19/hierarchical-model.html2020-09-19T00:00:00Z2020-09-19T22:51:03-07:00Jesse Fischer<p>In my <a href="/2020/09/06/empirical-bayes.html">last post</a> I showed how, when faced with limited data, you can use Empirical Bayes (EB) to better evaluate a players three-point shooting. We can apply this same technique to NCAA three-point shooting across top projects in the upcoming NBA draft.</p>
<style type="text/css">
table {
border-collapse: collapse;
width: 100%;
}
table th, table td {
padding: 4px;
border-bottom: 1px solid #ddd;
}
tr:hover {background-color: #ddd;}
</style>
<table>
<thead>
<tr>
<th>name</th>
<th>team</th>
<th style="text-align: center">3p% (eb)</th>
<th style="text-align: center">3p%</th>
<th style="text-align: center">3pm</th>
<th style="text-align: center">3pa</th>
</tr>
</thead>
<tbody>
<tr>
<td>Anthony Edwards</td>
<td>Georgia</td>
<td style="text-align: center">0.312</td>
<td style="text-align: center">0.294</td>
<td style="text-align: center">72</td>
<td style="text-align: center">245</td>
</tr>
<tr>
<td>James Wiseman</td>
<td>Memphis</td>
<td style="text-align: center">0.329</td>
<td style="text-align: center">0.000</td>
<td style="text-align: center">0</td>
<td style="text-align: center">1</td>
</tr>
</tbody>
</table>
<p><br />James Wiseman, who missed his only three-point attempt has an EB estimate of 32.9%. His actual shooting percentage had very little impact on his EB estimate. Essentially his percentage was fully regressed to the empirical prior (i.e. league average).</p>
<p>We can see that Wiseman had an EB estimate higher than Anthony Edwards (31.2%), even though Edwards had a higher 3P% (29.4%) - but do we really think Wiseman is a better three-point shooter? What else do we know about these players?</p>
<p>As a Bayesian, we should define our priors about three-point shooting.</p>
<ol>
<li>Good shooters are good shooters<sup id="fnref:1"><a href="#fn:1" class="footnote">1</a></sup> (i.e. Higher FT% = Higher 3P%)</li>
<li>You only get to shoot 3s if you can - there are <a href="https://www.basketball-reference.com/players/f/fergute01.html">always exceptions</a> (i.e. Higher 3PAR = Higher 3P%)</li>
</ol>
<p>While still small sample sizes, we can take advantage of having slightly more data on FT% and 3PAR - let's see how Wiseman and Edwards stack up in these other areas.</p>
<table>
<thead>
<tr>
<th>name</th>
<th>team</th>
<th style="text-align: center">ft%</th>
<th style="text-align: center">3par</th>
</tr>
</thead>
<tbody>
<tr>
<td>Anthony Edwards</td>
<td>Georgia</td>
<td style="text-align: center">0.772</td>
<td style="text-align: center">0.485</td>
</tr>
<tr>
<td>James Wiseman</td>
<td>Memphis</td>
<td style="text-align: center">0.704</td>
<td style="text-align: center">0.039</td>
</tr>
</tbody>
</table>
<p><br />Edwards was a better free-throw shooter (77.2% vs. 70.4%). He also had a significantly higher 3PAR (0.485 vs. 0.039). Based on these additional data points, our assumption is that Edwards is probably a better three-point shooter.</p>
<p>Now how can we factor this additional information into our prior…Bayesian hierarchical modeling!</p>
<blockquote>
<p><strong>Bayesian hierarchical modeling</strong> is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method. The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the uncertainty that is present.</p>
</blockquote>
<p>There are many different ways to approach hierarchical modeling. You could extend our <a href="/2020/09/06/empirical-bayes.html">previous empirical bayes approach</a> as described <a href="http://varianceexplained.org/r/hierarchical_bayes_baseball/">here</a> (which might include using the <a href="https://github.com/dgrtwo/ebbr">ebbr package</a>). However, if you are anything like me, once you get a taste of Bayesian statistical modeling you will quickly find yourself deep down a rabbit hole - exploring all the different probabilistic programming frameworks out there, such as <a href="https://docs.pymc.io/">PyMC</a> and <a href="https://mc-stan.org/">Stan</a>.</p>
<p>For a basic introduction, you can find sports related examples like <a href="https://calogica.com/pymc3/python/2019/12/08/nfl-4thdown-attempts.html">analyzing NFL 4th down attempts</a> or <a href="https://docs.pymc.io/notebooks/rugby_analytics.html">predicting rugby outcomes</a>. For a more in-depth understanding, I recommend reading more about <a href="https://docs.pymc.io/notebooks/multilevel_modeling.html">multilevel modeling</a>, <a href="https://www.databozo.com/deep-in-the-weeds-complex-hierarchical-models-in-pymc3">complex hierarchical modeling</a>, or scaling your model <a href="https://docs.pymc.io/notebooks/bayesian_neural_network_advi.html">via variational inference</a>.</p>
<p>Now back to apply our problem! As I said, there is no single right way to setup a hierarchical model. It is also worth mentioning that I'm relatively new to Baysian modeling so I won't claim to know what is actually best (feedback please!). With that out of the way, one approach is to use a hierarchical prior based on a players FT% and 3PAR quartile. Using <a href="https://docs.pymc.io/">PyMC3</a> I am able to model three-point shooting as a <a href="http://varianceexplained.org/r/beta_binomial_baseball/">beta binomial distribution</a> (I'll repeat - feedback from any experts please!).</p>
<p><a href="/images/eb/pymc3_model-a04b65c6.png"><img alt="PyMC3 Model" src="/images/eb/pymc3_model-a04b65c6.png" /></a></p>
<p>One benefit of using Bayesian modeling tooling, is that with a few lines of code you get pretty charts like this.</p>
<p><a href="/images/eb/pymc3_results-b8cf9362.png"><img alt="PyMC3 Results" src="/images/eb/pymc3_results-b8cf9362.png" /></a></p>
<p>You can also calculate a <a href="http://varianceexplained.org/r/credible_intervals_baseball/">credible interval</a> to see how the expected distribution changes based on your different groups (in our case FT% and 3PAR quartiles).</p>
<p><a href="/images/eb/pymc3_ci-cdc50ba3.png"><img alt="PyMC3 Credible Interval" src="/images/eb/pymc3_ci-cdc50ba3.png" /></a></p>
<p>In the chart above we can see how players with a high FT% and 3PAR (like Anthony Edwards) have a higher credible interval distribution than a player with above average FT% but low 3PAR (like James Wiseman).</p>
<table>
<thead>
<tr>
<th>name</th>
<th>team</th>
<th style="text-align: center">3p% (hierarchical)</th>
<th style="text-align: center">3p% (eb)</th>
<th style="text-align: center">3p% (actual)</th>
<th style="text-align: center">3pm</th>
<th>3pa</th>
</tr>
</thead>
<tbody>
<tr>
<td>Anthony Edwards</td>
<td>Georgia</td>
<td style="text-align: center">0.302</td>
<td style="text-align: center">0.312</td>
<td style="text-align: center">0.294</td>
<td style="text-align: center">72</td>
<td>245</td>
</tr>
<tr>
<td>James Wiseman</td>
<td>Memphis</td>
<td style="text-align: center">0.256</td>
<td style="text-align: center">0.329</td>
<td style="text-align: center">0.000</td>
<td style="text-align: center">0</td>
<td>1</td>
</tr>
</tbody>
</table>
<p><br /> The hierarchical model pulls Wiseman's estimate toward a more informed prior, which makes his three-point shooting estimate now much lower than that of Edwards (25.6% vs. 30.2%).</p>
<p>Below we can see what the hierarchical model infers about 2020 college performances from the <a href="https://www.espn.com/nba/draft/bestavailable">ESPN Top 60</a> in the upcoming draft.</p>
<table>
<thead>
<tr>
<th style="text-align: center">espn</th>
<th>name</th>
<th>team</th>
<th style="text-align: center">3p% (hierarchical)</th>
<th style="text-align: center">3p% (eb)</th>
<th style="text-align: center">3p% (actual)</th>
<th style="text-align: center">3pm</th>
<th style="text-align: center">3pa</th>
<th style="text-align: center">ft%</th>
<th style="text-align: center">3par</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: center">11</td>
<td>Aaron Nesmith</td>
<td>Vanderbilt</td>
<td style="text-align: center">0.455</td>
<td style="text-align: center">0.391</td>
<td style="text-align: center">0.522</td>
<td style="text-align: center">60</td>
<td style="text-align: center">115</td>
<td style="text-align: center">0.825</td>
<td style="text-align: center">0.561</td>
</tr>
<tr>
<td style="text-align: center">41</td>
<td>Desmond Bane</td>
<td>Texas Christian</td>
<td style="text-align: center">0.419</td>
<td style="text-align: center">0.381</td>
<td style="text-align: center">0.442</td>
<td style="text-align: center">92</td>
<td style="text-align: center">208</td>
<td style="text-align: center">0.789</td>
<td style="text-align: center">0.477</td>
</tr>
<tr>
<td style="text-align: center">18</td>
<td>Saddiq Bey</td>
<td>Villanova</td>
<td style="text-align: center">0.418</td>
<td style="text-align: center">0.38</td>
<td style="text-align: center">0.451</td>
<td style="text-align: center">79</td>
<td style="text-align: center">175</td>
<td style="text-align: center">0.769</td>
<td style="text-align: center">0.477</td>
</tr>
<tr>
<td style="text-align: center">30</td>
<td>Cassius Winston</td>
<td>Michigan State</td>
<td style="text-align: center">0.408</td>
<td style="text-align: center">0.371</td>
<td style="text-align: center">0.432</td>
<td style="text-align: center">73</td>
<td style="text-align: center">169</td>
<td style="text-align: center">0.852</td>
<td style="text-align: center">0.409</td>
</tr>
<tr>
<td style="text-align: center">52</td>
<td>Immanuel Quickley</td>
<td>Kentucky</td>
<td style="text-align: center">0.401</td>
<td style="text-align: center">0.366</td>
<td style="text-align: center">0.428</td>
<td style="text-align: center">62</td>
<td style="text-align: center">145</td>
<td style="text-align: center">0.923</td>
<td style="text-align: center">0.438</td>
</tr>
<tr>
<td style="text-align: center">37</td>
<td>Payton Pritchard</td>
<td>Oregon</td>
<td style="text-align: center">0.398</td>
<td style="text-align: center">0.369</td>
<td style="text-align: center">0.415</td>
<td style="text-align: center">88</td>
<td style="text-align: center">212</td>
<td style="text-align: center">0.821</td>
<td style="text-align: center">0.459</td>
</tr>
<tr>
<td style="text-align: center">29</td>
<td>Jahmi'us Ramsey</td>
<td>Texas Tech</td>
<td style="text-align: center">0.395</td>
<td style="text-align: center">0.367</td>
<td style="text-align: center">0.432</td>
<td style="text-align: center">60</td>
<td style="text-align: center">139</td>
<td style="text-align: center">0.641</td>
<td style="text-align: center">0.415</td>
</tr>
<tr>
<td style="text-align: center">8</td>
<td>Tyrese Haliburton</td>
<td>Iowa State</td>
<td style="text-align: center">0.394</td>
<td style="text-align: center">0.36</td>
<td style="text-align: center">0.419</td>
<td style="text-align: center">52</td>
<td style="text-align: center">124</td>
<td style="text-align: center">0.822</td>
<td style="text-align: center">0.508</td>
</tr>
<tr>
<td style="text-align: center">42</td>
<td>Tyrell Terry</td>
<td>Stanford</td>
<td style="text-align: center">0.388</td>
<td style="text-align: center">0.36</td>
<td style="text-align: center">0.408</td>
<td style="text-align: center">62</td>
<td style="text-align: center">152</td>
<td style="text-align: center">0.891</td>
<td style="text-align: center">0.456</td>
</tr>
<tr>
<td style="text-align: center">44</td>
<td>Jordan Nwora</td>
<td>Louisville</td>
<td style="text-align: center">0.387</td>
<td style="text-align: center">0.361</td>
<td style="text-align: center">0.402</td>
<td style="text-align: center">76</td>
<td style="text-align: center">189</td>
<td style="text-align: center">0.812</td>
<td style="text-align: center">0.44</td>
</tr>
<tr>
<td style="text-align: center">57</td>
<td>Kaleb Wesson</td>
<td>Ohio State</td>
<td style="text-align: center">0.38</td>
<td style="text-align: center">0.358</td>
<td style="text-align: center">0.425</td>
<td style="text-align: center">45</td>
<td style="text-align: center">106</td>
<td style="text-align: center">0.731</td>
<td style="text-align: center">0.346</td>
</tr>
<tr>
<td style="text-align: center">45</td>
<td>Skylar Mays</td>
<td>LSU</td>
<td style="text-align: center">0.375</td>
<td style="text-align: center">0.352</td>
<td style="text-align: center">0.394</td>
<td style="text-align: center">50</td>
<td style="text-align: center">127</td>
<td style="text-align: center">0.854</td>
<td style="text-align: center">0.369</td>
</tr>
<tr>
<td style="text-align: center">16</td>
<td>Devin Vassell</td>
<td>Florida State</td>
<td style="text-align: center">0.37</td>
<td style="text-align: center">0.356</td>
<td style="text-align: center">0.415</td>
<td style="text-align: center">44</td>
<td style="text-align: center">106</td>
<td style="text-align: center">0.738</td>
<td style="text-align: center">0.361</td>
</tr>
<tr>
<td style="text-align: center">53</td>
<td>Killian Tillie</td>
<td>Gonzaga</td>
<td style="text-align: center">0.368</td>
<td style="text-align: center">0.349</td>
<td style="text-align: center">0.4</td>
<td style="text-align: center">36</td>
<td style="text-align: center">90</td>
<td style="text-align: center">0.726</td>
<td style="text-align: center">0.391</td>
</tr>
<tr>
<td style="text-align: center">38</td>
<td>Malachi Flynn</td>
<td>San Diego State</td>
<td style="text-align: center">0.366</td>
<td style="text-align: center">0.349</td>
<td style="text-align: center">0.373</td>
<td style="text-align: center">76</td>
<td style="text-align: center">204</td>
<td style="text-align: center">0.857</td>
<td style="text-align: center">0.489</td>
</tr>
<tr>
<td style="text-align: center">26</td>
<td>Robert Woodard</td>
<td>Mississippi State</td>
<td style="text-align: center">0.363</td>
<td style="text-align: center">0.352</td>
<td style="text-align: center">0.429</td>
<td style="text-align: center">30</td>
<td style="text-align: center">70</td>
<td style="text-align: center">0.641</td>
<td style="text-align: center">0.255</td>
</tr>
<tr>
<td style="text-align: center">25</td>
<td>Kira Lewis</td>
<td>Alabama</td>
<td style="text-align: center">0.355</td>
<td style="text-align: center">0.344</td>
<td style="text-align: center">0.366</td>
<td style="text-align: center">56</td>
<td style="text-align: center">153</td>
<td style="text-align: center">0.802</td>
<td style="text-align: center">0.341</td>
</tr>
<tr>
<td style="text-align: center">6</td>
<td>Obi Toppin</td>
<td>Dayton</td>
<td style="text-align: center">0.354</td>
<td style="text-align: center">0.345</td>
<td style="text-align: center">0.39</td>
<td style="text-align: center">32</td>
<td style="text-align: center">82</td>
<td style="text-align: center">0.702</td>
<td style="text-align: center">0.212</td>
</tr>
<tr>
<td style="text-align: center">39</td>
<td>Grant Riller</td>
<td>Charleston</td>
<td style="text-align: center">0.351</td>
<td style="text-align: center">0.341</td>
<td style="text-align: center">0.362</td>
<td style="text-align: center">47</td>
<td style="text-align: center">130</td>
<td style="text-align: center">0.827</td>
<td style="text-align: center">0.286</td>
</tr>
<tr>
<td style="text-align: center">22</td>
<td>Josh Green</td>
<td>Arizona</td>
<td style="text-align: center">0.349</td>
<td style="text-align: center">0.338</td>
<td style="text-align: center">0.361</td>
<td style="text-align: center">30</td>
<td style="text-align: center">83</td>
<td style="text-align: center">0.78</td>
<td style="text-align: center">0.288</td>
</tr>
<tr>
<td style="text-align: center">43</td>
<td>Elijah Hughes</td>
<td>Syracuse</td>
<td style="text-align: center">0.346</td>
<td style="text-align: center">0.336</td>
<td style="text-align: center">0.342</td>
<td style="text-align: center">78</td>
<td style="text-align: center">228</td>
<td style="text-align: center">0.813</td>
<td style="text-align: center">0.491</td>
</tr>
<tr>
<td style="text-align: center">46</td>
<td>Isaiah Joe</td>
<td>Arkansas</td>
<td style="text-align: center">0.345</td>
<td style="text-align: center">0.336</td>
<td style="text-align: center">0.342</td>
<td style="text-align: center">94</td>
<td style="text-align: center">275</td>
<td style="text-align: center">0.89</td>
<td style="text-align: center">0.764</td>
</tr>
<tr>
<td style="text-align: center">20</td>
<td>Jalen Smith</td>
<td>Maryland</td>
<td style="text-align: center">0.345</td>
<td style="text-align: center">0.34</td>
<td style="text-align: center">0.368</td>
<td style="text-align: center">32</td>
<td style="text-align: center">87</td>
<td style="text-align: center">0.75</td>
<td style="text-align: center">0.279</td>
</tr>
<tr>
<td style="text-align: center">14</td>
<td>Cole Anthony</td>
<td>North Carolina</td>
<td style="text-align: center">0.341</td>
<td style="text-align: center">0.337</td>
<td style="text-align: center">0.348</td>
<td style="text-align: center">49</td>
<td style="text-align: center">141</td>
<td style="text-align: center">0.75</td>
<td style="text-align: center">0.409</td>
</tr>
<tr>
<td style="text-align: center">34</td>
<td>Tre Jones</td>
<td>Duke</td>
<td style="text-align: center">0.341</td>
<td style="text-align: center">0.34</td>
<td style="text-align: center">0.361</td>
<td style="text-align: center">39</td>
<td style="text-align: center">108</td>
<td style="text-align: center">0.771</td>
<td style="text-align: center">0.282</td>
</tr>
<tr>
<td style="text-align: center">50</td>
<td>Cassius Stanley</td>
<td>Duke</td>
<td style="text-align: center">0.34</td>
<td style="text-align: center">0.338</td>
<td style="text-align: center">0.36</td>
<td style="text-align: center">31</td>
<td style="text-align: center">86</td>
<td style="text-align: center">0.733</td>
<td style="text-align: center">0.319</td>
</tr>
<tr>
<td style="text-align: center">21</td>
<td>Nico Mannion</td>
<td>Arizona</td>
<td style="text-align: center">0.335</td>
<td style="text-align: center">0.329</td>
<td style="text-align: center">0.327</td>
<td style="text-align: center">53</td>
<td style="text-align: center">162</td>
<td style="text-align: center">0.797</td>
<td style="text-align: center">0.441</td>
</tr>
<tr>
<td style="text-align: center">24</td>
<td>Jaden McDaniels</td>
<td>Washington</td>
<td style="text-align: center">0.334</td>
<td style="text-align: center">0.333</td>
<td style="text-align: center">0.339</td>
<td style="text-align: center">43</td>
<td style="text-align: center">127</td>
<td style="text-align: center">0.763</td>
<td style="text-align: center">0.378</td>
</tr>
<tr>
<td style="text-align: center">12</td>
<td>Patrick Williams</td>
<td>Florida State</td>
<td style="text-align: center">0.327</td>
<td style="text-align: center">0.329</td>
<td style="text-align: center">0.32</td>
<td style="text-align: center">16</td>
<td style="text-align: center">50</td>
<td style="text-align: center">0.838</td>
<td style="text-align: center">0.242</td>
</tr>
<tr>
<td style="text-align: center">49</td>
<td>Reggie Perry</td>
<td>Mississippi State</td>
<td style="text-align: center">0.318</td>
<td style="text-align: center">0.329</td>
<td style="text-align: center">0.324</td>
<td style="text-align: center">23</td>
<td style="text-align: center">71</td>
<td style="text-align: center">0.768</td>
<td style="text-align: center">0.194</td>
</tr>
<tr>
<td style="text-align: center">33</td>
<td>Devon Dotson</td>
<td>Kansas</td>
<td style="text-align: center">0.317</td>
<td style="text-align: center">0.323</td>
<td style="text-align: center">0.309</td>
<td style="text-align: center">38</td>
<td style="text-align: center">123</td>
<td style="text-align: center">0.83</td>
<td style="text-align: center">0.316</td>
</tr>
<tr>
<td style="text-align: center">28</td>
<td>Tyler Bey</td>
<td>Colorado</td>
<td style="text-align: center">0.309</td>
<td style="text-align: center">0.34</td>
<td style="text-align: center">0.419</td>
<td style="text-align: center">13</td>
<td style="text-align: center">31</td>
<td style="text-align: center">0.743</td>
<td style="text-align: center">0.117</td>
</tr>
<tr>
<td style="text-align: center">51</td>
<td>Paul Reed</td>
<td>DePaul</td>
<td style="text-align: center">0.308</td>
<td style="text-align: center">0.326</td>
<td style="text-align: center">0.308</td>
<td style="text-align: center">16</td>
<td style="text-align: center">52</td>
<td style="text-align: center">0.738</td>
<td style="text-align: center">0.147</td>
</tr>
<tr>
<td style="text-align: center">36</td>
<td>Daniel Oturu</td>
<td>Minnesota</td>
<td style="text-align: center">0.306</td>
<td style="text-align: center">0.336</td>
<td style="text-align: center">0.365</td>
<td style="text-align: center">19</td>
<td style="text-align: center">52</td>
<td style="text-align: center">0.707</td>
<td style="text-align: center">0.123</td>
</tr>
<tr>
<td style="text-align: center">15</td>
<td>Tyrese Maxey</td>
<td>Kentucky</td>
<td style="text-align: center">0.305</td>
<td style="text-align: center">0.318</td>
<td style="text-align: center">0.292</td>
<td style="text-align: center">33</td>
<td style="text-align: center">113</td>
<td style="text-align: center">0.833</td>
<td style="text-align: center">0.322</td>
</tr>
<tr>
<td style="text-align: center">1</td>
<td>Anthony Edwards</td>
<td>Georgia</td>
<td style="text-align: center">0.302</td>
<td style="text-align: center">0.312</td>
<td style="text-align: center">0.294</td>
<td style="text-align: center">72</td>
<td style="text-align: center">245</td>
<td style="text-align: center">0.772</td>
<td style="text-align: center">0.485</td>
</tr>
<tr>
<td style="text-align: center">54</td>
<td>Ashton Hagans</td>
<td>Kentucky</td>
<td style="text-align: center">0.296</td>
<td style="text-align: center">0.316</td>
<td style="text-align: center">0.258</td>
<td style="text-align: center">16</td>
<td style="text-align: center">62</td>
<td style="text-align: center">0.81</td>
<td style="text-align: center">0.234</td>
</tr>
<tr>
<td style="text-align: center">31</td>
<td>Udoka Azubuike</td>
<td>Kansas</td>
<td style="text-align: center">0.295</td>
<td style="text-align: center">0.33</td>
<td style="text-align: center">0.0</td>
<td style="text-align: center">0</td>
<td style="text-align: center">0</td>
<td style="text-align: center">0.441</td>
<td style="text-align: center">0.0</td>
</tr>
<tr>
<td style="text-align: center">7</td>
<td>Isaac Okoro</td>
<td>Auburn</td>
<td style="text-align: center">0.293</td>
<td style="text-align: center">0.321</td>
<td style="text-align: center">0.286</td>
<td style="text-align: center">20</td>
<td style="text-align: center">70</td>
<td style="text-align: center">0.672</td>
<td style="text-align: center">0.287</td>
</tr>
<tr>
<td style="text-align: center">40</td>
<td>Xavier Tillman</td>
<td>Michigan State</td>
<td style="text-align: center">0.282</td>
<td style="text-align: center">0.319</td>
<td style="text-align: center">0.26</td>
<td style="text-align: center">13</td>
<td style="text-align: center">50</td>
<td style="text-align: center">0.667</td>
<td style="text-align: center">0.167</td>
</tr>
<tr>
<td style="text-align: center">27</td>
<td>Isaiah Stewart II</td>
<td>Washington</td>
<td style="text-align: center">0.274</td>
<td style="text-align: center">0.324</td>
<td style="text-align: center">0.25</td>
<td style="text-align: center">5</td>
<td style="text-align: center">20</td>
<td style="text-align: center">0.774</td>
<td style="text-align: center">0.059</td>
</tr>
<tr>
<td style="text-align: center">35</td>
<td>Zeke Nnaji</td>
<td>Arizona</td>
<td style="text-align: center">0.267</td>
<td style="text-align: center">0.328</td>
<td style="text-align: center">0.294</td>
<td style="text-align: center">5</td>
<td style="text-align: center">17</td>
<td style="text-align: center">0.76</td>
<td style="text-align: center">0.054</td>
</tr>
<tr>
<td style="text-align: center">10</td>
<td>Precious Achiuwa</td>
<td>Memphis</td>
<td style="text-align: center">0.264</td>
<td style="text-align: center">0.33</td>
<td style="text-align: center">0.325</td>
<td style="text-align: center">13</td>
<td style="text-align: center">40</td>
<td style="text-align: center">0.599</td>
<td style="text-align: center">0.108</td>
</tr>
<tr>
<td style="text-align: center">32</td>
<td>Vernon Carey, Jr.</td>
<td>Duke</td>
<td style="text-align: center">0.264</td>
<td style="text-align: center">0.334</td>
<td style="text-align: center">0.381</td>
<td style="text-align: center">8</td>
<td style="text-align: center">21</td>
<td style="text-align: center">0.67</td>
<td style="text-align: center">0.061</td>
</tr>
<tr>
<td style="text-align: center">58</td>
<td>Nick Richards</td>
<td>Kentucky</td>
<td style="text-align: center">0.263</td>
<td style="text-align: center">0.33</td>
<td style="text-align: center">0.0</td>
<td style="text-align: center">0</td>
<td style="text-align: center">0</td>
<td style="text-align: center">0.752</td>
<td style="text-align: center">0.0</td>
</tr>
<tr>
<td style="text-align: center">5</td>
<td>Onyeka Okongwu</td>
<td>USC</td>
<td style="text-align: center">0.261</td>
<td style="text-align: center">0.329</td>
<td style="text-align: center">0.25</td>
<td style="text-align: center">1</td>
<td style="text-align: center">4</td>
<td style="text-align: center">0.72</td>
<td style="text-align: center">0.014</td>
</tr>
<tr>
<td style="text-align: center">3</td>
<td>James Wiseman</td>
<td>Memphis</td>
<td style="text-align: center">0.256</td>
<td style="text-align: center">0.329</td>
<td style="text-align: center">0.0</td>
<td style="text-align: center">0</td>
<td style="text-align: center">1</td>
<td style="text-align: center">0.704</td>
<td style="text-align: center">0.038</td>
</tr>
</tbody>
</table>
<p><br /> Below are some notable players that I thought stood out:</p>
<ol>
<li><strong>Vernon Carey</strong> - He shot a good percentage for a big (38.1%) but he only had 21 attempts and his lower FT% and 3PAR might make us reconsider how much of his shooting was due to luck.</li>
<li><strong>Tyler Bey</strong> - Similar to Carey, Bey shot extremely well on the season (41.9%) but he only had 31 attempts and with a low 3PAR, the numbers say he might have been closer to a 30.9% shooter over a larger sample.</li>
<li><strong>Ashton Hagans</strong> - With such a high FT% (81%), the hierarchical model suggests that Hagans had some bad luck and is a better three-point shooter than his percentage (25.8%) would indicate.</li>
</ol>
<p>In summary, a hierarchical model is more complex than basic <a href="/2020/09/06/empirical-bayes.html">empirical bayes</a> - however the added complexity allows us make to more accurately adjust our prior by incorporating additional information.</p>
<div class="footnotes">
<ol>
<li id="fn:1">
<p>Kevin Pelton has done work showing that college FT% is <a href="http://insider.espn.com/nba/draft2015/insider/story/_/id/13003659/nba-draft-michael-frazier-dangelo-russell-top-shooters-draft">predictive of NBA 3P%</a> <a href="#fnref:1" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>
Empirical Bayes-ketballhttp://tothemean.com/2020/09/06/empirical-bayes.html2020-09-06T00:00:00Z2020-09-19T12:49:42-07:00Jesse Fischer<script>
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<p><em>How much can you learn about the three-point shooting of a player when data is limited?</em></p>
<p><em>Potential lottery picks <a href="https://basketball.realgm.com/player/Cole-Anthony/Summary/105342">Cole Anthony</a> and <a href="https://basketball.realgm.com/player/Tyrese-Haliburton/Summary/132168">Tyrese Haliburton</a> only played 22 games before injuries cut their season short in 2020 (finishing with 141 and 124 three-point attempts respectively). Potential #1 draft pick <a href="https://basketball.realgm.com/player/LaMelo-Ball/Summary/103892">LaMelo Ball</a> had 80 three-point attempts in his 12 NBL games. The top high school recruit in the country <a href="https://basketball.realgm.com/player/James-Wiseman/Summary/107990">James Wiseman</a> missed his only three-point attempt in just 69 minutes at Memphis.</em></p>
<p><em>How do you confidently evaluate shooting performance based on such limited data?</em></p>
<p><em>This is especially important in a year where numerous NBA lottery picks will be selected based on so few data points.</em></p>
<hr />
<p>Trying to find a signal in the noise with such small sample sizes is not a new problem in sports analytics. This comes up every year in the MLB after a player starts the season on a hot streak, giving hope that they will be the first person to hit .400 since Ted Williams last did in 1941. As a good Bayesian we know that a player batting over .400 after 100 at bats has a better shot than another player after only 10 at bats, but neither are likely to top .400.</p>
<p>One simple approach to estimate a player's end of season batting average, is to regress their current average to the mean. For example, take a weighted average of current batting average with the league average, weighting based on how far along in the season they are (or better yet regress against their career average).</p>
<p>This simple concept is the basis for approaches referred to as the "stabilization rate" or "padding method" (often used by <a href="https://twitter.com/tangotiger">@Tangotiger</a>). You may have also heard of this in relation to a concept called "Empirical Bayes", as there is <a href="http://varianceexplained.org/posts/">a whole series of blog posts</a> that <a href="http://varianceexplained.org/statistics/beta_distribution_and_baseball">apply Bayes to batting averages</a> (along with many other interesting extensions).</p>
<hr />
<blockquote>
<p>Which NBA player has had the best three-point shooting season of all time?</p>
</blockquote>
<p>The easiest way to answer this question is to look at single season 3P% leaders. Note that for the sake of simplicity we will overlook shot difficulty and league-wide changes in three-point shooting trends.</p>
<table>
<thead>
<tr>
<th>rank </th>
<th>name</th>
<th>team </th>
<th>year </th>
<th style="text-align: center"> 3p% </th>
<th style="text-align: center"> 3pm </th>
<th style="text-align: center"> 3pa </th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>Jamie Feick</td>
<td>NJN</td>
<td>2000</td>
<td style="text-align: center">1.000</td>
<td style="text-align: center">3</td>
<td style="text-align: center">3</td>
</tr>
<tr>
<td>2</td>
<td>Raja Bell</td>
<td>GOS</td>
<td>2010</td>
<td style="text-align: center">1.000</td>
<td style="text-align: center">3</td>
<td style="text-align: center">3</td>
</tr>
<tr>
<td>3</td>
<td>Antonius Cleveland</td>
<td>ATL</td>
<td>2018</td>
<td style="text-align: center">1.000</td>
<td style="text-align: center">3</td>
<td style="text-align: center">3</td>
</tr>
<tr>
<td>4</td>
<td>Beno Udrih</td>
<td>MEM</td>
<td>2014</td>
<td style="text-align: center">1.000</td>
<td style="text-align: center">2</td>
<td style="text-align: center">2</td>
</tr>
<tr>
<td>5</td>
<td>Don MacLean</td>
<td>MIA</td>
<td>2001</td>
<td style="text-align: center">1.000</td>
<td style="text-align: center">2</td>
<td style="text-align: center">2</td>
</tr>
</tbody>
</table>
<p><br />Looks like the top seasons are all from players shooting 100% on only a few shot attempts - therefore it doesn't look like this approach is particularly informative.</p>
<p>As a next step, we can apply a filter to exclude seasons with <X three-point attempts (I choose an arbitrary threshold of 100 attempts below).</p>
<table>
<thead>
<tr>
<th>rank </th>
<th>name</th>
<th>team </th>
<th>year </th>
<th style="text-align: center"> 3p% </th>
<th style="text-align: center"> 3pm </th>
<th style="text-align: center"> 3pa </th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>Pau Gasol</td>
<td>SAN</td>
<td>2017</td>
<td style="text-align: center">0.538</td>
<td style="text-align: center">56</td>
<td style="text-align: center">104</td>
</tr>
<tr>
<td>2</td>
<td>Kyle Korver</td>
<td>UTH</td>
<td>2010</td>
<td style="text-align: center">0.536</td>
<td style="text-align: center">59</td>
<td style="text-align: center">110</td>
</tr>
<tr>
<td>3</td>
<td>Jason Kapono</td>
<td>MIA</td>
<td>2007</td>
<td style="text-align: center">0.514</td>
<td style="text-align: center">108</td>
<td style="text-align: center">210</td>
</tr>
<tr>
<td>4</td>
<td>Luke Babbitt</td>
<td>NOP</td>
<td>2015</td>
<td style="text-align: center">0.513</td>
<td style="text-align: center">59</td>
<td style="text-align: center">115</td>
</tr>
<tr>
<td>5</td>
<td>Kyle Korver</td>
<td>ATL</td>
<td>2015</td>
<td style="text-align: center">0.492</td>
<td style="text-align: center">221</td>
<td style="text-align: center">449</td>
</tr>
<tr>
<td>6</td>
<td>Hubert Davis</td>
<td>DAL</td>
<td>2000</td>
<td style="text-align: center">0.491</td>
<td style="text-align: center">82</td>
<td style="text-align: center">167</td>
</tr>
<tr>
<td>7</td>
<td>Kyle Korver</td>
<td>CLE</td>
<td>2017</td>
<td style="text-align: center">0.485</td>
<td style="text-align: center">97</td>
<td style="text-align: center">200</td>
</tr>
<tr>
<td>8</td>
<td>Troy Daniels</td>
<td>CHA</td>
<td>2016</td>
<td style="text-align: center">0.484</td>
<td style="text-align: center">59</td>
<td style="text-align: center">122</td>
</tr>
<tr>
<td>9</td>
<td>Fred Hoiberg</td>
<td>MIN</td>
<td>2005</td>
<td style="text-align: center">0.483</td>
<td style="text-align: center">70</td>
<td style="text-align: center">145</td>
</tr>
<tr>
<td>10</td>
<td>Jason Kapono</td>
<td>TOR</td>
<td>2008</td>
<td style="text-align: center">0.483</td>
<td style="text-align: center">57</td>
<td style="text-align: center">118</td>
</tr>
</tbody>
</table>
<p><br />This list is more intuitive but with Pau Gasol leading the pack and Steph Curry not even on the list…we remain skeptical. This approach is also sensitive to the specific threshold chosen which adds undesirable subjectivity to the process. There must be a better way…Empirical Bayes!</p>
<blockquote>
<p>Empirical Bayes methods are procedures for statistical inference in which the prior distribution is estimated from the data.</p>
</blockquote>
<p>Since <a href="https://twitter.com/drob">drob@</a> does a better job explaining these concepts than I ever will, I highly recommend reading his <a href="http://varianceexplained.org/r/empirical-bayes-book/">Empirical Bayes</a> book which is a compilation of <a href="http://varianceexplained.org/posts/">baseball themed blog posts</a> on the topic. He does an excellent job explaining concepts using practical examples and even includes sample code to follow along.</p>
<p>The only thing missing is Python specific code (<a href="https://stackoverflow.com/questions/54505173/finding-alpha-and-beta-of-beta-binomial-distribution-with-scipy-optimize-and-log">thanks stackoverflow!</a>) - which is why I've included a code snippet to aid others in performing their own Empirical Bayes! This code assumes a beta-binomial distribution, which is great for sports analytics because it can be applied to any "success/attempt statistic".</p>
<pre><code>from scipy.stats import betabinom<br />
from scipy.optimize import minimize<br /><br />
def betabinom_func(params, *args):<br />
 a, b = params[0], params[1]<br />
 k = args[0] # hits<br />
 n = args[1] # at_bats<br />
 return -np.sum(betabinom.logpmf(k, n, a, b))<br /><br />
def solve_a_b(hits, at_bats, max_iter=250):<br />
 result = minimize(betabinom_func, x0=[1, 10],<br />
 args=(hits, at_bats), bounds=((0, None), (0, None)),<br />
 method='L-BFGS-B', options={'disp': True, 'maxiter': max_iter})<br />
 a, b = result.x[0], result.x[1]<br />
 return a, b<br /><br />
# Sanity check your data to ensure hits <= at_bats, at_bats > 0, and both are type int<br />
def estimate_eb(hits, at_bats):<br />
 a, b = solve_a_b(hits, at_bats)<br />
 return ((hits+a) / (at_bats+a+b))<br /><br />
df['3p%_eb'] = estimate_eb(df['3pm'], df['3pa'])</code></pre>
<p>The results look much better after applying Empirical Bayes - many great shooters and multiple Curry sightings!</p>
<table>
<thead>
<tr>
<th>rank </th>
<th>name</th>
<th>team </th>
<th>year </th>
<th style="text-align: center">3p% (eb)</th>
<th style="text-align: center"> 3p% </th>
<th style="text-align: center"> 3pm </th>
<th style="text-align: center"> 3pa </th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>Kyle Korver</td>
<td>ATL</td>
<td>2015</td>
<td style="text-align: center"> 0.446 </td>
<td style="text-align: center">0.492</td>
<td style="text-align: center">221</td>
<td style="text-align: center">449</td>
</tr>
<tr>
<td>2</td>
<td>Stephen Curry</td>
<td>GOS</td>
<td>2016</td>
<td style="text-align: center">0.433</td>
<td style="text-align: center">0.454</td>
<td style="text-align: center">402</td>
<td style="text-align: center">886</td>
</tr>
<tr>
<td>3</td>
<td>J.J. Redick</td>
<td>LAC</td>
<td>2016</td>
<td style="text-align: center">0.433</td>
<td style="text-align: center">0.475</td>
<td style="text-align: center">200</td>
<td style="text-align: center">421</td>
</tr>
<tr>
<td>4</td>
<td>Joe Johnson</td>
<td>PHX</td>
<td>2005</td>
<td style="text-align: center">0.431</td>
<td style="text-align: center">0.478</td>
<td style="text-align: center">177</td>
<td style="text-align: center">370</td>
</tr>
<tr>
<td>5</td>
<td>Jason Kapono</td>
<td>MIA</td>
<td>2007</td>
<td style="text-align: center">0.431</td>
<td style="text-align: center">0.514</td>
<td style="text-align: center">108</td>
<td style="text-align: center">210</td>
</tr>
<tr>
<td>6</td>
<td>Glen Rice</td>
<td>CHA</td>
<td>1997</td>
<td style="text-align: center">0.431</td>
<td style="text-align: center">0.47</td>
<td style="text-align: center">207</td>
<td style="text-align: center">440</td>
</tr>
<tr>
<td>7</td>
<td>Joe Harris</td>
<td>BRK</td>
<td>2019</td>
<td style="text-align: center">0.429</td>
<td style="text-align: center">0.474</td>
<td style="text-align: center">183</td>
<td style="text-align: center">386</td>
</tr>
<tr>
<td>8</td>
<td>Kyle Korver</td>
<td>ATL</td>
<td>2014</td>
<td style="text-align: center">0.428</td>
<td style="text-align: center">0.472</td>
<td style="text-align: center">185</td>
<td style="text-align: center">392</td>
</tr>
<tr>
<td>9</td>
<td>Steve Nash</td>
<td>PHX</td>
<td>2008</td>
<td style="text-align: center">0.426</td>
<td style="text-align: center">0.47</td>
<td style="text-align: center">179</td>
<td style="text-align: center">381</td>
</tr>
<tr>
<td>10</td>
<td>Stephen Curry</td>
<td>GOS</td>
<td>2013</td>
<td style="text-align: center">0.426</td>
<td style="text-align: center">0.453</td>
<td style="text-align: center">272</td>
<td style="text-align: center">600</td>
</tr>
</tbody>
</table>
<p><br />It is also interesting to look at how strongly results are regressed towards the mean depending on how many attempts a player has (explore the drop-down for the same approach applied to other stats!).</p>
<center><select id="stat_type" onchange="document.getElementById('stat').src = stat_images[document.getElementById('stat_type').value]; document.getElementById('stat_a').href = stat_images[document.getElementById('stat_type').value]">
<option value="3p">3P%</option>
<option value="2p">2P%</option>
<option value="fg">FG%</option>
<option value="ft">FT%</option>
<option value="ast">AST%</option>
<option value="blk">BLK%</option>
<option value="drb">DRB%</option>
<option value="orb">ORB%</option>
<option value="stl">STL%</option>
<option value="pf">PF%</option>
<option value="tov">TOV%</option>
<option value="usg">USG%</option>
<option value="efg">EFG%</option>
<option value="ftr">FTR</option>
<option value="3par">3PAR</option>
</select></center>
<p><a href="/images/eb/3p.png" id="stat_a"><img src="/images/eb/3p.png" id="stat" /></a></p>
<p>I included the optimal alpha/beta values in a table below so you can regress statistics on your own<sup id="fnref:1"><a href="#fn:1" class="footnote">1</a></sup>. I'll leave it to the reader to compare these results with other techniques like <a href="https://kmedved.com/2020/08/06/nba-stabilization-rates-and-the-padding-approach/">NBA stabilization rates</a> (recent work by <a href="https://twitter.com/kmedved">@kmedved</a>).</p>
<table>
<thead>
<tr>
<th>stat </th>
<th>success </th>
<th>attempt</th>
<th style="text-align: center"> alpha </th>
<th style="text-align: center"> beta </th>
<th style="text-align: center"> avg </th>
</tr>
</thead>
<tbody>
<tr>
<td>3p%</td>
<td>3pm</td>
<td>3pa</td>
<td style="text-align: center">73.2</td>
<td style="text-align: center">137.3</td>
<td style="text-align: center">0.348</td>
</tr>
<tr>
<td>2p%</td>
<td>2pm</td>
<td>2pa</td>
<td style="text-align: center">54.9</td>
<td style="text-align: center">60.7</td>
<td style="text-align: center">0.475</td>
</tr>
<tr>
<td>fg%</td>
<td>fgm</td>
<td>fga</td>
<td style="text-align: center">44.4</td>
<td style="text-align: center">55.2</td>
<td style="text-align: center">0.446</td>
</tr>
<tr>
<td>ft%</td>
<td>ftm</td>
<td>fta</td>
<td style="text-align: center">15.5</td>
<td style="text-align: center">5.5</td>
<td style="text-align: center">0.736</td>
</tr>
<tr>
<td>ast%</td>
<td>ast</td>
<td>ast_opp</td>
<td style="text-align: center">2.1</td>
<td style="text-align: center">13.8</td>
<td style="text-align: center">13.5</td>
</tr>
<tr>
<td>blk%</td>
<td>blk</td>
<td>opp_2p_fga</td>
<td style="text-align: center">0.7</td>
<td style="text-align: center">20.7</td>
<td style="text-align: center">3.1</td>
</tr>
<tr>
<td>drb%</td>
<td>drb</td>
<td>drb_opp</td>
<td style="text-align: center">6.0</td>
<td style="text-align: center">35.4</td>
<td style="text-align: center">14.5</td>
</tr>
<tr>
<td>orb%</td>
<td>orb</td>
<td>orb_opp</td>
<td style="text-align: center">2.0</td>
<td style="text-align: center">33.0</td>
<td style="text-align: center">5.7</td>
</tr>
<tr>
<td>stl%</td>
<td>stl</td>
<td>poss</td>
<td style="text-align: center">8.4</td>
<td style="text-align: center">508.0</td>
<td style="text-align: center">1.6</td>
</tr>
<tr>
<td>pf%</td>
<td>pf</td>
<td>poss</td>
<td style="text-align: center">8.5</td>
<td style="text-align: center">159.8</td>
<td style="text-align: center">5.0</td>
</tr>
<tr>
<td>tov%</td>
<td>tov</td>
<td>poss</td>
<td style="text-align: center">13.3</td>
<td style="text-align: center">83.6</td>
<td style="text-align: center">13.8</td>
</tr>
<tr>
<td>usg%</td>
<td>usg_num</td>
<td>poss</td>
<td style="text-align: center">12.0</td>
<td style="text-align: center">52.2</td>
<td style="text-align: center">18.7</td>
</tr>
<tr>
<td>efg%</td>
<td>efg_num</td>
<td>fga</td>
<td style="text-align: center">60.4</td>
<td style="text-align: center">63.8</td>
<td style="text-align: center">0.486</td>
</tr>
<tr>
<td>ftr<sup id="fnref:2"><a href="#fn:2" class="footnote">2</a></sup></td>
<td>fta</td>
<td>fga</td>
<td style="text-align: center">2.8</td>
<td style="text-align: center">6.7</td>
<td style="text-align: center">0.292</td>
</tr>
<tr>
<td>3par</td>
<td>3pa</td>
<td>fga</td>
<td style="text-align: center">0.5</td>
<td style="text-align: center">1.9</td>
<td style="text-align: center">0.214</td>
</tr>
</tbody>
</table>
<p><br />Note that these numbers are based on NBA data dating back to the 1996-97 season. The game is continually evolving, which means different time periods can change results slightly. With additional complexity it is possible to enhance the approach by <a href="http://varianceexplained.org/r/empirical_bayes_baseball/">calculating different values for each season or decade</a>.</p>
<hr />
<p>When dealing with limited data (as is often the case in sports analytics), Empirical Bayes is a powerful tool. By objectively regressing towards the mean, we can avoid outlier data points and more accurately evaluate small sample performances.</p>
<p>In my <a href="/2020/09/19/hierarchical-model.html">next post</a>, I will discuss a related topic of "hierarchical modeling" and look at some specific examples from the 2020 draft class.</p>
<div class="footnotes">
<ol>
<li id="fn:1">
<p>As a reminder the calculation is "(success + alpha) / (attempt + alpha + beta)" <a href="#fnref:1" class="reversefootnote">↩</a></p>
</li>
<li id="fn:2">
<p>Note that the traditional free-throw rate metric (ft/fga) isn't a true rate statistic (but instead a proportion) so technically this isn't correct but since it is very rare to have a rate >1.0 the results still make sense - to make it fool proof we could instead change the statistic to "fta/(fta+fga)". <a href="#fnref:2" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>
2020 WNBA Draft Analyticshttp://tothemean.com/2020/04/12/wnba-draft-2020.html2020-04-12T00:00:00Z2020-04-18T16:38:05-07:00Jesse Fischer<script>
var player_header = {
"sabrina-ionescu-2020-oregon": "Sabrina Ionescu",
"lauren-cox-2020-baylor": "Lauren Cox",
"crystal-dangerfield-2020-uconn": "Crystal Dangerfield",
"megan-walker-2020-uconn": "Megan Walker",
"bella-alarie-2020-princeto": "Bella Alarie",
"tyasha-harris-2020-south-ca": "Tyasha Harris",
"satou-sabally-2020-oregon": "Satou Sabally",
"chennedy-carter-2020-texas-a&": "Chennedy Carter",
"ruthy-hebard-2020-oregon": "Ruthy Hebard",
"sug-sutton-2020-texas": "Sug Sutton",
"beatrice-mompremier-2020-miami-(f": "Beatrice Mompremier",
"mikayla-pivec-2020-oregon-s": "Mikayla Pivec",
"juicy-landrum-2020-baylor": "Juicy Landrum",
"te'a-cooper-2020-baylor": "Te'a Cooper",
"dijonai-carrington-2020-stanford": "Dijonai Carrington",
"joyner-holmes-2020-texas": "Joyner Holmes",
"jordan-danberry-2020-mississi": "Jordan Danberry",
"kaila-charles-2020-maryland": "Kaila Charles",
"nicki-ekhomu-2020-florida-": "Nicki Ekhomu",
"kylee-shook-2020-louisvil": "Kylee Shook",
"jazmine-jones-2020-louisvil": "Jazmine Jones",
"mikiah-herbert-harrigan-2020-south-ca": "Mikiah Herbert Harrigan",
"ayana-mitchell-2020-lsu": "Ayana Mitchell",
"kamiah-smalls-2020-james-ma": "Kamiah Smalls",
"stephanie-watts-2020-southern": "Stephanie Watts",
"leaonna-odom-2020-duke": "Leaonna Odom",
"stephanie-jones-2020-maryland": "Stephanie Jones",
"ciara-duffy-2020-south-da": "Ciara Duffy",
"sara-rhine-2020-drake": "Sara Rhine",
"haley-gorecki-2020-duke": "Haley Gorecki",
"kyra-lambert-2020-duke": "Kyra Lambert",
"kiah-gillespie-2020-florida-": "Kiah Gillespie",
"blair-watson-2020-maryland": "Blair Watson",
"becca-hittner-2020-drake": "Becca Hittner",
"kathleen-doyle-2020-iowa": "Kathleen Doyle",
"aislinn-konig-2020-nc-state": "Aislinn Konig",
"nadia-fingall-2020-stanford": "Nadia Fingall",
"reili-richardson-2020-arizona-": "Reili Richardson",
"abi-scheid-2020-northwes": "Abi Scheid",
"chanelle-molina-2020-washingt": "Chanelle Molina",
"ae'rianna-harris-2020-purdue": "Ae'Rianna Harris",
"jocelyn-willoughby-2020-virginia": "Jocelyn Willoughby",
"peyton-williams-2020-kansas-s": "Peyton Williams",
"shadeen-samuels-2020-seton-ha": "Shadeen Samuels",
"japreece-dean-2020-ucla": "Japreece Dean",
"brittany-brewer-2020-texas-te": "Brittany Brewer",
"minyon-moore-2020-oregon": "Minyon Moore",
"jaylyn-agnew-2020-creighto": "Jaylyn Agnew",
"dee-givens-2020-western-": "Dee Givens",
"chante-stonewall-2020-depaul": "Chante Stonewall",
"alexis-tolefree-2020-arkansas": "Alexis Tolefree",
"stella-johnson-2020-rider": "Stella Johnson",
"davion-wingate-2020-fgcu": "Davion Wingate",
"tynice-martin-2020-west-vir": "Tynice Martin",
"kayla-cooper-williams-2020-james-ma": "Kayla Cooper-Williams",
"borislava-hristova-2020-washingt": "Borislava Hristova",
"gia-pack-2020-new-mexi": "Gia Pack",
"null": null
};
var model_insight = {
"sabrina-ionescu-2020-oregon": ["ftp","ast%","rapm_off","blk%","drb%","3par"],
"lauren-cox-2020-baylor": ["hs_rank","blk%","pf%","ftr","fg2p","orb%"],
"crystal-dangerfield-2020-uconn": ["orb%","rapm_def","hs_rank","3par","fg2p","blk%"],
"megan-walker-2020-uconn": ["hs_rank","usg%","rapm_def","blk%","ftr","tov%"],
"bella-alarie-2020-princeto": ["height","usg%","rapm_def","drb%","3par","ftp"],
"tyasha-harris-2020-south-ca": ["ast%","pf%","rapm_def","ftr","usg%","efg%"],
"satou-sabally-2020-oregon": ["stl%","rapm_off","height","blk%","orb%","3par"],
"chennedy-carter-2020-texas-a&": ["orb%","usg%","ast%","pf%","stl%","drb%"],
"ruthy-hebard-2020-oregon": ["3par","rapm_off","orb%","tov%","ftr","drb%"],
"sug-sutton-2020-texas": ["tov%","pf%","drb%","efg%","fg3p","rapm_def"],
"beatrice-mompremier-2020-miami-(f": ["tov%","usg%","efg%","pf%","ftp","ast%"],
"mikayla-pivec-2020-oregon-s": ["tov%","pf%","drb%","orb%","usg%","ftp"],
"juicy-landrum-2020-baylor": ["rapm_def","pf%","rapm_off","fg2p","height","usg%"],
"te'a-cooper-2020-baylor": ["rapm_def","pf%","tov%","fg2p","height","drb%"],
"dijonai-carrington-2020-stanford": ["usg%","fg2p","tov%","pf%","rapm_off","ast%"],
"joyner-holmes-2020-texas": ["hs_rank","usg%","tov%","efg%","ftr","fg2p"],
"jordan-danberry-2020-mississi": ["rapm_off","ftr","ast%","pf%","usg%","orb%"],
"kaila-charles-2020-maryland": ["rapm_off","usg%","efg%","pf%","orb%","tov%"],
"nicki-ekhomu-2020-florida-": ["orb%","drb%","pf%","3par","ftp","ftr"],
"kylee-shook-2020-louisvil": ["height","rapm_def","pf%","drb%","tov%","ftp"],
"jazmine-jones-2020-louisvil": ["fg2p","rapm_off","3par","fg3p","ftp","drb%"],
"mikiah-herbert-harrigan-2020-south-ca": ["rapm_off","rapm_def","3par","usg%","height","fg3p"],
"ayana-mitchell-2020-lsu": ["fg2p","ftp","drb%","tov%","pf%","fg3p"],
"kamiah-smalls-2020-james-ma": ["pf%","usg%","tov%","rapm_off","hs_rank","height"],
"stephanie-watts-2020-southern": ["ftp","tov%","usg%","3par","pf%","rapm_off"],
"leaonna-odom-2020-duke": ["3par","fg2p","stl%","pf%","ast%","ftr"],
"stephanie-jones-2020-maryland": ["fg2p","efg%","rapm_def","ftp","usg%","tov%"],
"ciara-duffy-2020-south-da": ["rapm_off","rapm_def","3par","height","tov%","hs_rank"],
"sara-rhine-2020-drake": ["drb%","fg2p","pf%","rapm_def","tov%","hs_rank"],
"haley-gorecki-2020-duke": ["rapm_off","pf%","usg%","ftr","orb%","drb%"],
"kyra-lambert-2020-duke": ["orb%","efg%","fg3p","ast%","usg%","blk%"],
"kiah-gillespie-2020-florida-": ["pf%","fg2p","tov%","orb%","height","rapm_def"],
"blair-watson-2020-maryland": ["stl%","fg2p","pf%","ftr","usg%","3par"],
"becca-hittner-2020-drake": ["usg%","rapm_off","pf%","ftr","tov%","rapm_def"],
"kathleen-doyle-2020-iowa": ["usg%","rapm_off","ast%","rapm_def","ftr","efg%"],
"aislinn-konig-2020-nc-state": ["ftr","ast%","fg2p","usg%","3par","rapm_off"],
"nadia-fingall-2020-stanford": ["height","rapm_def","fg2p","usg%","3par","ftp"],
"reili-richardson-2020-arizona-": ["drb%","rapm_off","pf%","usg%","3par","tov%"],
"abi-scheid-2020-northwes": ["orb%","rapm_def","efg%","3par","usg%","tov%"],
"chanelle-molina-2020-washingt": ["ftr","fg2p","ast%","orb%","rapm_def","ftp"],
"ae'rianna-harris-2020-purdue": ["pf%","tov%","3par","rapm_off","height","ftp"],
"jocelyn-willoughby-2020-virginia": ["ftp","3par","stl%","height","ast%","rapm_off"],
"peyton-williams-2020-kansas-s": ["height","ftr","3par","rapm_off","efg%","hs_rank"],
"shadeen-samuels-2020-seton-ha": ["orb%","rapm_def","efg%","height","pf%","hs_rank"],
"japreece-dean-2020-ucla": ["usg%","ast%","drb%","efg%","tov%","height"],
"brittany-brewer-2020-texas-te": ["blk%","efg%","usg%","rapm_off","rapm_def","tov%"],
"minyon-moore-2020-oregon": ["drb%","fg3p","rapm_off","usg%","stl%","hs_rank"],
"jaylyn-agnew-2020-creighto": ["","","","","",""],
"dee-givens-2020-western-": ["drb%","ftr","pf%","rapm_def","hs_rank","rapm_off"],
"chante-stonewall-2020-depaul": ["rapm_off","ftr","usg%","rapm_def","hs_rank","efg%"],
"alexis-tolefree-2020-arkansas": ["rapm_off","fg2p","ftr","rapm_def","hs_rank","tov%"],
"stella-johnson-2020-rider": ["","","","","",""],
"davion-wingate-2020-fgcu": ["","","","","",""],
"tynice-martin-2020-west-vir": ["drb%","ftr","blk%","rapm_off","hs_rank","efg%"],
"kayla-cooper-williams-2020-james-ma": ["","","","","",""],
"borislava-hristova-2020-washingt": ["usg%","ftr","drb%","rapm_def","rapm_off","efg%"],
"gia-pack-2020-new-mexi": ["","","","","",""],
"null": ['','','','','','']
};
var player_info = {
"sabrina-ionescu-2020-oregon": "#20 | Oregon | SR | G | 5-10 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 4</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1845903'>ncaa</a>",
"lauren-cox-2020-baylor": "#15 | Baylor | SR | F | 6-4 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 1</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1847938'>ncaa</a>",
"crystal-dangerfield-2020-uconn": "#05 | UConn | SR | G | 5-5 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 3</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1847339'>ncaa</a>",
"megan-walker-2020-uconn": "#03 | UConn | JR | F | 6-0 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 1</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1955848'>ncaa</a>",
"bella-alarie-2020-princeto": "#31 | Princeton | SR | G | 6-4 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 83</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1848235'>ncaa</a>",
"tyasha-harris-2020-south-ca": "#52 | South Carolina | SR | G | 5-10 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 28</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1847111'>ncaa</a>",
"satou-sabally-2020-oregon": "#00 | Oregon | JR | F | 6-4 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 36</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1954549'>ncaa</a>",
"chennedy-carter-2020-texas-a&": "#3 | Texas A&M | JR | G | 5-7 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 6</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1956457'>ncaa</a>",
"ruthy-hebard-2020-oregon": "#24 | Oregon | SR | F | 6-4 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 40</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1845904'>ncaa</a>",
"sug-sutton-2020-texas": "#01 | Texas | SR | G | 5-8 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 6</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1846392'>ncaa</a>",
"beatrice-mompremier-2020-miami-(f": "#32 | Miami (FL) | SR | F | 6-4 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 20</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1734776'>ncaa</a>",
"mikayla-pivec-2020-oregon-s": "#00 | Oregon St. | SR | G | 5-10 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 26</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1847651'>ncaa</a>",
"juicy-landrum-2020-baylor": "#20 | Baylor | SR | G | 5-9 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 18</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1847939'>ncaa</a>",
"te'a-cooper-2020-baylor": "#4 | Baylor | SR | G | 5-8 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 12</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1735374'>ncaa</a>",
"dijonai-carrington-2020-stanford": "#21 | Stanford | SR | G | 5-11 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 34</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1846387'>ncaa</a>",
"joyner-holmes-2020-texas": "#24 | Texas | SR | F | 6-3 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 2</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1846390'>ncaa</a>",
"jordan-danberry-2020-mississi": "#24 | Mississippi St. | SR | G | 5-8 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 43</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1697107'>ncaa</a>",
"kaila-charles-2020-maryland": "#5 | Maryland | SR | G | 6-1 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 22</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1846039'>ncaa</a>",
"nicki-ekhomu-2020-florida-": "#12 | Florida St. | SR | G | 5-9 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 21</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1849082'>ncaa</a>",
"kylee-shook-2020-louisvil": "#21 | Louisville | SR | F | 6-4 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 17</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1842923'>ncaa</a>",
"jazmine-jones-2020-louisvil": "#23 | Louisville | SR | G | 6-0 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 43</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1842921'>ncaa</a>",
"mikiah-herbert-harrigan-2020-south-ca": "#21 | South Carolina | SR | F | 6-2 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 72</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1847112'>ncaa</a>",
"ayana-mitchell-2020-lsu": "#05 | LSU | SR | F | 6-2 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 63</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1735698'>ncaa</a>",
"kamiah-smalls-2020-james-ma": "#3 | James Madison | SR | G | 5-10 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1847610'>ncaa</a>",
"stephanie-watts-2020-southern": "#5 | Southern California | SR | G | 5-11 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 21</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1734881'>ncaa</a>",
"leaonna-odom-2020-duke": "#05 | Duke | SR | F | 6-2 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 9</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1845148'>ncaa</a>",
"stephanie-jones-2020-maryland": "#24 | Maryland | SR | F | 6-2 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 53</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1846044'>ncaa</a>",
"ciara-duffy-2020-south-da": "#24 | South Dakota | SR | G | 6-0 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1852523'>ncaa</a>",
"sara-rhine-2020-drake": "#50 | Drake | SR | F | 6-1 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1732232'>ncaa</a>",
"haley-gorecki-2020-duke": "#02 | Duke | SR | G | 6-0 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 52</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1733375'>ncaa</a>",
"kyra-lambert-2020-duke": "#15 | Duke | SR | G | 5-9 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 9</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1733377'>ncaa</a>",
"kiah-gillespie-2020-florida-": "#15 | Florida St. | SR | F | 6-2 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 25</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1734730'>ncaa</a>",
"blair-watson-2020-maryland": "#22 | Maryland | SR | G | 6-0 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 29</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1846043'>ncaa</a>",
"becca-hittner-2020-drake": "#5 | Drake | SR | G | 6-0 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1845835'>ncaa</a>",
"kathleen-doyle-2020-iowa": "#22 | Iowa | SR | G | 5-9 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 97</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1843770'>ncaa</a>",
"aislinn-konig-2020-nc-state": "#1 | NC State | SR | G | 5-9 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 38</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1846970'>ncaa</a>",
"nadia-fingall-2020-stanford": "#4 | Stanford | SR | F | 6-3 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 27</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1846388'>ncaa</a>",
"reili-richardson-2020-arizona-": "#1 | Arizona St. | SR | G | 5-11 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 47</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1848838'>ncaa</a>",
"abi-scheid-2020-northwes": "#44 | Northwestern | SR | C | 6-2 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 66</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1848346'>ncaa</a>",
"chanelle-molina-2020-washingt": "#11 | Washington St. | SR | G | 5-9 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 36</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1847630'>ncaa</a>",
"ae'rianna-harris-2020-purdue": "#32 | Purdue | SR | F | 6-1 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 20</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1844962'>ncaa</a>",
"jocelyn-willoughby-2020-virginia": "#13 | Virginia | SR | G | 6-0 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 48</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1844534'>ncaa</a>",
"peyton-williams-2020-kansas-s": "#11 | Kansas St. | SR | F | 6-4 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1847317'>ncaa</a>",
"shadeen-samuels-2020-seton-ha": "#24 | Seton Hall | SR | F | 6-0 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1844779'>ncaa</a>",
"japreece-dean-2020-ucla": "#24 | UCLA | SR | G | 5-6 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 86</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1738896'>ncaa</a>",
"brittany-brewer-2020-texas-te": "#20 | Texas Tech | SR | F | 6-4 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 76</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1849152'>ncaa</a>",
"minyon-moore-2020-oregon": "#23 | Oregon | SR | G | 5-8 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1844717'>ncaa</a>",
"jaylyn-agnew-2020-creighto": "#5 | Creighton | SR | F | 5-11 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: 100</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1733404'>ncaa</a>",
"dee-givens-2020-western-": "#4 | Western Ky. | SR | F | 6-1 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1734852'>ncaa</a>",
"chante-stonewall-2020-depaul": "#22 | DePaul | SR | F | 6-1 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1848292'>ncaa</a>",
"alexis-tolefree-2020-arkansas": "#2 | Arkansas | SR | G | 5-8 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=2080695'>ncaa</a>",
"stella-johnson-2020-rider": "#04 | Rider | SR | G | 5-10 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1843512'>ncaa</a>",
"davion-wingate-2020-fgcu": "#0 | FGCU | SR | G | 5-6 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1731453'>ncaa</a>",
"tynice-martin-2020-west-vir": "#5 | West Virginia | SR | G | 5-10 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1712144'>ncaa</a>",
"kayla-cooper-williams-2020-james-ma": "#31 | James Madison | SR | C | 6-2 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1736353'>ncaa</a>",
"borislava-hristova-2020-washingt": "#45 | Washington St. | SR | F | 6-0 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1733196'>ncaa</a>",
"gia-pack-2020-new-mexi": "#30 | New Mexico St. | SR | G | 5-10 | <a href='http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/'>hs rank: N/A</a> | <a href='https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1849478'>ncaa</a>",
"null": null
};
var player_growth = {
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"lauren-cox-2020-baylor": "/images/wnba_draft/2020/players/lauren-cox-2020-baylor_growth-f23dd819.png",
"crystal-dangerfield-2020-uconn": "/images/wnba_draft/2020/players/crystal-dangerfield-2020-uconn_growth-3e60307e.png",
"megan-walker-2020-uconn": "/images/wnba_draft/2020/players/megan-walker-2020-uconn_growth-6e125727.png",
"bella-alarie-2020-princeto": "/images/wnba_draft/2020/players/bella-alarie-2020-princeto_growth-490f356e.png",
"tyasha-harris-2020-south-ca": "/images/wnba_draft/2020/players/tyasha-harris-2020-south-ca_growth-c3714c5f.png",
"satou-sabally-2020-oregon": "/images/wnba_draft/2020/players/satou-sabally-2020-oregon_growth-558173b2.png",
"chennedy-carter-2020-texas-a&": "/images/wnba_draft/2020/players/chennedy-carter-2020-texas-a&_growth-3c8f9aa9.png",
"ruthy-hebard-2020-oregon": "/images/wnba_draft/2020/players/ruthy-hebard-2020-oregon_growth-e0ae1d9c.png",
"sug-sutton-2020-texas": "/images/wnba_draft/2020/players/sug-sutton-2020-texas_growth-64222829.png",
"beatrice-mompremier-2020-miami-(f": "/images/wnba_draft/2020/players/beatrice-mompremier-2020-miami-(f_growth-9f3e9a6d.png",
"mikayla-pivec-2020-oregon-s": "/images/wnba_draft/2020/players/mikayla-pivec-2020-oregon-s_growth-e4a9f1be.png",
"juicy-landrum-2020-baylor": "/images/wnba_draft/2020/players/juicy-landrum-2020-baylor_growth-e42d5c43.png",
"te'a-cooper-2020-baylor": "/images/wnba_draft/2020/players/te'a-cooper-2020-baylor_growth-97faa5da.png",
"dijonai-carrington-2020-stanford": "/images/wnba_draft/2020/players/dijonai-carrington-2020-stanford_growth-24c4a530.png",
"joyner-holmes-2020-texas": "/images/wnba_draft/2020/players/joyner-holmes-2020-texas_growth-b91d93a7.png",
"jordan-danberry-2020-mississi": "/images/wnba_draft/2020/players/jordan-danberry-2020-mississi_growth-4641da96.png",
"kaila-charles-2020-maryland": "/images/wnba_draft/2020/players/kaila-charles-2020-maryland_growth-c7bc723c.png",
"nicki-ekhomu-2020-florida-": "/images/wnba_draft/2020/players/nicki-ekhomu-2020-florida-_growth-c948fb80.png",
"kylee-shook-2020-louisvil": "/images/wnba_draft/2020/players/kylee-shook-2020-louisvil_growth-43e41c86.png",
"jazmine-jones-2020-louisvil": "/images/wnba_draft/2020/players/jazmine-jones-2020-louisvil_growth-025cfca4.png",
"mikiah-herbert-harrigan-2020-south-ca": "/images/wnba_draft/2020/players/mikiah-herbert-harrigan-2020-south-ca_growth-f1b22358.png",
"ayana-mitchell-2020-lsu": "/images/wnba_draft/2020/players/ayana-mitchell-2020-lsu_growth-68711e69.png",
"kamiah-smalls-2020-james-ma": "/images/wnba_draft/2020/players/kamiah-smalls-2020-james-ma_growth-b215039c.png",
"stephanie-watts-2020-southern": "/images/wnba_draft/2020/players/stephanie-watts-2020-southern_growth-0fb120f4.png",
"leaonna-odom-2020-duke": "/images/wnba_draft/2020/players/leaonna-odom-2020-duke_growth-6119046d.png",
"stephanie-jones-2020-maryland": "/images/wnba_draft/2020/players/stephanie-jones-2020-maryland_growth-2efc8d84.png",
"ciara-duffy-2020-south-da": "/images/wnba_draft/2020/players/ciara-duffy-2020-south-da_growth-47720c91.png",
"sara-rhine-2020-drake": "/images/wnba_draft/2020/players/sara-rhine-2020-drake_growth-1b1b4e38.png",
"haley-gorecki-2020-duke": "/images/wnba_draft/2020/players/haley-gorecki-2020-duke_growth-5b5a4248.png",
"kyra-lambert-2020-duke": "/images/wnba_draft/2020/players/kyra-lambert-2020-duke_growth-68fd9a56.png",
"kiah-gillespie-2020-florida-": "/images/wnba_draft/2020/players/kiah-gillespie-2020-florida-_growth-ea493883.png",
"blair-watson-2020-maryland": "/images/wnba_draft/2020/players/blair-watson-2020-maryland_growth-aa47af32.png",
"becca-hittner-2020-drake": "/images/wnba_draft/2020/players/becca-hittner-2020-drake_growth-0f689681.png",
"kathleen-doyle-2020-iowa": "/images/wnba_draft/2020/players/kathleen-doyle-2020-iowa_growth-25c1042b.png",
"aislinn-konig-2020-nc-state": "/images/wnba_draft/2020/players/aislinn-konig-2020-nc-state_growth-189fe286.png",
"nadia-fingall-2020-stanford": "/images/wnba_draft/2020/players/nadia-fingall-2020-stanford_growth-100f8d37.png",
"reili-richardson-2020-arizona-": "/images/wnba_draft/2020/players/reili-richardson-2020-arizona-_growth-38936e03.png",
"abi-scheid-2020-northwes": "/images/wnba_draft/2020/players/abi-scheid-2020-northwes_growth-e856512a.png",
"chanelle-molina-2020-washingt": "/images/wnba_draft/2020/players/chanelle-molina-2020-washingt_growth-54b72fdf.png",
"ae'rianna-harris-2020-purdue": "/images/wnba_draft/2020/players/ae'rianna-harris-2020-purdue_growth-0cc177fe.png",
"jocelyn-willoughby-2020-virginia": "/images/wnba_draft/2020/players/jocelyn-willoughby-2020-virginia_growth-596fba3a.png",
"peyton-williams-2020-kansas-s": "/images/wnba_draft/2020/players/peyton-williams-2020-kansas-s_growth-0e217731.png",
"shadeen-samuels-2020-seton-ha": "/images/wnba_draft/2020/players/shadeen-samuels-2020-seton-ha_growth-329daac0.png",
"japreece-dean-2020-ucla": "/images/wnba_draft/2020/players/japreece-dean-2020-ucla_growth-ab8cde4d.png",
"brittany-brewer-2020-texas-te": "/images/wnba_draft/2020/players/brittany-brewer-2020-texas-te_growth-651a6406.png",
"minyon-moore-2020-oregon": "/images/wnba_draft/2020/players/minyon-moore-2020-oregon_growth-b5dd99e4.png",
"jaylyn-agnew-2020-creighto": "/images/wnba_draft/2020/players/jaylyn-agnew-2020-creighto_growth-cf7b780d.png",
"dee-givens-2020-western-": "/images/wnba_draft/2020/players/dee-givens-2020-western-_growth-c2ec73a0.png",
"chante-stonewall-2020-depaul": "/images/wnba_draft/2020/players/chante-stonewall-2020-depaul_growth-bdaa26ee.png",
"alexis-tolefree-2020-arkansas": "/images/wnba_draft/2020/players/alexis-tolefree-2020-arkansas_growth-d739215e.png",
"stella-johnson-2020-rider": "/images/wnba_draft/2020/players/stella-johnson-2020-rider_growth-9b8add95.png",
"davion-wingate-2020-fgcu": "/images/wnba_draft/2020/players/davion-wingate-2020-fgcu_growth-0944e084.png",
"tynice-martin-2020-west-vir": "/images/wnba_draft/2020/players/tynice-martin-2020-west-vir_growth-1d831b23.png",
"kayla-cooper-williams-2020-james-ma": "/images/wnba_draft/2020/players/kayla-cooper-williams-2020-james-ma_growth-cf8e1698.png",
"borislava-hristova-2020-washingt": "/images/wnba_draft/2020/players/borislava-hristova-2020-washingt_growth-6262ac5f.png",
"gia-pack-2020-new-mexi": "/images/wnba_draft/2020/players/gia-pack-2020-new-mexi_growth-e33e578c.png",
"null": null
};
var player_stats = {
"sabrina-ionescu-2020-oregon": "/images/wnba_draft/2020/players/sabrina-ionescu-2020-oregon_stats-d00f4eec.png",
"lauren-cox-2020-baylor": "/images/wnba_draft/2020/players/lauren-cox-2020-baylor_stats-388c6927.png",
"crystal-dangerfield-2020-uconn": "/images/wnba_draft/2020/players/crystal-dangerfield-2020-uconn_stats-cbfd1966.png",
"megan-walker-2020-uconn": "/images/wnba_draft/2020/players/megan-walker-2020-uconn_stats-85c90804.png",
"bella-alarie-2020-princeto": "/images/wnba_draft/2020/players/bella-alarie-2020-princeto_stats-1f664801.png",
"tyasha-harris-2020-south-ca": "/images/wnba_draft/2020/players/tyasha-harris-2020-south-ca_stats-ee4a2073.png",
"satou-sabally-2020-oregon": "/images/wnba_draft/2020/players/satou-sabally-2020-oregon_stats-8c0de8ad.png",
"chennedy-carter-2020-texas-a&": "/images/wnba_draft/2020/players/chennedy-carter-2020-texas-a&_stats-3a194744.png",
"ruthy-hebard-2020-oregon": "/images/wnba_draft/2020/players/ruthy-hebard-2020-oregon_stats-a9010375.png",
"sug-sutton-2020-texas": "/images/wnba_draft/2020/players/sug-sutton-2020-texas_stats-dc02f582.png",
"beatrice-mompremier-2020-miami-(f": "/images/wnba_draft/2020/players/beatrice-mompremier-2020-miami-(f_stats-f4d82aaa.png",
"mikayla-pivec-2020-oregon-s": "/images/wnba_draft/2020/players/mikayla-pivec-2020-oregon-s_stats-3f75ccd3.png",
"juicy-landrum-2020-baylor": "/images/wnba_draft/2020/players/juicy-landrum-2020-baylor_stats-6932ed4e.png",
"te'a-cooper-2020-baylor": "/images/wnba_draft/2020/players/te'a-cooper-2020-baylor_stats-716c9189.png",
"dijonai-carrington-2020-stanford": "/images/wnba_draft/2020/players/dijonai-carrington-2020-stanford_stats-0db770db.png",
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"borislava-hristova-2020-washingt": "/images/wnba_draft/2020/players/borislava-hristova-2020-washingt_stats-0f7c6c9e.png",
"gia-pack-2020-new-mexi": "/images/wnba_draft/2020/players/gia-pack-2020-new-mexi_stats-adc8fc3e.png",
"null": null
};
var player_comps = {
"sabrina-ionescu-2020-oregon": "/images/wnba_draft/2020/players/sabrina-ionescu-2020-oregon_comps-f6a27a7c.png",
"lauren-cox-2020-baylor": "/images/wnba_draft/2020/players/lauren-cox-2020-baylor_comps-dff7fad9.png",
"crystal-dangerfield-2020-uconn": "/images/wnba_draft/2020/players/crystal-dangerfield-2020-uconn_comps-dc0f7f23.png",
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"bella-alarie-2020-princeto": "/images/wnba_draft/2020/players/bella-alarie-2020-princeto_comps-edd4b1dc.png",
"tyasha-harris-2020-south-ca": "/images/wnba_draft/2020/players/tyasha-harris-2020-south-ca_comps-3389d8aa.png",
"satou-sabally-2020-oregon": "/images/wnba_draft/2020/players/satou-sabally-2020-oregon_comps-a6df4ad2.png",
"chennedy-carter-2020-texas-a&": "/images/wnba_draft/2020/players/chennedy-carter-2020-texas-a&_comps-ce58d7f2.png",
"ruthy-hebard-2020-oregon": "/images/wnba_draft/2020/players/ruthy-hebard-2020-oregon_comps-1508c893.png",
"sug-sutton-2020-texas": "/images/wnba_draft/2020/players/sug-sutton-2020-texas_comps-9b48fb9f.png",
"beatrice-mompremier-2020-miami-(f": "/images/wnba_draft/2020/players/beatrice-mompremier-2020-miami-(f_comps-e400f29d.png",
"mikayla-pivec-2020-oregon-s": "/images/wnba_draft/2020/players/mikayla-pivec-2020-oregon-s_comps-f407d829.png",
"juicy-landrum-2020-baylor": "/images/wnba_draft/2020/players/juicy-landrum-2020-baylor_comps-5071af43.png",
"te'a-cooper-2020-baylor": "/images/wnba_draft/2020/players/te'a-cooper-2020-baylor_comps-4a29c457.png",
"dijonai-carrington-2020-stanford": "/images/wnba_draft/2020/players/dijonai-carrington-2020-stanford_comps-373a68a8.png",
"joyner-holmes-2020-texas": "/images/wnba_draft/2020/players/joyner-holmes-2020-texas_comps-5fdb5358.png",
"jordan-danberry-2020-mississi": "/images/wnba_draft/2020/players/jordan-danberry-2020-mississi_comps-c1f12376.png",
"kaila-charles-2020-maryland": "/images/wnba_draft/2020/players/kaila-charles-2020-maryland_comps-1e489108.png",
"nicki-ekhomu-2020-florida-": "/images/wnba_draft/2020/players/nicki-ekhomu-2020-florida-_comps-96e0ed8b.png",
"kylee-shook-2020-louisvil": "/images/wnba_draft/2020/players/kylee-shook-2020-louisvil_comps-8cefea3f.png",
"jazmine-jones-2020-louisvil": "/images/wnba_draft/2020/players/jazmine-jones-2020-louisvil_comps-9ec902a4.png",
"mikiah-herbert-harrigan-2020-south-ca": "/images/wnba_draft/2020/players/mikiah-herbert-harrigan-2020-south-ca_comps-352b7bb5.png",
"ayana-mitchell-2020-lsu": "/images/wnba_draft/2020/players/ayana-mitchell-2020-lsu_comps-a634d62b.png",
"kamiah-smalls-2020-james-ma": "/images/wnba_draft/2020/players/kamiah-smalls-2020-james-ma_comps-dacfaddd.png",
"stephanie-watts-2020-southern": "/images/wnba_draft/2020/players/stephanie-watts-2020-southern_comps-1bd85fbe.png",
"leaonna-odom-2020-duke": "/images/wnba_draft/2020/players/leaonna-odom-2020-duke_comps-b90bb90c.png",
"stephanie-jones-2020-maryland": "/images/wnba_draft/2020/players/stephanie-jones-2020-maryland_comps-0bd3c339.png",
"ciara-duffy-2020-south-da": "/images/wnba_draft/2020/players/ciara-duffy-2020-south-da_comps-43f557ef.png",
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"haley-gorecki-2020-duke": "/images/wnba_draft/2020/players/haley-gorecki-2020-duke_comps-8fc21659.png",
"kyra-lambert-2020-duke": "/images/wnba_draft/2020/players/kyra-lambert-2020-duke_comps-bda7098a.png",
"kiah-gillespie-2020-florida-": "/images/wnba_draft/2020/players/kiah-gillespie-2020-florida-_comps-1af9b9ef.png",
"blair-watson-2020-maryland": "/images/wnba_draft/2020/players/blair-watson-2020-maryland_comps-15938dbd.png",
"becca-hittner-2020-drake": "/images/wnba_draft/2020/players/becca-hittner-2020-drake_comps-77a34c5a.png",
"kathleen-doyle-2020-iowa": "/images/wnba_draft/2020/players/kathleen-doyle-2020-iowa_comps-46e1edf5.png",
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"jocelyn-willoughby-2020-virginia": "/images/wnba_draft/2020/players/jocelyn-willoughby-2020-virginia_comps-57d7e669.png",
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</script>
<ul>
<li><a href="#plum">PLUM Draft Model</a></li>
<li><a href="#top">2020 PLUM Rankings</a>
<ul>
<li><a href="#top">Top 36</a></li>
<li><a href="#guards">Guards</a></li>
<li><a href="#bigs">Bigs</a></li>
<li><a href="#star">All Star Potential</a></li>
</ul>
</li>
<li><a href="#profiles">Player Profiles</a></li>
<li><a href="#actual">Actual</a></li>
<li><a href="#mock">Mock Draft Comparison</a></li>
</ul>
<hr />
<h3 id="a-nameplumplum-draft-modela"><a name="plum">PLUM Draft Model</a></h3>
<p>The <strong>PLUM</strong> draft model (<a href="/2017/04/13/plum-draft-model.html">named after Kelsey Plum</a>) utilizes machine learning to objectively predict which players will succeed in the WNBA.</p>
<p>The model incorporates advanced statistics derived from college play-by-play data which are not available anywhere else (<a href="/2019/05/03/ncaaw-rapm.html">Bayesian RAPM</a>, <a href="/2019/06/01/rapm-stats.html">"Adjusted" box score stats</a>, rate stats, etc.). These statistics isolate the impact and efficiency of a single player by controlling for playing time, pace, other players on the court (opponents, teammates), etc. The model also uses player characteristics (year in school, height). Lastly, a big improvement this year is the addition of the <a href="http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/">espnW 100 HoopGurlz</a> high school recruiting rankings.</p>
<p>If you want to read more about modeling details, check out analysis from prior years such as <a href="http://tothemean.com/2018/04/11/wnba-draft-2018.html">2018</a> or <a href="http://tothemean.com/2019/04/20/wnba-draft-2019.html">2019</a> or reach out to me on <a href="https://twitter.com/jessefischer33">Twitter</a>.</p>
<hr />
<h3 id="a-nametop2020-plum-rankingsa"><a name="top">2020 PLUM Rankings</a></h3>
<p>Below are the Top 36 players - <a href="/images/wnba_draft/2020/top_2020_extended-b240f72c.png">an extended view can be found here</a>.</p>
<p><a href="/images/wnba_draft/2020/top_2020-96ab44b0.png"><img alt="Plum 2020" src="/images/wnba_draft/2020/top_2020-96ab44b0.png" /></a></p>
<hr />
<h3 id="a-nameguardstop-guardsa"><a name="guards">Top Guards</a></h3>
<p><a href="/images/wnba_draft/2020/top_2020_guards-e0c4c3a6.png"><img alt="Guards" src="/images/wnba_draft/2020/top_2020_guards-e0c4c3a6.png" /></a></p>
<p><a href="/images/wnba_draft/2020/top_2020_guards_stats-88b90bfe.png"><img alt="Guards" src="/images/wnba_draft/2020/top_2020_guards_stats-88b90bfe.png" /></a></p>
<hr />
<h3 id="a-namebigstop-bigsa"><a name="bigs">Top Bigs</a></h3>
<p><a href="/images/wnba_draft/2020/top_2020_bigs-51394b69.png"><img alt="Bigs" src="/images/wnba_draft/2020/top_2020_bigs-51394b69.png" /></a></p>
<p><a href="/images/wnba_draft/2020/top_2020_bigs_stats-1c93d021.png"><img alt="Bigs" src="/images/wnba_draft/2020/top_2020_bigs_stats-1c93d021.png" /></a></p>
<hr />
<h3 id="a-namestarall-star-potentiala"><a name="star">All Star Potential</a></h3>
<p>Below are players with a >=1% WNBA All Star probability.</p>
<p><a href="/images/wnba_draft/2020/star_2020-3f4f5500.png"><img alt="All Star Potential" src="/images/wnba_draft/2020/star_2020-3f4f5500.png" /></a></p>
<hr />
<h3 id="a-nameprofilesplayer-profilesa"><a name="profiles">Player Profiles</a></h3>
<p>Select a player to see their draft profile:</p>
<center><select id="player_name" onchange="document.getElementById('player_header').innerHTML = player_header[this.value]; document.getElementById('player_info').innerHTML = player_info[this.value]; document.getElementById('player_growth').src = player_growth[this.value]; document.getElementById('player_growth_a').href = player_growth[this.value]; document.getElementById('player_stats').src = player_stats[this.value]; document.getElementById('player_stats_a').href = player_stats[this.value]; document.getElementById('player_comps').src = player_comps[this.value]; document.getElementById('player_comps_a').href = player_comps[this.value]; document.getElementById('insight1').innerHTML = model_insight[this.value][0]; document.getElementById('insight2').innerHTML = model_insight[this.value][1]; document.getElementById('insight3').innerHTML = model_insight[this.value][2]; document.getElementById('insight4').innerHTML = model_insight[this.value][3]; document.getElementById('insight5').innerHTML = model_insight[this.value][4]; document.getElementById('insight6').innerHTML = model_insight[this.value][5]; ">
<option value="sabrina-ionescu-2020-oregon">1. Sabrina Ionescu - Oregon</option>
<option value="lauren-cox-2020-baylor">2. Lauren Cox - Baylor</option>
<option value="crystal-dangerfield-2020-uconn">3. Crystal Dangerfield - UConn</option>
<option value="megan-walker-2020-uconn">4. Megan Walker - UConn</option>
<option value="bella-alarie-2020-princeto">5. Bella Alarie - Princeton</option>
<option value="tyasha-harris-2020-south-ca">6. Tyasha Harris - South Carolina</option>
<option value="satou-sabally-2020-oregon">7. Satou Sabally - Oregon</option>
<option value="chennedy-carter-2020-texas-a&">8. Chennedy Carter - Texas A&M</option>
<option value="ruthy-hebard-2020-oregon">9. Ruthy Hebard - Oregon</option>
<option value="sug-sutton-2020-texas">10. Sug Sutton - Texas</option>
<option value="beatrice-mompremier-2020-miami-(f">11. Beatrice Mompremier - Miami (FL)</option>
<option value="mikayla-pivec-2020-oregon-s">12. Mikayla Pivec - Oregon St.</option>
<option value="juicy-landrum-2020-baylor">13. Juicy Landrum - Baylor</option>
<option value="te'a-cooper-2020-baylor">14. Te'a Cooper - Baylor</option>
<option value="dijonai-carrington-2020-stanford">15. Dijonai Carrington - Stanford</option>
<option value="joyner-holmes-2020-texas">16. Joyner Holmes - Texas</option>
<option value="jordan-danberry-2020-mississi">17. Jordan Danberry - Mississippi St.</option>
<option value="kaila-charles-2020-maryland">18. Kaila Charles - Maryland</option>
<option value="nicki-ekhomu-2020-florida-">19. Nicki Ekhomu - Florida St.</option>
<option value="kylee-shook-2020-louisvil">20. Kylee Shook - Louisville</option>
<option value="jazmine-jones-2020-louisvil">21. Jazmine Jones - Louisville</option>
<option value="mikiah-herbert-harrigan-2020-south-ca">22. Mikiah Herbert Harrigan - South Carolina</option>
<option value="ayana-mitchell-2020-lsu">23. Ayana Mitchell - LSU</option>
<option value="kamiah-smalls-2020-james-ma">24. Kamiah Smalls - James Madison</option>
<option value="stephanie-watts-2020-southern">25. Stephanie Watts - Southern California</option>
<option value="leaonna-odom-2020-duke">26. Leaonna Odom - Duke</option>
<option value="stephanie-jones-2020-maryland">27. Stephanie Jones - Maryland</option>
<option value="ciara-duffy-2020-south-da">28. Ciara Duffy - South Dakota</option>
<option value="sara-rhine-2020-drake">29. Sara Rhine - Drake</option>
<option value="haley-gorecki-2020-duke">30. Haley Gorecki - Duke</option>
<option value="kyra-lambert-2020-duke">31. Kyra Lambert - Duke</option>
<option value="kiah-gillespie-2020-florida-">32. Kiah Gillespie - Florida St.</option>
<option value="blair-watson-2020-maryland">33. Blair Watson - Maryland</option>
<option value="becca-hittner-2020-drake">34. Becca Hittner - Drake</option>
<option value="kathleen-doyle-2020-iowa">35. Kathleen Doyle - Iowa</option>
<option value="aislinn-konig-2020-nc-state">36. Aislinn Konig - NC State</option>
<option value="nadia-fingall-2020-stanford">37. Nadia Fingall - Stanford</option>
<option value="reili-richardson-2020-arizona-">39. Reili Richardson - Arizona St.</option>
<option value="abi-scheid-2020-northwes">44. Abi Scheid - Northwestern</option>
<option value="chanelle-molina-2020-washingt">49. Chanelle Molina - Washington St.</option>
<option value="ae'rianna-harris-2020-purdue">50. Ae'Rianna Harris - Purdue</option>
<option value="jocelyn-willoughby-2020-virginia">51. Jocelyn Willoughby - Virginia</option>
<option value="peyton-williams-2020-kansas-s">60. Peyton Williams - Kansas St.</option>
<option value="shadeen-samuels-2020-seton-ha">62. Shadeen Samuels - Seton Hall</option>
<option value="japreece-dean-2020-ucla">66. Japreece Dean - UCLA</option>
<option value="brittany-brewer-2020-texas-te">68. Brittany Brewer - Texas Tech</option>
<option value="minyon-moore-2020-oregon">69. Minyon Moore - Oregon</option>
<option value="jaylyn-agnew-2020-creighto">85. Jaylyn Agnew - Creighton</option>
<option value="dee-givens-2020-western-">91. Dee Givens - Western Ky.</option>
<option value="chante-stonewall-2020-depaul">92. Chante Stonewall - DePaul</option>
<option value="alexis-tolefree-2020-arkansas">100. Alexis Tolefree - Arkansas</option>
<option value="stella-johnson-2020-rider">101. Stella Johnson - Rider</option>
<option value="davion-wingate-2020-fgcu">127. Davion Wingate - FGCU</option>
<option value="tynice-martin-2020-west-vir">128. Tynice Martin - West Virginia</option>
<option value="kayla-cooper-williams-2020-james-ma">133. Kayla Cooper-Williams - James Madison</option>
<option value="borislava-hristova-2020-washingt">134. Borislava Hristova - Washington St.</option>
<option value="gia-pack-2020-new-mexi">148. Gia Pack - New Mexico St.</option>
</select></center>
<h3 id="a-idplayerheadersabrina-ionescua"><strong><a id="player_header">Sabrina Ionescu</a></strong></h3>
<text id="player_info">#20 | Oregon | SR | G | 5-10 | <a href="http://www.espn.com/high-school/girls-basketball/recruiting/rankings/_/class/2016">hs rank: 4</a> | <a href="https://stats.ncaa.org/player/index?game_sport_year_ctl_id=15002&stats_player_seq=1845903">ncaa</a></text>
<p><a href="/images/wnba_draft/2020/players/sabrina-ionescu-2020-oregon_growth.png" id="player_growth_a"><img src="/images/wnba_draft/2020/players/sabrina-ionescu-2020-oregon_growth.png" id="player_growth" /></a></p>
<h4 id="statistical-profile">Statistical Profile</h4>
<p><a href="/images/wnba_draft/2020/players/sabrina-ionescu-2020-oregon_stats.png" id="player_stats_a"><img src="/images/wnba_draft/2020/players/sabrina-ionescu-2020-oregon_stats.png" id="player_stats" /></a></p>
<h4 id="playing-style-comps">Playing Style Comps</h4>
<p><a href="/images/wnba_draft/2020/players/sabrina-ionescu-2020-oregon_comps.png" id="player_comps_a"><img src="/images/wnba_draft/2020/players/sabrina-ionescu-2020-oregon_comps.png" id="player_comps" /></a></p>
<h4 id="draft-model-insight">Draft Model Insight</h4>
<p><span class="fa fa-plus" style="color:green"></span> <text id="insight1">ftp</text>, <text id="insight2">ast%</text>, <text id="insight3">rapm_off</text><br />
<span class="fa fa-minus" style="color:red"></span> <text id="insight4">blk%</text>, <text id="insight5">drb%</text>, <text id="insight6">3par</text><br /></p>
<hr />
<h3 id="a-nameactualactuala"><a name="actual">Actual</a></h3>
<p><a href="/images/wnba_draft/2020/actual_2020-65f0b875.png"><img alt="Actual" src="/images/wnba_draft/2020/actual_2020-65f0b875.png" /></a></p>
<hr />
<h3 id="a-namemockmock-draft-comparisona"><a name="mock">Mock Draft Comparison</a></h3>
<p>Here is how the PLUM ranking compares with various mock drafts (<a href="https://www.bball-index.com/2020-wnba-draft-central/">bball-index</a>, <a href="https://www.draftsite.com/wnba/mock-draft/2020/">draftsite.com</a>, <a href="https://www.espn.com/wnba/story/_/id/29008593/wnba-mock-draft-2020-oregon-sabrina-ionescu-satou-sabally-projected-go-1-2">espn</a>, <a href="https://highposthoops.com/wnba-draft/2020-wnba-draft-big-board/">highposthoops</a>, <a href="https://www.swishappeal.com/wnba/2020/4/9/21195744/wnba-2020-mock-draft-dream-sky-sun-wing-fever-aces-sparks-lynx-liberty-storm-mystics-mercury">swishappeal</a>, and <a href="https://wbasketballblog.com/2020/04/08/2020-final-wnba-mock-draft/">wbasketballblog</a>).</p>
<p><a href="/images/wnba_draft/2020/mocks_2020-1ecfe115.png"><img alt="Mocks" src="/images/wnba_draft/2020/mocks_2020-1ecfe115.png" /></a></p>
<p><a href="/images/wnba_draft/2020/mocks_actual_2020-8d473208.png"><img alt="Mocks Actual" src="/images/wnba_draft/2020/mocks_actual_2020-8d473208.png" /></a></p>
2019 NBA Draft Analyticshttp://tothemean.com/2019/06/16/nba-draft-2019.html2019-06-16T00:00:00Z2019-06-20T03:02:08-07:00Jesse Fischer<script>
var player_header = {
"zion-williamson-2019-duke": "Zion Williamson",
"rj-barrett-2019-duke": "R.J. Barrett",
"bol-bol-2019-oregon": "Bol Bol",
"jaxson-hayes-2019-texas": "Jaxson Hayes",
"tacko-fall-2019-ucf": "Tacko Fall",
"charles-bassey-2019-western-": "Charles Bassey",
"jontay-porter-2018-missouri": "Jontay Porter",
"ja-morant-2019-murray-s": "Ja Morant",
"moses-brown-2019-ucla": "Moses Brown",
"nicolas-claxton-2019-georgia": "Nicolas Claxton",
"daniel-gafford-2019-arkansas": "Daniel Gafford",
"nassir-little-2019-unc": "Nassir Little",
"de'andre-hunter-2019-virginia": "De'Andre Hunter",
"romeo-langford-2019-indiana": "Romeo Langford",
"dean-wade-2019-kansas-s": "Dean Wade",
"tyler-herro-2019-kentucky": "Tyler Herro",
"grant-williams-2019-tennesse": "Grant Williams",
"pj-washington-2019-kentucky": "PJ Washington",
"jarrett-culver-2019-texas-te": "Jarrett Culver",
"dedric-lawson-2019-kansas": "Dedric Lawson",
"talen-horton-tucker-2019-iowa-sta": "Talen Horton-Tucker",
"nickeil-alexander-walker-2019-virginia": "Nickeil Alexander-Walker",
"bruno-fernando-2019-maryland": "Bruno Fernando",
"chuma-okeke-2019-auburn": "Chuma Okeke",
"brandon-clarke-2019-gonzaga": "Brandon Clarke",
"admiral-schofield-2019-tennesse": "Admiral Schofield",
"keldon-johnson-2019-kentucky": "Keldon Johnson",
"rui-hachimura-2019-gonzaga": "Rui Hachimura",
"cam-reddish-2019-duke": "Cam Reddish",
"donta-hall-2019-alabama": "Donta Hall",
"carsen-edwards-2019-purdue": "Carsen Edwards",
"coby-white-2019-unc": "Coby White",
"dylan-windler-2019-belmont": "Dylan Windler",
"zach-norvell-jr-2019-gonzaga": "Zach Norvell Jr.",
"naz-reid-2019-lsu": "Naz Reid",
"jordan-poole-2019-michigan": "Jordan Poole",
"jaylen-nowell-2019-washingt": "Jaylen Nowell",
"terance-mann-2019-florida-": "Terance Mann",
"tyler-cook-2019-iowa": "Tyler Cook",
"quinndary-weatherspoon-2019-mississi": "Quinndary Weatherspoon",
"ignas-brazdeikis-2019-michigan": "Ignas Brazdeikis",
"kevin-porter-jr-2019-usc": "Kevin Porter Jr",
"simisola-shittu-2019-vanderbi": "Simisola Shittu",
"john-konchar-2018-purdue-f": "John Konchar",
"cameron-johnson-2019-unc": "Cameron Johnson",
"eric-paschall-2019-villanov": "Eric Paschall",
"cameron-oliver-2017-nevada": "Cameron Oliver",
"kenny-wooten-2019-oregon": "Kenny Wooten",
"eric-mika-2017-byu": "Eric Mika",
"josh-reaves-2019-penn-sta": "Josh Reaves",
"jalen-mcdaniels-2019-san-dieg": "Jalen McDaniels",
"robert-franks-2019-washingt": "Robert Franks",
"kerwin-roach-jr-2019-texas": "Kerwin Roach Jr.",
"shamorie-ponds-2019-st-john'": "Shamorie Ponds",
"louis-king-2019-oregon": "Louis King",
"darius-garland-2019-vanderbi": "Darius Garland",
"ty-jerome-2019-virginia": "Ty Jerome",
"luguentz-dort-2019-arizona-": "Luguentz Dort",
"isaiah-roby-2019-nebraska": "Isaiah Roby",
"mfiondu-kabengele-2019-florida-": "Mfiondu Kabengele",
"null": null
};
var player_info = {
"zion-williamson-2019-duke": "Duke | FR | F | 6-7 | 285 | 18.8 | rsci: 4 | <a href='http://www.sports-reference.com/cbb/players/zion-williamson-1.html'>s-ref</a>",
"rj-barrett-2019-duke": "Duke | FR | F | 6-7 | 202 | 18.9 | rsci: 1 | <a href='http://www.sports-reference.com/cbb/players/rj-barrett-1.html'>s-ref</a>",
"bol-bol-2019-oregon": "Oregon | FR | C | 7-2 | 235 | 19.5 | rsci: 6 | <a href='http://www.sports-reference.com/cbb/players/bol-bol-1.html'>s-ref</a>",
"jaxson-hayes-2019-texas": "Texas | FR | F | 6-11 | 220 | 19.0 | <a href='http://www.sports-reference.com/cbb/players/jaxson-hayes-1.html'>s-ref</a>",
"tacko-fall-2019-ucf": "UCF | SR | C | 7-6 | 310 | 23.4 | <a href='http://www.sports-reference.com/cbb/players/tacko-fall-1.html'>s-ref</a>",
"charles-bassey-2019-western-": "Western Kentucky | FR | C | 6-11 | 245 | 18.5 | rsci: 9 | <a href='http://www.sports-reference.com/cbb/players/charles-bassey-1.html'>s-ref</a>",
"jontay-porter-2018-missouri": "Missouri | FR | F | 6-11 | 240 | 18.5 | rsci: 53 | <a href='http://www.sports-reference.com/cbb/players/jontay-porter-1.html'>s-ref</a>",
"ja-morant-2019-murray-s": "Murray State | SO | G | 6-3 | 175 | 19.7 | <a href='http://www.sports-reference.com/cbb/players/temetrius-morant-1.html'>s-ref</a>",
"moses-brown-2019-ucla": "UCLA | FR | C | 7-1 | 245 | 19.6 | rsci: 24 | <a href='http://www.sports-reference.com/cbb/players/moses-brown-1.html'>s-ref</a>",
"nicolas-claxton-2019-georgia": "Georgia | SO | F | 6-11 | 220 | 20.1 | <a href='http://www.sports-reference.com/cbb/players/nicolas-claxton-1.html'>s-ref</a>",
"daniel-gafford-2019-arkansas": "Arkansas | SO | F | 6-11 | 233 | 20.6 | rsci: 36 | <a href='http://www.sports-reference.com/cbb/players/daniel-gafford-1.html'>s-ref</a>",
"nassir-little-2019-unc": "UNC | FR | F | 6-6 | 220 | 19.2 | rsci: 3 | <a href='http://www.sports-reference.com/cbb/players/nassir-little-1.html'>s-ref</a>",
"de'andre-hunter-2019-virginia": "Virginia | SO | G | 6-7 | 225 | 21.4 | rsci: 74 | <a href='http://www.sports-reference.com/cbb/players/deandre-hunter-1.html'>s-ref</a>",
"romeo-langford-2019-indiana": "Indiana | FR | G | 6-6 | 215 | 19.5 | rsci: 5 | <a href='http://www.sports-reference.com/cbb/players/romeo-langford-1.html'>s-ref</a>",
"dean-wade-2019-kansas-s": "Kansas State | SR | F | 6-10 | 228 | 22.5 | <a href='http://www.sports-reference.com/cbb/players/dean-wade-1.html'>s-ref</a>",
"tyler-herro-2019-kentucky": "Kentucky | FR | G | 6-5 | 195 | 19.3 | rsci: 35 | <a href='http://www.sports-reference.com/cbb/players/tyler-herro-1.html'>s-ref</a>",
"grant-williams-2019-tennesse": "Tennessee | JR | F | 6-7 | 236 | 20.4 | <a href='http://www.sports-reference.com/cbb/players/grant-williams-1.html'>s-ref</a>",
"pj-washington-2019-kentucky": "Kentucky | SO | F | 6-8 | 228 | 20.7 | rsci: 14 | <a href='http://www.sports-reference.com/cbb/players/pj-washington-1.html'>s-ref</a>",
"jarrett-culver-2019-texas-te": "Texas Tech | SO | G | 6-5 | 195 | 20.2 | <a href='http://www.sports-reference.com/cbb/players/jarrett-culver-1.html'>s-ref</a>",
"dedric-lawson-2019-kansas": "Kansas | JR | G | 6-9 | 235 | 21.6 | rsci: 32 | <a href='http://www.sports-reference.com/cbb/players/dedric-lawson-1.html'>s-ref</a>",
"talen-horton-tucker-2019-iowa-sta": "Iowa State | FR | G | 6-4 | 233 | 18.4 | rsci: 50 | <a href='http://www.sports-reference.com/cbb/players/talen-horton-tucker-1.html'>s-ref</a>",
"nickeil-alexander-walker-2019-virginia": "Virginia Tech | SO | G | 6-5 | 205 | 20.7 | rsci: 33 | <a href='http://www.sports-reference.com/cbb/players/nickeil-alexander-walker-1.html'>s-ref</a>",
"bruno-fernando-2019-maryland": "Maryland | SO | F | 6-10 | 240 | 20.7 | rsci: 93 | <a href='http://www.sports-reference.com/cbb/players/bruno-fernando-1.html'>s-ref</a>",
"chuma-okeke-2019-auburn": "Auburn | SO | F | 6-8 | 230 | 20.7 | rsci: 48 | <a href='http://www.sports-reference.com/cbb/players/chuma-okeke-1.html'>s-ref</a>",
"brandon-clarke-2019-gonzaga": "Gonzaga | JR | F | 6-8 | 215 | 22.6 | <a href='http://www.sports-reference.com/cbb/players/brandon-clarke-1.html'>s-ref</a>",
"admiral-schofield-2019-tennesse": "Tennessee | SR | G | 6-6 | 241 | 22.1 | <a href='http://www.sports-reference.com/cbb/players/admiral-schofield-1.html'>s-ref</a>",
"keldon-johnson-2019-kentucky": "Kentucky | FR | G | 6-6 | 211 | 19.6 | rsci: 12 | <a href='http://www.sports-reference.com/cbb/players/keldon-johnson-1.html'>s-ref</a>",
"rui-hachimura-2019-gonzaga": "Gonzaga | JR | F | 6-8 | 230 | 21.2 | <a href='http://www.sports-reference.com/cbb/players/rui-hachimura-1.html'>s-ref</a>",
"cam-reddish-2019-duke": "Duke | FR | F | 6-8 | 218 | 19.7 | rsci: 2 | <a href='http://www.sports-reference.com/cbb/players/cam-reddish-1.html'>s-ref</a>",
"donta-hall-2019-alabama": "Alabama | SR | F | 6-9 | 230 | 21.7 | <a href='http://www.sports-reference.com/cbb/players/donta-hall-1.html'>s-ref</a>",
"carsen-edwards-2019-purdue": "Purdue | JR | G | 6-1 | 200 | 21.2 | <a href='http://www.sports-reference.com/cbb/players/carsen-edwards-1.html'>s-ref</a>",
"coby-white-2019-unc": "UNC | FR | G | 6-5 | 185 | 19.2 | rsci: 27 | <a href='http://www.sports-reference.com/cbb/players/coby-white-1.html'>s-ref</a>",
"dylan-windler-2019-belmont": "Belmont | SR | F | 6-8 | 200 | 22.6 | <a href='http://www.sports-reference.com/cbb/players/dylan-windler-1.html'>s-ref</a>",
"zach-norvell-jr-2019-gonzaga": "Gonzaga | SO | G | 6-5 | 205 | 21.4 | <a href='http://www.sports-reference.com/cbb/players/zach-norvelljr-1.html'>s-ref</a>",
"naz-reid-2019-lsu": "LSU | FR | F | 6-10 | 250 | 19.7 | rsci: 18 | <a href='http://www.sports-reference.com/cbb/players/naz-reid-1.html'>s-ref</a>",
"jordan-poole-2019-michigan": "Michigan | SO | G | 6-5 | 195 | 19.9 | rsci: 99 | <a href='http://www.sports-reference.com/cbb/players/jordan-poole-1.html'>s-ref</a>",
"jaylen-nowell-2019-washingt": "Washington | SO | G | 6-4 | 200 | 19.8 | rsci: 66 | <a href='http://www.sports-reference.com/cbb/players/jaylen-nowell-1.html'>s-ref</a>",
"terance-mann-2019-florida-": "Florida State | SR | G | 6-7 | 215 | 22.5 | <a href='http://www.sports-reference.com/cbb/players/terance-mann-1.html'>s-ref</a>",
"tyler-cook-2019-iowa": "Iowa | JR | F | 6-9 | 250 | 21.6 | rsci: 63 | <a href='http://www.sports-reference.com/cbb/players/tyler-cook-1.html'>s-ref</a>",
"quinndary-weatherspoon-2019-mississi": "Mississippi State | SR | G | 6-4 | 205 | 22.7 | rsci: 98 | <a href='http://www.sports-reference.com/cbb/players/quinndary-weatherspoon-1.html'>s-ref</a>",
"ignas-brazdeikis-2019-michigan": "Michigan | FR | F | 6-7 | 215 | 20.3 | rsci: 74 | <a href='http://www.sports-reference.com/cbb/players/ignas-brazdeikis-1.html'>s-ref</a>",
"kevin-porter-jr-2019-usc": "USC | FR | G | 6-6 | 218 | 19.0 | rsci: 28 | <a href='http://www.sports-reference.com/cbb/players/kevin-porterjr-1.html'>s-ref</a>",
"simisola-shittu-2019-vanderbi": "Vanderbilt | FR | F | 6-10 | 240 | 19.5 | rsci: 10 | <a href='http://www.sports-reference.com/cbb/players/simisola-shittu-1.html'>s-ref</a>",
"john-konchar-2018-purdue-f": "Purdue-Fort Wayne | JR | G | 6-5 | 210 | 22.1 | <a href='http://www.sports-reference.com/cbb/players/john-konchar-1.html'>s-ref</a>",
"cameron-johnson-2019-unc": "UNC | SR | G | 6-9 | 210 | 23.2 | <a href='http://www.sports-reference.com/cbb/players/cameron-johnson-4.html'>s-ref</a>",
"eric-paschall-2019-villanov": "Villanova | SR | F | 6-8 | 255 | 22.5 | <a href='http://www.sports-reference.com/cbb/players/eric-paschall-1.html'>s-ref</a>",
"cameron-oliver-2017-nevada": "Nevada | SO | F | 6-8 | 225 | 20.8 | <a href='http://www.sports-reference.com/cbb/players/cameron-oliver-1.html'>s-ref</a>",
"kenny-wooten-2019-oregon": "Oregon | SO | F | 6-9 | 235 | 21.1 | <a href='http://www.sports-reference.com/cbb/players/kenny-wooten-1.html'>s-ref</a>",
"eric-mika-2017-byu": "BYU | SO | F | 6-10 | 230 | 22.3 | rsci: 39 | <a href='http://www.sports-reference.com/cbb/players/eric-mika-2.html'>s-ref</a>",
"josh-reaves-2019-penn-sta": "Penn State | SR | G | 6-5 | 214 | 21.9 | <a href='http://www.sports-reference.com/cbb/players/josh-reaves-1.html'>s-ref</a>",
"jalen-mcdaniels-2019-san-dieg": "San Diego State | SO | F | 6-10 | 195 | 21.3 | <a href='http://www.sports-reference.com/cbb/players/jalen-mcdaniels-1.html'>s-ref</a>",
"robert-franks-2019-washingt": "Washington State | SR | F | 6-9 | 225 | 22.4 | <a href='http://www.sports-reference.com/cbb/players/robert-franks-1.html'>s-ref</a>",
"kerwin-roach-jr-2019-texas": "Texas | SR | G | 6-4 | 180 | 22.5 | rsci: 39 | <a href='http://www.sports-reference.com/cbb/players/kerwin-roachjr-1.html'>s-ref</a>",
"shamorie-ponds-2019-st-john'": "St. John's (NY) | JR | G | 6-1 | 175 | 20.9 | rsci: 36 | <a href='http://www.sports-reference.com/cbb/players/shamorie-ponds-1.html'>s-ref</a>",
"louis-king-2019-oregon": "Oregon | FR | F | 6-9 | 205 | 20.1 | rsci: 20 | <a href='http://www.sports-reference.com/cbb/players/louis-king-1.html'>s-ref</a>",
"darius-garland-2019-vanderbi": "Vanderbilt | FR | G | 6-2 | 175 | 19.3 | rsci: 15 | <a href='http://www.sports-reference.com/cbb/players/darius-garland-1.html'>s-ref</a>",
"ty-jerome-2019-virginia": "Virginia | JR | G | 6-5 | 195 | 21.8 | rsci: 46 | <a href='http://www.sports-reference.com/cbb/players/ty-jerome-1.html'>s-ref</a>",
"luguentz-dort-2019-arizona-": "Arizona State | FR | G | 6-4 | 215 | 20.0 | rsci: 76 | <a href='http://www.sports-reference.com/cbb/players/luguentz-dort-1.html'>s-ref</a>",
"isaiah-roby-2019-nebraska": "Nebraska | JR | F | 6-8 | 230 | 21.3 | <a href='http://www.sports-reference.com/cbb/players/isaiah-roby-1.html'>s-ref</a>",
"mfiondu-kabengele-2019-florida-": "Florida State | SO | F | 6-10 | 250 | 21.7 | <a href='http://www.sports-reference.com/cbb/players/mfiondu-kabengele-1.html'>s-ref</a>",
"null": null
};
var player_growth = {
"zion-williamson-2019-duke": "/images/nba_draft/2019/players/zion-williamson-2019-duke_growth-d21bf0b1.png",
"rj-barrett-2019-duke": "/images/nba_draft/2019/players/rj-barrett-2019-duke_growth-996f70e3.png",
"bol-bol-2019-oregon": "/images/nba_draft/2019/players/bol-bol-2019-oregon_growth-afa0cf4b.png",
"jaxson-hayes-2019-texas": "/images/nba_draft/2019/players/jaxson-hayes-2019-texas_growth-61adc02f.png",
"tacko-fall-2019-ucf": "/images/nba_draft/2019/players/tacko-fall-2019-ucf_growth-92e65884.png",
"charles-bassey-2019-western-": "/images/nba_draft/2019/players/charles-bassey-2019-western-_growth-4d653f4a.png",
"jontay-porter-2018-missouri": "/images/nba_draft/2019/players/jontay-porter-2018-missouri_growth-61a9b863.png",
"ja-morant-2019-murray-s": "/images/nba_draft/2019/players/ja-morant-2019-murray-s_growth-5f316d10.png",
"moses-brown-2019-ucla": "/images/nba_draft/2019/players/moses-brown-2019-ucla_growth-ca5955db.png",
"nicolas-claxton-2019-georgia": "/images/nba_draft/2019/players/nicolas-claxton-2019-georgia_growth-446e4ac5.png",
"daniel-gafford-2019-arkansas": "/images/nba_draft/2019/players/daniel-gafford-2019-arkansas_growth-27d9381f.png",
"nassir-little-2019-unc": "/images/nba_draft/2019/players/nassir-little-2019-unc_growth-8ac2604c.png",
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"romeo-langford-2019-indiana": "/images/nba_draft/2019/players/romeo-langford-2019-indiana_growth-e95028e1.png",
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<p>Anyone who has analyzed historical NBA draft picks should know that translating college success to the NBA is never a sure thing. No matter how good the scout, GM, or draft model, there is still a high level of uncertainty involved in predicting NBA success.</p>
<p>My goal is to highlight this uncertainty. By putting less emphasis on a single number, and more emphasis on the range of outcomes, our evaluation of players can be more representative of the roll of the dice that NBA teams actually face.</p>
<p><em>To learn more - see <a href="/2018/06/10/nba-draft-2018.html">last years draft model blog post</a>. If you just want to see the results then skip ahead to <a href="#rankings">2019 rankings</a>!</em></p>
<hr />
<ul>
<li><a href="#details">Modeling Details</a>
<ul>
<li><a href="#data">Data</a></li>
<li><a href="#quant">Quant Model</a></li>
<li><a href="#apex">APEX Model</a></li>
<li><a href="#star">Star Model</a></li>
<li><a href="#comps">Comps</a></li>
</ul>
</li>
<li><a href="#rankings">2019 Rankings</a>
<ul>
<li><a href="#top60">Top 60</a></li>
<li><a href="#guards">Top Guards</a></li>
<li><a href="#bigs">Top Bigs</a></li>
<li><a href="#all_star">All Star Potential</a></li>
</ul>
</li>
<li><a href="#players">Player Profiles</a></li>
<li><a href="#models">Draft Model Comparison</a></li>
<li><a href="#glossary">Glossary</a></li>
</ul>
<hr />
<h2 id="a-namedetailsmodeling-detailsa"><a name="details">Modeling Details</a></h2>
<h3 id="a-namedatadataa"><a name="data">Data</a></h3>
<p>The biggest improvement to this years draft model is that it utilizes innovative statistics that can't be found anywhere else including: <a href="/2019/04/27/ncaa-rapm.html">Bayesian Adjusted RAPM</a>, <a href="/2019/05/26/estimated-advanced-stats.html">"Actual" Advanced Stats</a>, and <a href="/2019/06/01/rapm-stats.html">Player Impact Stats</a>. These stats isolate the true impact of a player controlling for efficiency (minutes), level of competition (opponent), and situation (team). Other inputs also include scouting (high school ranking) and player characteristics (age, height, weight, combine).</p>
<h3 id="a-namequantquant-modela"><a name="quant">Quant Model</a></h3>
<p><strong>Quant</strong> is a gradient boosting quantile regression model which predicts a players NBA peak single season win shares. By using a <a href="https://en.wikipedia.org/wiki/Quantile_regression">quantile regression model</a>, it allows you to evaluate predictions across quantiles, highlighting differences in risk and upside. By looking at the 50th, 75th, and 90th percentile outcomes for a player we can see which players have a lower floor (q50) versus higher upside (q90).</p>
<h3 id="a-nameapexapex-modela"><a name="apex">APEX Model</a></h3>
<p>While I recommend focusing on the full spectrum of Quant outcomes, I realize there are times when a single number is unavoidable (i.e. draft board rank). Therefore, <strong>APEX</strong> is a single number interpretation of Quant. Given that star players are so important in the NBA, APEX is calculated by averaging the higher upside outcomes (q75 and q90). In cases where a player has multiple season's worth of pre-NBA data, the players overall APEX value is a minute weighted average of all APEX values.</p>
<h3 id="a-namestarstar-modela"><a name="star">Star Model</a></h3>
<p><strong>Star</strong> is a classification model which predicts the probability of being an All Star (star), Starter (start), Role Player (role), or Bust (bust).<sup id="fnref:3"><a href="#fn:3" class="footnote">1</a></sup> The advantage of the Star model is that the results are intuitive, however keep in mind that being a Starter or Role Player in the NBA is sometimes about situation and does not imply success or efficiency (which is what is captured in the Quant model).</p>
<h3 id="a-namecompscompsa"><a name="comps">Comps</a></h3>
<p>To give insight into playing style and NBA combine comparables, I have a <a href="https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm">K-nearest neighbor</a> model which shows historical players that are most similar.</p>
<hr />
<h2 id="a-namerankings2019-rankingsa"><a name="rankings">2019 Rankings</a></h2>
<h3 id="a-nametop60top-60a"><a name="top60">Top 60</a></h3>
<p><a href="/images/nba_draft/2019/top_2019-6e33a5b3.png"><img alt="Top" src="/images/nba_draft/2019/top_2019-6e33a5b3.png" /></a></p>
<hr />
<h3 id="a-nameguardsguardsa"><a name="guards">Guards</a></h3>
<p>Below are the top Guards - <a href="/images/nba_draft/2019/top_2019_guards_stats-2530b570.png">a statistical profile view can be found here</a>.</p>
<p><a href="/images/nba_draft/2019/top_2019_guards-38aafec5.png"><img alt="Guards" src="/images/nba_draft/2019/top_2019_guards-38aafec5.png" /></a></p>
<h3 id="a-namebigsbigsa"><a name="bigs">Bigs</a></h3>
<p>Below are the top Bigs - <a href="/images/nba_draft/2019/top_2019_bigs_stats-74c61322.png">a statistical profile view can be found here</a>.</p>
<p><a href="/images/nba_draft/2019/top_2019_bigs-0dce84ae.png"><img alt="Bigs" src="/images/nba_draft/2019/top_2019_bigs-0dce84ae.png" /></a></p>
<hr />
<h3 id="a-nameallstarstar-modela"><a name="all_star">Star Model</a></h3>
<p><a href="/images/nba_draft/2019/star_2019-42e36d0f.png"><img alt="All Star Potential" src="/images/nba_draft/2019/star_2019-42e36d0f.png" /></a></p>
<hr />
<h2 id="a-nameplayersplayer-profilesa"><a name="players">Player Profiles</a></h2>
<p>Select a player to see a players draft profile including:</p>
<ul>
<li><strong>Statistical Profile</strong> - visualize the strengths, weaknesses, and growth trajectory of individual players over their college careers</li>
<li><strong>Playing Style Comps</strong> - find the most similar player seasons compared to the potential draftees most recent season, which can keep you honest on a players expected outcome</li>
</ul>
<hr />
<center><select id="player_name" onchange="document.getElementById('player_header').innerHTML = player_header[this.value]; document.getElementById('player_info').innerHTML = player_info[this.value]; document.getElementById('player_growth').src = player_growth[this.value]; document.getElementById('player_growth_a').href = player_growth[this.value]; document.getElementById('player_stats').src = player_stats[this.value]; document.getElementById('player_stats_a').href = player_stats[this.value]; document.getElementById('player_comps').src = player_comps[this.value]; document.getElementById('player_comps_a').href = player_comps[this.value]">
<option value="zion-williamson-2019-duke">1. Zion Williamson - Duke</option>
<option value="rj-barrett-2019-duke">2. R.J. Barrett - Duke</option>
<option value="bol-bol-2019-oregon">3. Bol Bol - Oregon</option>
<option value="jaxson-hayes-2019-texas">4. Jaxson Hayes - Texas</option>
<option value="tacko-fall-2019-ucf">5. Tacko Fall - UCF</option>
<option value="charles-bassey-2019-western-">6. Charles Bassey - Western Kentucky</option>
<option value="jontay-porter-2018-missouri">7. Jontay Porter - Missouri</option>
<option value="ja-morant-2019-murray-s">8. Ja Morant - Murray State</option>
<option value="moses-brown-2019-ucla">9. Moses Brown - UCLA</option>
<option value="nicolas-claxton-2019-georgia">10. Nicolas Claxton - Georgia</option>
<option value="daniel-gafford-2019-arkansas">11. Daniel Gafford - Arkansas</option>
<option value="nassir-little-2019-unc">12. Nassir Little - UNC</option>
<option value="de'andre-hunter-2019-virginia">13. De'Andre Hunter - Virginia</option>
<option value="romeo-langford-2019-indiana">14. Romeo Langford - Indiana</option>
<option value="dean-wade-2019-kansas-s">15. Dean Wade - Kansas State</option>
<option value="tyler-herro-2019-kentucky">16. Tyler Herro - Kentucky</option>
<option value="grant-williams-2019-tennesse">17. Grant Williams - Tennessee</option>
<option value="pj-washington-2019-kentucky">18. PJ Washington - Kentucky</option>
<option value="jarrett-culver-2019-texas-te">19. Jarrett Culver - Texas Tech</option>
<option value="dedric-lawson-2019-kansas">20. Dedric Lawson - Kansas</option>
<option value="talen-horton-tucker-2019-iowa-sta">21. Talen Horton-Tucker - Iowa State</option>
<option value="nickeil-alexander-walker-2019-virginia">22. Nickeil Alexander-Walker - Virginia Tech</option>
<option value="bruno-fernando-2019-maryland">23. Bruno Fernando - Maryland</option>
<option value="chuma-okeke-2019-auburn">24. Chuma Okeke - Auburn</option>
<option value="brandon-clarke-2019-gonzaga">25. Brandon Clarke - Gonzaga</option>
<option value="admiral-schofield-2019-tennesse">26. Admiral Schofield - Tennessee</option>
<option value="keldon-johnson-2019-kentucky">27. Keldon Johnson - Kentucky</option>
<option value="rui-hachimura-2019-gonzaga">28. Rui Hachimura - Gonzaga</option>
<option value="cam-reddish-2019-duke">29. Cam Reddish - Duke</option>
<option value="donta-hall-2019-alabama">30. Donta Hall - Alabama</option>
<option value="carsen-edwards-2019-purdue">31. Carsen Edwards - Purdue</option>
<option value="coby-white-2019-unc">32. Coby White - UNC</option>
<option value="dylan-windler-2019-belmont">33. Dylan Windler - Belmont</option>
<option value="zach-norvell-jr-2019-gonzaga">34. Zach Norvell Jr. - Gonzaga</option>
<option value="naz-reid-2019-lsu">35. Naz Reid - LSU</option>
<option value="jordan-poole-2019-michigan">36. Jordan Poole - Michigan</option>
<option value="jaylen-nowell-2019-washingt">37. Jaylen Nowell - Washington</option>
<option value="terance-mann-2019-florida-">38. Terance Mann - Florida State</option>
<option value="tyler-cook-2019-iowa">39. Tyler Cook - Iowa</option>
<option value="quinndary-weatherspoon-2019-mississi">40. Quinndary Weatherspoon - Mississippi State</option>
<option value="ignas-brazdeikis-2019-michigan">41. Ignas Brazdeikis - Michigan</option>
<option value="kevin-porter-jr-2019-usc">42. Kevin Porter Jr - USC</option>
<option value="simisola-shittu-2019-vanderbi">43. Simisola Shittu - Vanderbilt</option>
<option value="john-konchar-2018-purdue-f">44. John Konchar - Purdue-Fort Wayne</option>
<option value="cameron-johnson-2019-unc">45. Cameron Johnson - UNC</option>
<option value="eric-paschall-2019-villanov">46. Eric Paschall - Villanova</option>
<option value="cameron-oliver-2017-nevada">47. Cameron Oliver - Nevada</option>
<option value="kenny-wooten-2019-oregon">48. Kenny Wooten - Oregon</option>
<option value="eric-mika-2017-byu">49. Eric Mika - BYU</option>
<option value="josh-reaves-2019-penn-sta">50. Josh Reaves - Penn State</option>
<option value="jalen-mcdaniels-2019-san-dieg">51. Jalen McDaniels - San Diego State</option>
<option value="robert-franks-2019-washingt">52. Robert Franks - Washington State</option>
<option value="kerwin-roach-jr-2019-texas">53. Kerwin Roach Jr. - Texas</option>
<option value="shamorie-ponds-2019-st-john'">54. Shamorie Ponds - St. John's (NY)</option>
<option value="louis-king-2019-oregon">55. Louis King - Oregon</option>
<option value="darius-garland-2019-vanderbi">56. Darius Garland - Vanderbilt</option>
<option value="ty-jerome-2019-virginia">57. Ty Jerome - Virginia</option>
<option value="luguentz-dort-2019-arizona-">58. Luguentz Dort - Arizona State</option>
<option value="isaiah-roby-2019-nebraska">59. Isaiah Roby - Nebraska</option>
<option value="mfiondu-kabengele-2019-florida-">60. Mfiondu Kabengele - Florida State</option>
</select></center>
<h3 id="a-idplayerheaderzion-williamsona"><strong><a id="player_header">Zion Williamson</a></strong></h3>
<text id="player_info">Duke | FR | F | 6-7 | 285 | 18.8 | rsci: 4 | <a href="http://www.sports-reference.com/cbb/players/zion-williamson-1.html">s-ref</a></text>
<p><a href="/images/nba_draft/2019/players/zion-williamson-2019-duke_growth.png" id="player_growth_a"><img src="/images/nba_draft/2019/players/zion-williamson-2019-duke_growth.png" id="player_growth" /></a></p>
<h4 id="statistical-profile">Statistical Profile</h4>
<p><a href="/images/nba_draft/2019/players/zion-williamson-2019-duke_stats.png" id="player_stats_a"><img src="/images/nba_draft/2019/players/zion-williamson-2019-duke_stats.png" id="player_stats" /></a></p>
<h4 id="playing-style-comps">Playing Style Comps</h4>
<p><a href="/images/nba_draft/2019/players/zion-williamson-2019-duke_comps.png" id="player_comps_a"><img src="/images/nba_draft/2019/players/zion-williamson-2019-duke_comps.png" id="player_comps" /></a></p>
<hr />
<h3 id="a-namemodelsdraft-model-comparisona"><a name="models">Draft Model Comparison</a></h3>
<p><a href="/images/nba_draft/2019/models_2019-364bf676.png"><img alt="Models" src="/images/nba_draft/2019/models_2019-364bf676.png" /></a></p>
<hr />
<h2 id="a-nameglossaryglossarya"><a name="glossary">Glossary</a></h2>
<ul>
<li>q50 = Predicted 50th percentile outcome</li>
<li>q75 = Predicted 75th percentile outcome</li>
<li>q90 = Predicted 90th percentile outcome</li>
<li>apex = Average of q75 and q90</li>
<li>rsci = High School Rank</li>
<li>star = NBA All Star probability</li>
<li>start = NBA Starter probability (starter for >60 NBA games in a season)</li>
<li>role = NBA Role Player probability (played in >60 NBA games in a season)</li>
<li>bust = NBA Bust probability</li>
<li>ht = Height</li>
<li>wt = Weight</li>
<li>gs = Games Started</li>
<li>gp = Games Played</li>
<li>mpg = Minutes Per Game</li>
<li>ts = True Shooting Percentage</li>
<li>efg = Effective Field Goal Percentage</li>
<li>3par = 3 Point Attempt Rate</li>
<li>ftr = Free Throw Rate</li>
<li>usg = Usage Rate</li>
<li>pk = NBA Draft Pick</li>
<li>sim = Player Similarity</li>
</ul>
<div class="footnotes">
<ol>
<li id="fn:3">
<p>The definition of All Star is self-explanatory, whereas I arbitrarily defined Starter as having started 60 games in a NBA season, Role Player as having played 60 games in a NBA season, and Bust as everyone else. <a href="#fnref:3" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>
What is the true impact of a player?http://tothemean.com/2019/06/01/rapm-stats.html2019-06-01T00:00:00Z2019-06-02T22:55:28-07:00Jesse Fischer<script>
var table_text = {
"aSTL": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aSTL</th><th>STL%</th></tr></thead><tbody><tr><td>Russ Smith</td><td>Louisville</td><td>2012</td><td>2.277</td><td>6</td></tr><tr><td>Kyle Anderson</td><td>UCLA</td><td>2014</td><td>1.74</td><td>3.1</td></tr><tr><td>Shabazz Napier</td><td>UConn</td><td>2011</td><td>1.695</td><td>4.3</td></tr><tr><td>Iman Shumpert</td><td>Georgia Tech</td><td>2011</td><td>1.692</td><td>5.1</td></tr><tr><td>Jevon Carter</td><td>West Virginia</td><td>2018</td><td>1.662</td><td>5</td></tr><tr><td>Jordan Adams</td><td>UCLA</td><td>2014</td><td>1.66</td><td>5.1</td></tr><tr><td>Arsalan Kazemi</td><td>Rice</td><td>2012</td><td>1.571</td><td>4.3</td></tr><tr><td>Jevon Carter</td><td>West Virginia</td><td>2017</td><td>1.568</td><td>4.6</td></tr><tr><td>Jevon Carter</td><td>West Virginia</td><td>2015</td><td>1.565</td><td>4.8</td></tr><tr><td>Kim English</td><td>Missouri</td><td>2010</td><td>1.56</td><td>3.2</td></tr><tr><td>Dion Waiters</td><td>Syracuse</td><td>2012</td><td>1.536</td><td>4.9</td></tr><tr><td>Russ Smith</td><td>Louisville</td><td>2013</td><td>1.477</td><td>4.2</td></tr><tr><td>Marcus Smart</td><td>Oklahoma State</td><td>2014</td><td>1.454</td><td>5.2</td></tr><tr><td>Jared Cunningham</td><td>Oregon State</td><td>2011</td><td>1.423</td><td>5.5</td></tr><tr><td>Sterling Brown</td><td>SMU</td><td>2014</td><td>1.372</td><td>2.2</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Gani Lawal</td><td>Georgia Tech</td><td>2010</td><td>-0.743</td><td>1</td></tr><tr><td>Dwayne Collins</td><td>Miami (FL)</td><td>2010</td><td>-0.787</td><td>1.5</td></tr><tr><td>Caleb Swanigan</td><td>Purdue</td><td>2017</td><td>-0.797</td><td>0.8</td></tr><tr><td>Thomas Bryant</td><td>Indiana</td><td>2016</td><td>-0.818</td><td>1.3</td></tr><tr><td>Kostas Antetokounmpo</td><td>Dayton</td><td>2018</td><td>-0.822</td><td>1</td></tr><tr><td>Myles Turner</td><td>Texas</td><td>2015</td><td>-0.863</td><td>0.9</td></tr><tr><td>Luke Harangody</td><td>Notre Dame</td><td>2010</td><td>-0.871</td><td>1</td></tr><tr><td>Marcus Thornton</td><td>William & Mary</td><td>2012</td><td>-0.889</td><td>0.8</td></tr><tr><td>Doug McDermott</td><td>Creighton</td><td>2014</td><td>-0.898</td><td>0.4</td></tr><tr><td>Mike Muscala</td><td>Bucknell</td><td>2010</td><td>-0.959</td><td>0.8</td></tr><tr><td>Caleb Swanigan</td><td>Purdue</td><td>2016</td><td>-0.97</td><td>0.8</td></tr><tr><td>Miles Bridges</td><td>Michigan State</td><td>2017</td><td>-1.022</td><td>1.3</td></tr><tr><td>George King</td><td>Colorado</td><td>2018</td><td>-1.04</td><td>1.1</td></tr><tr><td>A.J. Hammons</td><td>Purdue</td><td>2013</td><td>-1.11</td><td>0.9</td></tr><tr><td>Joel Bolomboy</td><td>Weber State</td><td>2013</td><td>-1.126</td><td>1.1</td></tr></tbody>',
"aSTLA": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aSTLA</th><th>TOV%</th></tr></thead><tbody><tr><td>Tyler Zeller</td><td>UNC</td><td>2010</td><td>1.052</td><td>13.6</td></tr><tr><td>Sterling Brown</td><td>SMU</td><td>2014</td><td>1.027</td><td>22.7</td></tr><tr><td>Shake Milton</td><td>SMU</td><td>2016</td><td>0.981</td><td>15.1</td></tr><tr><td>Justin Jackson</td><td>Maryland</td><td>2018</td><td>0.882</td><td>22</td></tr><tr><td>Fab Melo</td><td>Syracuse</td><td>2012</td><td>0.829</td><td>17.7</td></tr><tr><td>Josh Richardson</td><td>Tennessee</td><td>2012</td><td>0.823</td><td>22.1</td></tr><tr><td>Perry Jones</td><td>Baylor</td><td>2011</td><td>0.817</td><td>16.3</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2012</td><td>0.674</td><td>19.4</td></tr><tr><td>George King</td><td>Colorado</td><td>2018</td><td>0.668</td><td>15.2</td></tr><tr><td>Dexter Pittman</td><td>Texas</td><td>2010</td><td>0.667</td><td>18</td></tr><tr><td>Dwayne Collins</td><td>Miami (FL)</td><td>2010</td><td>0.656</td><td>20.1</td></tr><tr><td>Denzel Valentine</td><td>Michigan State</td><td>2013</td><td>0.63</td><td>29.2</td></tr><tr><td>Robert Williams</td><td>Texas A&M</td><td>2017</td><td>0.626</td><td>14.5</td></tr><tr><td>Trey Thompkins</td><td>Georgia</td><td>2010</td><td>0.616</td><td>15.5</td></tr><tr><td>Branden Dawson</td><td>Michigan State</td><td>2013</td><td>0.615</td><td>19.7</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Sam Dekker</td><td>Wisconsin</td><td>2015</td><td>-0.871</td><td>7.3</td></tr><tr><td>Cory Joseph</td><td>Texas</td><td>2011</td><td>-0.876</td><td>13.2</td></tr><tr><td>Norris Cole</td><td>Cleveland State</td><td>2010</td><td>-0.876</td><td>15.4</td></tr><tr><td>Erick Green</td><td>Virginia Tech</td><td>2013</td><td>-0.91</td><td>9.4</td></tr><tr><td>Elliot Williams</td><td>Memphis</td><td>2010</td><td>-0.927</td><td>16.6</td></tr><tr><td>Devon Hall</td><td>Virginia</td><td>2018</td><td>-0.942</td><td>9.6</td></tr><tr><td>Mikal Bridges</td><td>Villanova</td><td>2018</td><td>-0.991</td><td>9.2</td></tr><tr><td>Robbie Hummel</td><td>Purdue</td><td>2012</td><td>-0.998</td><td>5.7</td></tr><tr><td>Frank Jackson</td><td>Duke</td><td>2017</td><td>-1.001</td><td>13.1</td></tr><tr><td>Kentavious Caldwell-Pope</td><td>Georgia</td><td>2012</td><td>-1.018</td><td>7.9</td></tr><tr><td>Ryan Kelly</td><td>Duke</td><td>2013</td><td>-1.046</td><td>8.4</td></tr><tr><td>Andrew Harrison</td><td>Kentucky</td><td>2015</td><td>-1.047</td><td>16</td></tr><tr><td>Deshaun Thomas</td><td>Ohio State</td><td>2012</td><td>-1.056</td><td>8.4</td></tr><tr><td>Kawhi Leonard</td><td>San Diego State</td><td>2011</td><td>-1.073</td><td>12.4</td></tr><tr><td>Monte Morris</td><td>Iowa State</td><td>2017</td><td>-1.101</td><td>7.6</td></tr></tbody>',
"aTOV": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aTOV</th><th>TOV%</th></tr></thead><tbody><tr><td>Jared Cunningham</td><td>Oregon State</td><td>2010</td><td>2.061</td><td>31.4</td></tr><tr><td>Justin Jackson</td><td>Maryland</td><td>2018</td><td>1.624</td><td>22</td></tr><tr><td>Ater Majok</td><td>UConn</td><td>2010</td><td>1.558</td><td>23.7</td></tr><tr><td>Sterling Brown</td><td>SMU</td><td>2014</td><td>1.469</td><td>22.7</td></tr><tr><td>Ryan Reid</td><td>Florida State</td><td>2010</td><td>1.344</td><td>20.2</td></tr><tr><td>Chimezie Metu</td><td>USC</td><td>2016</td><td>1.342</td><td>14.9</td></tr><tr><td>Joel Embiid</td><td>Kansas</td><td>2014</td><td>1.218</td><td>22</td></tr><tr><td>Meyers Leonard</td><td>Illinois</td><td>2011</td><td>1.181</td><td>28.7</td></tr><tr><td>Pascal Siakam</td><td>New Mexico State</td><td>2015</td><td>1.156</td><td>15.4</td></tr><tr><td>Gorgui Dieng</td><td>Louisville</td><td>2012</td><td>1.152</td><td>19.8</td></tr><tr><td>Kostas Antetokounmpo</td><td>Dayton</td><td>2018</td><td>1.141</td><td>23.2</td></tr><tr><td>Tyler Zeller</td><td>UNC</td><td>2010</td><td>1.135</td><td>13.6</td></tr><tr><td>Peyton Siva</td><td>Louisville</td><td>2010</td><td>1.108</td><td>30.3</td></tr><tr><td>Shake Milton</td><td>SMU</td><td>2016</td><td>1.1</td><td>15.1</td></tr><tr><td>Caleb Swanigan</td><td>Purdue</td><td>2016</td><td>1.073</td><td>21.8</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Erick Green</td><td>Virginia Tech</td><td>2011</td><td>-1.983</td><td>9.4</td></tr><tr><td>Nate Wolters</td><td>South Dakota State</td><td>2011</td><td>-1.995</td><td>11.5</td></tr><tr><td>JaJuan Johnson</td><td>Purdue</td><td>2011</td><td>-2.034</td><td>8.4</td></tr><tr><td>Shelvin Mack</td><td>Butler</td><td>2010</td><td>-2.042</td><td>14.1</td></tr><tr><td>Ryan Kelly</td><td>Duke</td><td>2013</td><td>-2.158</td><td>8.4</td></tr><tr><td>Erick Green</td><td>Virginia Tech</td><td>2013</td><td>-2.175</td><td>9.4</td></tr><tr><td>Jalen Brunson</td><td>Villanova</td><td>2018</td><td>-2.209</td><td>10.8</td></tr><tr><td>Jimmy Butler</td><td>Marquette</td><td>2010</td><td>-2.222</td><td>9.4</td></tr><tr><td>Jawun Evans</td><td>Oklahoma State</td><td>2017</td><td>-2.252</td><td>13.7</td></tr><tr><td>Monte Morris</td><td>Iowa State</td><td>2017</td><td>-2.294</td><td>7.6</td></tr><tr><td>Cory Joseph</td><td>Texas</td><td>2011</td><td>-2.368</td><td>13.2</td></tr><tr><td>Sam Dekker</td><td>Wisconsin</td><td>2015</td><td>-2.395</td><td>7.3</td></tr><tr><td>Robbie Hummel</td><td>Purdue</td><td>2012</td><td>-2.396</td><td>5.7</td></tr><tr><td>Luke Harangody</td><td>Notre Dame</td><td>2010</td><td>-2.417</td><td>8.4</td></tr><tr><td>Mikal Bridges</td><td>Villanova</td><td>2018</td><td>-2.693</td><td>9.2</td></tr></tbody>',
"aTOVA": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aTOVA</th><th>STL%</th></tr></thead><tbody><tr><td>Jevon Carter</td><td>West Virginia</td><td>2018</td><td>2.549</td><td>5</td></tr><tr><td>Jevon Carter</td><td>West Virginia</td><td>2017</td><td>2.401</td><td>4.6</td></tr><tr><td>Russ Smith</td><td>Louisville</td><td>2012</td><td>2.192</td><td>6</td></tr><tr><td>Kim English</td><td>Missouri</td><td>2010</td><td>1.99</td><td>3.2</td></tr><tr><td>Russ Smith</td><td>Louisville</td><td>2013</td><td>1.987</td><td>4.2</td></tr><tr><td>Victor Oladipo</td><td>Indiana</td><td>2013</td><td>1.838</td><td>4.7</td></tr><tr><td>Darrun Hilliard</td><td>Villanova</td><td>2015</td><td>1.799</td><td>4</td></tr><tr><td>Dion Waiters</td><td>Syracuse</td><td>2012</td><td>1.76</td><td>4.9</td></tr><tr><td>Sindarius Thornwell</td><td>South Carolina</td><td>2017</td><td>1.76</td><td>3.7</td></tr><tr><td>Jerami Grant</td><td>Syracuse</td><td>2014</td><td>1.727</td><td>1.8</td></tr><tr><td>Shabazz Napier</td><td>UConn</td><td>2011</td><td>1.715</td><td>4.3</td></tr><tr><td>Isaiah Whitehead</td><td>Seton Hall</td><td>2016</td><td>1.677</td><td>2.1</td></tr><tr><td>Sterling Brown</td><td>SMU</td><td>2014</td><td>1.669</td><td>2.2</td></tr><tr><td>Fab Melo</td><td>Syracuse</td><td>2012</td><td>1.665</td><td>1.2</td></tr><tr><td>Kyle Anderson</td><td>UCLA</td><td>2014</td><td>1.665</td><td>3.1</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Jarnell Stokes</td><td>Tennessee</td><td>2013</td><td>-1.313</td><td>1.6</td></tr><tr><td>TJ Leaf</td><td>UCLA</td><td>2017</td><td>-1.315</td><td>1.1</td></tr><tr><td>Dwayne Collins</td><td>Miami (FL)</td><td>2010</td><td>-1.315</td><td>1.5</td></tr><tr><td>Thomas Welsh</td><td>UCLA</td><td>2018</td><td>-1.325</td><td>1.1</td></tr><tr><td>Norman Powell</td><td>UCLA</td><td>2013</td><td>-1.38</td><td>1.9</td></tr><tr><td>Festus Ezeli</td><td>Vanderbilt</td><td>2012</td><td>-1.417</td><td>1.2</td></tr><tr><td>Archie Goodwin</td><td>Kentucky</td><td>2013</td><td>-1.428</td><td>2.1</td></tr><tr><td>Luke Harangody</td><td>Notre Dame</td><td>2010</td><td>-1.456</td><td>1</td></tr><tr><td>Alex Oriakhi</td><td>UConn</td><td>2012</td><td>-1.458</td><td>0.4</td></tr><tr><td>Mike Muscala</td><td>Bucknell</td><td>2010</td><td>-1.518</td><td>0.8</td></tr><tr><td>Alize Johnson</td><td>Missouri State</td><td>2018</td><td>-1.546</td><td>0.9</td></tr><tr><td>George King</td><td>Colorado</td><td>2018</td><td>-1.656</td><td>1.1</td></tr><tr><td>Caleb Swanigan</td><td>Purdue</td><td>2016</td><td>-1.775</td><td>0.8</td></tr><tr><td>Kyle OQuinn</td><td>Norfolk State</td><td>2011</td><td>-1.834</td><td>1</td></tr><tr><td>Marcus Thornton</td><td>William & Mary</td><td>2012</td><td>-2.043</td><td>0.8</td></tr></tbody>',
"aORB": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aORB</th><th>ORB%</th></tr></thead><tbody><tr><td>Kenneth Faried</td><td>Morehead State</td><td>2011</td><td>5.072</td><td>20.6</td></tr><tr><td>Derrick Favors</td><td>Georgia Tech</td><td>2010</td><td>4.556</td><td>13</td></tr><tr><td>Steven Adams</td><td>Pitt</td><td>2013</td><td>4.141</td><td>15.6</td></tr><tr><td>K.J. McDaniels</td><td>Clemson</td><td>2012</td><td>3.788</td><td>13.9</td></tr><tr><td>Kevon Looney</td><td>UCLA</td><td>2015</td><td>3.77</td><td>12.1</td></tr><tr><td>Jakob Poeltl</td><td>Utah</td><td>2015</td><td>3.759</td><td>16.6</td></tr><tr><td>Deyonta Davis</td><td>Michigan State</td><td>2016</td><td>3.754</td><td>13.6</td></tr><tr><td>Tyler Zeller</td><td>UNC</td><td>2012</td><td>3.706</td><td>14.6</td></tr><tr><td>John Henson</td><td>UNC</td><td>2012</td><td>3.671</td><td>9.5</td></tr><tr><td>Justin Jackson</td><td>Maryland</td><td>2018</td><td>3.657</td><td>11.7</td></tr><tr><td>Mitch McGary</td><td>Michigan</td><td>2013</td><td>3.621</td><td>15.7</td></tr><tr><td>T.J. Warren</td><td>NC State</td><td>2014</td><td>3.61</td><td>11.1</td></tr><tr><td>Branden Dawson</td><td>Michigan State</td><td>2012</td><td>3.605</td><td>13.8</td></tr><tr><td>Quincy Pondexter</td><td>Washington</td><td>2010</td><td>3.566</td><td>10.7</td></tr><tr><td>Brice Johnson</td><td>UNC</td><td>2016</td><td>3.529</td><td>11.9</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Andrew Goudelock</td><td>College of Charleston</td><td>2010</td><td>-1.631</td><td>2.4</td></tr><tr><td>Olivier Hanlan</td><td>Boston College</td><td>2015</td><td>-1.643</td><td>2.6</td></tr><tr><td>Spencer Dinwiddie</td><td>Colorado</td><td>2012</td><td>-1.646</td><td>3.1</td></tr><tr><td>Marcus Thornton</td><td>William & Mary</td><td>2013</td><td>-1.676</td><td>1.4</td></tr><tr><td>Monte Morris</td><td>Iowa State</td><td>2014</td><td>-1.736</td><td>2.1</td></tr><tr><td>Damian Lillard</td><td>Weber State</td><td>2012</td><td>-1.74</td><td>2</td></tr><tr><td>Tim Hardaway</td><td>Michigan</td><td>2011</td><td>-1.869</td><td>3.2</td></tr><tr><td>Marcus Thornton</td><td>William & Mary</td><td>2015</td><td>-1.888</td><td>1</td></tr><tr><td>Norman Powell</td><td>UCLA</td><td>2013</td><td>-1.983</td><td>0.6</td></tr><tr><td>D.J. Wilson</td><td>Michigan</td><td>2016</td><td>-2.142</td><td>3.4</td></tr><tr><td>Marcus Thornton</td><td>William & Mary</td><td>2012</td><td>-2.201</td><td>1.7</td></tr><tr><td>Isaiah Cousins</td><td>Oklahoma</td><td>2013</td><td>-2.249</td><td>1.4</td></tr><tr><td>Marcus Thornton</td><td>William & Mary</td><td>2014</td><td>-2.407</td><td>0.8</td></tr><tr><td>Kay Felder</td><td>Oakland</td><td>2014</td><td>-2.48</td><td>1.7</td></tr><tr><td>Grayson Allen</td><td>Duke</td><td>2017</td><td>-2.733</td><td>2.8</td></tr></tbody>',
"aDRB": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aDRB</th><th>DRB%</th></tr></thead><tbody><tr><td>Devon Hall</td><td>Virginia</td><td>2017</td><td>3.437</td><td>18.2</td></tr><tr><td>Denzel Valentine</td><td>Michigan State</td><td>2014</td><td>3.401</td><td>18.9</td></tr><tr><td>Malcolm Brogdon</td><td>Virginia</td><td>2012</td><td>3.369</td><td>12.5</td></tr><tr><td>Shelvin Mack</td><td>Butler</td><td>2010</td><td>3.332</td><td>13.4</td></tr><tr><td>Jared Sullinger</td><td>Ohio State</td><td>2011</td><td>3.248</td><td>27.4</td></tr><tr><td>Kentavious Caldwell-Pope</td><td>Georgia</td><td>2013</td><td>3.084</td><td>20.7</td></tr><tr><td>Moritz Wagner</td><td>Michigan</td><td>2017</td><td>3.07</td><td>16.3</td></tr><tr><td>Alize Johnson</td><td>Missouri State</td><td>2018</td><td>3.066</td><td>31</td></tr><tr><td>Draymond Green</td><td>Michigan State</td><td>2012</td><td>3.032</td><td>29.8</td></tr><tr><td>Dakari Johnson</td><td>Kentucky</td><td>2014</td><td>2.996</td><td>15.6</td></tr><tr><td>Arnett Moultrie</td><td>Mississippi State</td><td>2012</td><td>2.975</td><td>22.1</td></tr><tr><td>Joe Harris</td><td>Virginia</td><td>2014</td><td>2.969</td><td>10.2</td></tr><tr><td>Jared Sullinger</td><td>Ohio State</td><td>2012</td><td>2.896</td><td>23.9</td></tr><tr><td>Landry Shamet</td><td>Wichita State</td><td>2017</td><td>2.892</td><td>9.1</td></tr><tr><td>George King</td><td>Colorado</td><td>2018</td><td>2.841</td><td>23.5</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Charles Jenkins</td><td>Hofstra</td><td>2011</td><td>-1.219</td><td>9</td></tr><tr><td>Mason Plumlee</td><td>Duke</td><td>2011</td><td>-1.268</td><td>22.8</td></tr><tr><td>Michael Carter-Williams</td><td>Syracuse</td><td>2012</td><td>-1.314</td><td>12.1</td></tr><tr><td>Kris Joseph</td><td>Syracuse</td><td>2012</td><td>-1.341</td><td>10.9</td></tr><tr><td>Jawun Evans</td><td>Oklahoma State</td><td>2017</td><td>-1.391</td><td>11</td></tr><tr><td>Jalen Brunson</td><td>Villanova</td><td>2016</td><td>-1.404</td><td>6.2</td></tr><tr><td>Tyler Lydon</td><td>Syracuse</td><td>2016</td><td>-1.405</td><td>16.6</td></tr><tr><td>Dion Waiters</td><td>Syracuse</td><td>2011</td><td>-1.471</td><td>8.1</td></tr><tr><td>Luke Kennard</td><td>Duke</td><td>2016</td><td>-1.579</td><td>10.8</td></tr><tr><td>Maurice Harkless</td><td>St. Johns (NY)</td><td>2012</td><td>-1.66</td><td>18.3</td></tr><tr><td>Chimezie Metu</td><td>USC</td><td>2016</td><td>-1.707</td><td>11.2</td></tr><tr><td>C.J. McCollum</td><td>Lehigh</td><td>2013</td><td>-1.716</td><td>14.5</td></tr><tr><td>K.J. McDaniels</td><td>Clemson</td><td>2014</td><td>-1.849</td><td>15.9</td></tr><tr><td>Cheick Diallo</td><td>Kansas</td><td>2016</td><td>-2.198</td><td>25.9</td></tr><tr><td>Andrew Goudelock</td><td>College of Charleston</td><td>2010</td><td>-2.291</td><td>11</td></tr></tbody>',
"aAST": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aAST</th><th>AST%</th></tr></thead><tbody><tr><td>Denzel Valentine</td><td>Michigan State</td><td>2016</td><td>6.929</td><td>45.3</td></tr><tr><td>Lonzo Ball</td><td>UCLA</td><td>2017</td><td>5.568</td><td>31.7</td></tr><tr><td>Andy Rautins</td><td>Syracuse</td><td>2010</td><td>4.6</td><td>24.1</td></tr><tr><td>Landry Shamet</td><td>Wichita State</td><td>2018</td><td>4.582</td><td>28.9</td></tr><tr><td>Joel Embiid</td><td>Kansas</td><td>2014</td><td>4.531</td><td>11.9</td></tr><tr><td>Draymond Green</td><td>Michigan State</td><td>2010</td><td>4.276</td><td>23</td></tr><tr><td>Caleb Swanigan</td><td>Purdue</td><td>2017</td><td>4.138</td><td>18.4</td></tr><tr><td>Caleb Swanigan</td><td>Purdue</td><td>2016</td><td>4.078</td><td>13.6</td></tr><tr><td>Draymond Green</td><td>Michigan State</td><td>2012</td><td>3.971</td><td>24.6</td></tr><tr><td>Miles Bridges</td><td>Michigan State</td><td>2018</td><td>3.952</td><td>16.9</td></tr><tr><td>Robert Williams</td><td>Texas A&M</td><td>2017</td><td>3.806</td><td>12.1</td></tr><tr><td>Jerian Grant</td><td>Notre Dame</td><td>2014</td><td>3.765</td><td>34.6</td></tr><tr><td>Kyle Anderson</td><td>UCLA</td><td>2014</td><td>3.706</td><td>33</td></tr><tr><td>Denzel Valentine</td><td>Michigan State</td><td>2013</td><td>3.7</td><td>21.7</td></tr><tr><td>Cory Jefferson</td><td>Baylor</td><td>2014</td><td>3.605</td><td>7.5</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2012</td><td>-2.725</td><td>14.4</td></tr><tr><td>Andre Roberson</td><td>Colorado</td><td>2013</td><td>-2.874</td><td>9.2</td></tr><tr><td>Josh Jackson</td><td>Kansas</td><td>2017</td><td>-2.895</td><td>18.2</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2013</td><td>-2.918</td><td>13.7</td></tr><tr><td>Malcolm Brogdon</td><td>Virginia</td><td>2012</td><td>-2.943</td><td>13.4</td></tr><tr><td>Erick Green</td><td>Virginia Tech</td><td>2013</td><td>-2.953</td><td>26.4</td></tr><tr><td>Rodney Hood</td><td>Mississippi State</td><td>2012</td><td>-2.99</td><td>11.9</td></tr><tr><td>Josh Richardson</td><td>Tennessee</td><td>2013</td><td>-3.112</td><td>11.3</td></tr><tr><td>Tyler Harvey</td><td>Eastern Washington</td><td>2015</td><td>-3.221</td><td>13.9</td></tr><tr><td>K.J. McDaniels</td><td>Clemson</td><td>2012</td><td>-3.301</td><td>5.1</td></tr><tr><td>Shelvin Mack</td><td>Butler</td><td>2011</td><td>-3.355</td><td>24.4</td></tr><tr><td>Jaron Blossomgame</td><td>Clemson</td><td>2014</td><td>-3.551</td><td>3.7</td></tr><tr><td>Alize Johnson</td><td>Missouri State</td><td>2017</td><td>-3.719</td><td>14.6</td></tr><tr><td>Jordan Clarkson</td><td>Tulsa</td><td>2011</td><td>-3.875</td><td>18.6</td></tr><tr><td>Dwayne Bacon</td><td>Florida State</td><td>2016</td><td>-4.1</td><td>10.5</td></tr></tbody>',
"aASTA": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aASTA</th></tr></thead><tbody><tr><td>R.J. Hunter</td><td>Georgia State</td><td>2015</td><td>3.587</td></tr><tr><td>Taurean Prince</td><td>Baylor</td><td>2015</td><td>3.569</td></tr><tr><td>Colton Iverson</td><td>Minnesota</td><td>2011</td><td>3.46</td></tr><tr><td>Paul George</td><td>Fresno State</td><td>2010</td><td>3.318</td></tr><tr><td>Tyler Lydon</td><td>Syracuse</td><td>2017</td><td>3.278</td></tr><tr><td>Cory Jefferson</td><td>Baylor</td><td>2014</td><td>3.267</td></tr><tr><td>Tyler Ennis</td><td>Syracuse</td><td>2014</td><td>3.261</td></tr><tr><td>Michael Gbinije</td><td>Syracuse</td><td>2014</td><td>3.258</td></tr><tr><td>Michael Gbinije</td><td>Syracuse</td><td>2015</td><td>3.155</td></tr><tr><td>Kris Joseph</td><td>Syracuse</td><td>2012</td><td>2.982</td></tr><tr><td>Armon Johnson</td><td>Nevada</td><td>2010</td><td>2.882</td></tr><tr><td>Semaj Christon</td><td>Xavier</td><td>2014</td><td>2.847</td></tr><tr><td>Taurean Prince</td><td>Baylor</td><td>2016</td><td>2.835</td></tr><tr><td>Josh Richardson</td><td>Tennessee</td><td>2015</td><td>2.801</td></tr><tr><td>Arsalan Kazemi</td><td>Rice</td><td>2010</td><td>2.707</td></tr><tr><td>...</td><td></td><td></td><td></td></tr><tr><td>T.J. Warren</td><td>NC State</td><td>2013</td><td>-3.352</td></tr><tr><td>Landry Shamet</td><td>Wichita State</td><td>2017</td><td>-3.361</td></tr><tr><td>Tyler Ulis</td><td>Kentucky</td><td>2016</td><td>-3.427</td></tr><tr><td>Andrew Harrison</td><td>Kentucky</td><td>2015</td><td>-3.498</td></tr><tr><td>Travis Leslie</td><td>Georgia</td><td>2011</td><td>-3.516</td></tr><tr><td>Markel Brown</td><td>Oklahoma State</td><td>2014</td><td>-3.524</td></tr><tr><td>Colton Iverson</td><td>Colorado State</td><td>2013</td><td>-3.549</td></tr><tr><td>Nick Johnson</td><td>Arizona</td><td>2014</td><td>-3.598</td></tr><tr><td>Jabari Bird</td><td>California</td><td>2016</td><td>-3.642</td></tr><tr><td>Trey Lyles</td><td>Kentucky</td><td>2015</td><td>-3.671</td></tr><tr><td>Mason Plumlee</td><td>Duke</td><td>2013</td><td>-3.674</td></tr><tr><td>John Jenkins</td><td>Vanderbilt</td><td>2011</td><td>-3.757</td></tr><tr><td>Reggie Bullock</td><td>UNC</td><td>2012</td><td>-3.763</td></tr><tr><td>Sam Dekker</td><td>Wisconsin</td><td>2013</td><td>-3.789</td></tr><tr><td>Jordan Mickey</td><td>LSU</td><td>2015</td><td>-4.091</td></tr></tbody>',
"aBLK": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aBLK</th><th>BLK%</th></tr></thead><tbody><tr><td>Hassan Whiteside</td><td>Marshall</td><td>2010</td><td>3.782</td><td>18.4</td></tr><tr><td>Myles Turner</td><td>Texas</td><td>2015</td><td>3.195</td><td>12.4</td></tr><tr><td>Jarvis Varnado</td><td>Mississippi State</td><td>2010</td><td>3.19</td><td>14.1</td></tr><tr><td>Jeff Withey</td><td>Kansas</td><td>2012</td><td>3.152</td><td>15</td></tr><tr><td>Jaren Jackson Jr.</td><td>Michigan State</td><td>2018</td><td>3.084</td><td>14.3</td></tr><tr><td>Anthony Davis</td><td>Kentucky</td><td>2012</td><td>3.083</td><td>14</td></tr><tr><td>Hamady NDiaye</td><td>Rutgers</td><td>2010</td><td>2.855</td><td>14.1</td></tr><tr><td>Willie Cauley-Stein</td><td>Kentucky</td><td>2014</td><td>2.626</td><td>12.5</td></tr><tr><td>Robert Williams</td><td>Texas A&M</td><td>2017</td><td>2.571</td><td>10.8</td></tr><tr><td>Bernard James</td><td>Florida State</td><td>2011</td><td>2.569</td><td>13.3</td></tr><tr><td>Nerlens Noel</td><td>Kentucky</td><td>2013</td><td>2.567</td><td>13.1</td></tr><tr><td>Karl-Anthony Towns</td><td>Kentucky</td><td>2015</td><td>2.56</td><td>11.7</td></tr><tr><td>Robert Williams</td><td>Texas A&M</td><td>2018</td><td>2.515</td><td>9.8</td></tr><tr><td>Terrence Jones</td><td>Kentucky</td><td>2012</td><td>2.43</td><td>5.7</td></tr><tr><td>John Henson</td><td>UNC</td><td>2011</td><td>2.38</td><td>11.2</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Pat Connaughton</td><td>Notre Dame</td><td>2012</td><td>-0.6</td><td>0.6</td></tr><tr><td>Josh Selby</td><td>Kansas</td><td>2011</td><td>-0.604</td><td>0.2</td></tr><tr><td>Nik Stauskas</td><td>Michigan</td><td>2014</td><td>-0.606</td><td>0.9</td></tr><tr><td>Kevin Hervey</td><td>Texas-Arlington</td><td>2017</td><td>-0.619</td><td>1.8</td></tr><tr><td>Deshaun Thomas</td><td>Ohio State</td><td>2011</td><td>-0.641</td><td>1.3</td></tr><tr><td>Chandler Hutchison</td><td>Boise State</td><td>2015</td><td>-0.644</td><td>1.4</td></tr><tr><td>Georges Niang</td><td>Iowa State</td><td>2013</td><td>-0.648</td><td>1</td></tr><tr><td>Shelvin Mack</td><td>Butler</td><td>2010</td><td>-0.664</td><td>0.5</td></tr><tr><td>C.J. McCollum</td><td>Lehigh</td><td>2013</td><td>-0.692</td><td>1.1</td></tr><tr><td>Nate Wolters</td><td>South Dakota State</td><td>2012</td><td>-0.741</td><td>0.2</td></tr><tr><td>Kevin Murphy</td><td>Tennessee Tech</td><td>2010</td><td>-0.75</td><td>0.4</td></tr><tr><td>Mike Scott</td><td>Virginia</td><td>2010</td><td>-0.765</td><td>1.1</td></tr><tr><td>Shelvin Mack</td><td>Butler</td><td>2011</td><td>-0.782</td><td>0.3</td></tr><tr><td>Kay Felder</td><td>Oakland</td><td>2015</td><td>-0.899</td><td>0.7</td></tr><tr><td>Doug McDermott</td><td>Creighton</td><td>2014</td><td>-1.069</td><td>0.5</td></tr></tbody>',
"aBLKA": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aBLKA</th><th>Height</th></tr></thead><tbody><tr><td>Cady Lalanne</td><td>UMass</td><td>2014</td><td>0.907</td><td>6-10</td></tr><tr><td>Anthony Brown</td><td>Stanford</td><td>2012</td><td>0.903</td><td>6-6</td></tr><tr><td>Wesley Iwundu</td><td>Kansas State</td><td>2015</td><td>0.761</td><td>6-7</td></tr><tr><td>George King</td><td>Colorado</td><td>2016</td><td>0.754</td><td>6-6</td></tr><tr><td>Cody Zeller</td><td>Indiana</td><td>2012</td><td>0.744</td><td>7-0</td></tr><tr><td>Victor Oladipo</td><td>Indiana</td><td>2011</td><td>0.741</td><td>6-5</td></tr><tr><td>Kelly Oubre</td><td>Kansas</td><td>2015</td><td>0.729</td><td>6-7</td></tr><tr><td>Elfrid Payton</td><td>Louisiana</td><td>2012</td><td>0.709</td><td>6-3</td></tr><tr><td>Xavier Thames</td><td>San Diego State</td><td>2012</td><td>0.67</td><td>6-3</td></tr><tr><td>Cady Lalanne</td><td>UMass</td><td>2013</td><td>0.668</td><td>6-10</td></tr><tr><td>John Collins</td><td>Wake Forest</td><td>2017</td><td>0.667</td><td>6-10</td></tr><tr><td>Sterling Brown</td><td>SMU</td><td>2016</td><td>0.666</td><td>6-6</td></tr><tr><td>Elfrid Payton</td><td>Louisiana</td><td>2014</td><td>0.649</td><td>6-3</td></tr><tr><td>Mason Plumlee</td><td>Duke</td><td>2010</td><td>0.633</td><td>6-10</td></tr><tr><td>Chandler Hutchison</td><td>Boise State</td><td>2017</td><td>0.621</td><td>6-7</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Kevin Hervey</td><td>Texas-Arlington</td><td>2018</td><td>-0.843</td><td>6-7</td></tr><tr><td>Joseph Young</td><td>Oregon</td><td>2015</td><td>-0.85</td><td>6-2</td></tr><tr><td>Keita Bates-Diop</td><td>Ohio State</td><td>2016</td><td>-0.857</td><td>6-7</td></tr><tr><td>Robert Williams</td><td>Texas A&M</td><td>2018</td><td>-0.858</td><td>6-9</td></tr><tr><td>Lonzo Ball</td><td>UCLA</td><td>2017</td><td>-0.875</td><td>6-6</td></tr><tr><td>Trevor Booker</td><td>Clemson</td><td>2010</td><td>-0.875</td><td>6-7</td></tr><tr><td>Abdel Nader</td><td>Iowa State</td><td>2015</td><td>-0.906</td><td>6-6</td></tr><tr><td>Vernon Macklin</td><td>Florida</td><td>2011</td><td>-0.92</td><td>6-9</td></tr><tr><td>Peyton Siva</td><td>Louisville</td><td>2013</td><td>-0.965</td><td>6-0</td></tr><tr><td>Miles Plumlee</td><td>Duke</td><td>2010</td><td>-0.98</td><td>6-10</td></tr><tr><td>Rodney Hood</td><td>Mississippi State</td><td>2012</td><td>-1.028</td><td>6-8</td></tr><tr><td>Damyean Dotson</td><td>Oregon</td><td>2013</td><td>-1.029</td><td>6-5</td></tr><tr><td>Perry Jones</td><td>Baylor</td><td>2012</td><td>-1.049</td><td>6-11</td></tr><tr><td>Doron Lamb</td><td>Kentucky</td><td>2012</td><td>-1.056</td><td>6-4</td></tr><tr><td>Marvin Bagley III</td><td>Duke</td><td>2018</td><td>-1.07</td><td>6-11</td></tr></tbody>',
"aPF": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aPF</th><th>PF%</th></tr></thead><tbody><tr><td>Jevon Carter</td><td>West Virginia</td><td>2015</td><td>3.176</td><td>4.8</td></tr><tr><td>Arsalan Kazemi</td><td>Rice</td><td>2010</td><td>2.427</td><td>6</td></tr><tr><td>Taurean Prince</td><td>Baylor</td><td>2014</td><td>2.191</td><td>9.6</td></tr><tr><td>Xavier Thames</td><td>Washington State</td><td>2010</td><td>2.098</td><td>6.8</td></tr><tr><td>Kostas Antetokounmpo</td><td>Dayton</td><td>2018</td><td>1.996</td><td>9.4</td></tr><tr><td>Markel Brown</td><td>Oklahoma State</td><td>2011</td><td>1.988</td><td>4.5</td></tr><tr><td>Lamar Patterson</td><td>Pitt</td><td>2011</td><td>1.919</td><td>5.9</td></tr><tr><td>Peyton Siva</td><td>Louisville</td><td>2010</td><td>1.861</td><td>10.8</td></tr><tr><td>Kelly Olynyk</td><td>Gonzaga</td><td>2010</td><td>1.807</td><td>9.7</td></tr><tr><td>Russ Smith</td><td>Louisville</td><td>2012</td><td>1.785</td><td>7.5</td></tr><tr><td>Norman Powell</td><td>UCLA</td><td>2012</td><td>1.763</td><td>5</td></tr><tr><td>Darius Miller</td><td>Kentucky</td><td>2012</td><td>1.692</td><td>5.2</td></tr><tr><td>Taurean Prince</td><td>Baylor</td><td>2013</td><td>1.641</td><td>13.9</td></tr><tr><td>Roy Devyn Marble</td><td>Iowa</td><td>2012</td><td>1.517</td><td>3.4</td></tr><tr><td>Joel Bolomboy</td><td>Weber State</td><td>2013</td><td>1.494</td><td>6.7</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Nick Johnson</td><td>Arizona</td><td>2014</td><td>-2.59</td><td>3.8</td></tr><tr><td>Moritz Wagner</td><td>Michigan</td><td>2017</td><td>-2.611</td><td>7.3</td></tr><tr><td>Solomon Alabi</td><td>Florida State</td><td>2010</td><td>-2.672</td><td>5.7</td></tr><tr><td>Kendall Marshall</td><td>UNC</td><td>2011</td><td>-2.718</td><td>3.1</td></tr><tr><td>Darrun Hilliard</td><td>Villanova</td><td>2015</td><td>-2.733</td><td>5</td></tr><tr><td>Alex Oriakhi</td><td>Missouri</td><td>2013</td><td>-2.778</td><td>5.6</td></tr><tr><td>Nik Stauskas</td><td>Michigan</td><td>2013</td><td>-2.918</td><td>1.5</td></tr><tr><td>Larry Sanders</td><td>VCU</td><td>2010</td><td>-2.982</td><td>6.8</td></tr><tr><td>Dexter Pittman</td><td>Texas</td><td>2010</td><td>-3.113</td><td>7.7</td></tr><tr><td>Reggie Bullock</td><td>UNC</td><td>2013</td><td>-3.133</td><td>2.6</td></tr><tr><td>Georges Niang</td><td>Iowa State</td><td>2016</td><td>-3.178</td><td>5.6</td></tr><tr><td>Vernon Macklin</td><td>Florida</td><td>2010</td><td>-3.333</td><td>6</td></tr><tr><td>Alex Oriakhi</td><td>UConn</td><td>2011</td><td>-3.375</td><td>5.5</td></tr><tr><td>Jakob Poeltl</td><td>Utah</td><td>2016</td><td>-3.381</td><td>4.7</td></tr><tr><td>Justin Hamilton</td><td>Iowa State</td><td>2010</td><td>-3.873</td><td>6.5</td></tr></tbody>',
"aPFD": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aPFD</th><th>FTr</th></tr></thead><tbody><tr><td>Andrew Harrison</td><td>Kentucky</td><td>2015</td><td>2.689</td><td>0.596</td></tr><tr><td>Jeffery Taylor</td><td>Vanderbilt</td><td>2010</td><td>2.598</td><td>0.63</td></tr><tr><td>Mikal Bridges</td><td>Villanova</td><td>2016</td><td>2.541</td><td>0.455</td></tr><tr><td>Andre Roberson</td><td>Colorado</td><td>2011</td><td>2.519</td><td>0.437</td></tr><tr><td>Cameron Bairstow</td><td>New Mexico</td><td>2013</td><td>2.504</td><td>0.709</td></tr><tr><td>Robert Sacre</td><td>Gonzaga</td><td>2011</td><td>2.417</td><td>0.7</td></tr><tr><td>Markieff Morris</td><td>Kansas</td><td>2010</td><td>2.412</td><td>0.645</td></tr><tr><td>Chandler Hutchison</td><td>Boise State</td><td>2017</td><td>2.407</td><td>0.421</td></tr><tr><td>Russ Smith</td><td>Louisville</td><td>2012</td><td>2.404</td><td>0.344</td></tr><tr><td>Aaron White</td><td>Iowa</td><td>2014</td><td>2.379</td><td>0.657</td></tr><tr><td>Shai Gilgeous-Alexander</td><td>Kentucky</td><td>2018</td><td>2.371</td><td>0.464</td></tr><tr><td>Gordon Hayward</td><td>Butler</td><td>2010</td><td>2.338</td><td>0.579</td></tr><tr><td>Victor Oladipo</td><td>Indiana</td><td>2011</td><td>2.326</td><td>0.528</td></tr><tr><td>Patrick McCaw</td><td>UNLV</td><td>2015</td><td>2.315</td><td>0.215</td></tr><tr><td>Grayson Allen</td><td>Duke</td><td>2017</td><td>2.306</td><td>0.445</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Monte Morris</td><td>Iowa State</td><td>2016</td><td>-1.406</td><td>0.249</td></tr><tr><td>Josh Selby</td><td>Kansas</td><td>2011</td><td>-1.418</td><td>0.192</td></tr><tr><td>Gary Harris</td><td>Michigan State</td><td>2013</td><td>-1.425</td><td>0.298</td></tr><tr><td>Derrick Caracter</td><td>UTEP</td><td>2010</td><td>-1.436</td><td>0.456</td></tr><tr><td>Peyton Siva</td><td>Louisville</td><td>2013</td><td>-1.452</td><td>0.285</td></tr><tr><td>Grant Jerrett</td><td>Arizona</td><td>2013</td><td>-1.488</td><td>0.143</td></tr><tr><td>D.J. Wilson</td><td>Michigan</td><td>2017</td><td>-1.534</td><td>0.197</td></tr><tr><td>Nik Stauskas</td><td>Michigan</td><td>2013</td><td>-1.597</td><td>0.292</td></tr><tr><td>Branden Dawson</td><td>Michigan State</td><td>2013</td><td>-1.87</td><td>0.305</td></tr><tr><td>Lavoy Allen</td><td>Temple</td><td>2011</td><td>-1.984</td><td>0.308</td></tr><tr><td>Fab Melo</td><td>Syracuse</td><td>2011</td><td>-2.028</td><td>0.446</td></tr><tr><td>Thomas Welsh</td><td>UCLA</td><td>2017</td><td>-2.092</td><td>0.182</td></tr><tr><td>Norman Powell</td><td>UCLA</td><td>2014</td><td>-2.164</td><td>0.429</td></tr><tr><td>Erik Murphy</td><td>Florida</td><td>2010</td><td>-2.262</td><td>0.375</td></tr><tr><td>Nigel Williams-Goss</td><td>Washington</td><td>2014</td><td>-2.335</td><td>0.229</td></tr></tbody>',
"aFGP": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aFGP</th><th>FG%</th></tr></thead><tbody><tr><td>TJ Leaf</td><td>UCLA</td><td>2017</td><td>0.035</td><td>0.617</td></tr><tr><td>Georges Niang</td><td>Iowa State</td><td>2013</td><td>0.033</td><td>0.515</td></tr><tr><td>Georges Niang</td><td>Iowa State</td><td>2016</td><td>0.033</td><td>0.546</td></tr><tr><td>Donte DiVincenzo</td><td>Villanova</td><td>2018</td><td>0.031</td><td>0.481</td></tr><tr><td>Jakob Poeltl</td><td>Utah</td><td>2015</td><td>0.031</td><td>0.681</td></tr><tr><td>Will Barton</td><td>Memphis</td><td>2012</td><td>0.031</td><td>0.509</td></tr><tr><td>Larry Nance</td><td>Wyoming</td><td>2014</td><td>0.03</td><td>0.544</td></tr><tr><td>T.J. Warren</td><td>NC State</td><td>2013</td><td>0.03</td><td>0.622</td></tr><tr><td>Justise Winslow</td><td>Duke</td><td>2015</td><td>0.03</td><td>0.486</td></tr><tr><td>Anthony Davis</td><td>Kentucky</td><td>2012</td><td>0.029</td><td>0.623</td></tr><tr><td>Marcus Morris</td><td>Kansas</td><td>2011</td><td>0.029</td><td>0.57</td></tr><tr><td>Doug McDermott</td><td>Creighton</td><td>2012</td><td>0.029</td><td>0.601</td></tr><tr><td>Rondae Hollis-Jefferson</td><td>Arizona</td><td>2015</td><td>0.029</td><td>0.502</td></tr><tr><td>Justin Patton</td><td>Creighton</td><td>2017</td><td>0.028</td><td>0.676</td></tr><tr><td>Robert Williams</td><td>Texas A&M</td><td>2018</td><td>0.028</td><td>0.632</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Kentavious Caldwell-Pope</td><td>Georgia</td><td>2012</td><td>-0.007</td><td>0.396</td></tr><tr><td>Sindarius Thornwell</td><td>South Carolina</td><td>2015</td><td>-0.007</td><td>0.34</td></tr><tr><td>George King</td><td>Colorado</td><td>2014</td><td>-0.007</td><td>0.282</td></tr><tr><td>Tony Carr</td><td>Penn State</td><td>2017</td><td>-0.008</td><td>0.377</td></tr><tr><td>Melvin Frazier</td><td>Tulane</td><td>2016</td><td>-0.008</td><td>0.401</td></tr><tr><td>Nate Wolters</td><td>South Dakota State</td><td>2010</td><td>-0.008</td><td>0.381</td></tr><tr><td>Isaiah Cousins</td><td>Oklahoma</td><td>2013</td><td>-0.009</td><td>0.279</td></tr><tr><td>Josh Richardson</td><td>Tennessee</td><td>2012</td><td>-0.009</td><td>0.353</td></tr><tr><td>Josh Selby</td><td>Kansas</td><td>2011</td><td>-0.009</td><td>0.373</td></tr><tr><td>Grant Jerrett</td><td>Arizona</td><td>2013</td><td>-0.01</td><td>0.409</td></tr><tr><td>Frank Kaminsky</td><td>Wisconsin</td><td>2012</td><td>-0.01</td><td>0.411</td></tr><tr><td>Johnny OBryant</td><td>LSU</td><td>2012</td><td>-0.013</td><td>0.399</td></tr><tr><td>George King</td><td>Colorado</td><td>2016</td><td>-0.013</td><td>0.446</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2012</td><td>-0.014</td><td>0.337</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2013</td><td>-0.018</td><td>0.337</td></tr></tbody>',
"aDFGP": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aDFGP</th></tr></thead><tbody><tr><td>Tyler Harvey</td><td>Eastern Washington</td><td>2015</td><td>0.015</td></tr><tr><td>Mike Scott</td><td>Virginia</td><td>2011</td><td>0.015</td></tr><tr><td>Damian Lillard</td><td>Weber State</td><td>2011</td><td>0.014</td></tr><tr><td>Melvin Frazier</td><td>Tulane</td><td>2017</td><td>0.012</td></tr><tr><td>Royce White</td><td>Iowa State</td><td>2012</td><td>0.012</td></tr><tr><td>Harry Giles</td><td>Duke</td><td>2017</td><td>0.011</td></tr><tr><td>Jerome Robinson</td><td>Boston College</td><td>2017</td><td>0.011</td></tr><tr><td>Marcus Thornton</td><td>William & Mary</td><td>2014</td><td>0.011</td></tr><tr><td>T.J. Warren</td><td>NC State</td><td>2013</td><td>0.011</td></tr><tr><td>Erik Murphy</td><td>Florida</td><td>2010</td><td>0.01</td></tr><tr><td>Kevin Murphy</td><td>Tennessee Tech</td><td>2010</td><td>0.01</td></tr><tr><td>Khyri Thomas</td><td>Creighton</td><td>2018</td><td>0.01</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2012</td><td>0.009</td></tr><tr><td>Taurean Prince</td><td>Baylor</td><td>2016</td><td>0.009</td></tr><tr><td>Moritz Wagner</td><td>Michigan</td><td>2017</td><td>0.009</td></tr><tr><td>...</td><td></td><td></td><td></td></tr><tr><td>Al-Farouq Aminu</td><td>Wake Forest</td><td>2010</td><td>-0.024</td></tr><tr><td>Ekpe Udoh</td><td>Baylor</td><td>2010</td><td>-0.024</td></tr><tr><td>Ryan Kelly</td><td>Duke</td><td>2013</td><td>-0.024</td></tr><tr><td>Mason Plumlee</td><td>Duke</td><td>2011</td><td>-0.024</td></tr><tr><td>Tyshawn Taylor</td><td>Kansas</td><td>2010</td><td>-0.024</td></tr><tr><td>Bernard James</td><td>Florida State</td><td>2011</td><td>-0.025</td></tr><tr><td>Deyonta Davis</td><td>Michigan State</td><td>2016</td><td>-0.025</td></tr><tr><td>Caleb Swanigan</td><td>Purdue</td><td>2016</td><td>-0.025</td></tr><tr><td>Rondae Hollis-Jefferson</td><td>Arizona</td><td>2015</td><td>-0.025</td></tr><tr><td>Dion Waiters</td><td>Syracuse</td><td>2012</td><td>-0.026</td></tr><tr><td>K.J. McDaniels</td><td>Clemson</td><td>2014</td><td>-0.026</td></tr><tr><td>Keita Bates-Diop</td><td>Ohio State</td><td>2018</td><td>-0.026</td></tr><tr><td>Chris Singleton</td><td>Florida State</td><td>2010</td><td>-0.028</td></tr><tr><td>Jaren Jackson Jr.</td><td>Michigan State</td><td>2018</td><td>-0.029</td></tr><tr><td>Jeff Withey</td><td>Kansas</td><td>2012</td><td>-0.037</td></tr></tbody>',
"aFG3P": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aFG3P</th><th>3P%</th></tr></thead><tbody><tr><td>Jon Diebler</td><td>Ohio State</td><td>2011</td><td>0.013</td><td>0.502</td></tr><tr><td>Buddy Hield</td><td>Oklahoma</td><td>2016</td><td>0.012</td><td>0.457</td></tr><tr><td>Denzel Valentine</td><td>Michigan State</td><td>2016</td><td>0.012</td><td>0.444</td></tr><tr><td>Doug McDermott</td><td>Creighton</td><td>2012</td><td>0.01</td><td>0.486</td></tr><tr><td>Kim English</td><td>Missouri</td><td>2012</td><td>0.01</td><td>0.459</td></tr><tr><td>Doug McDermott</td><td>Creighton</td><td>2014</td><td>0.01</td><td>0.449</td></tr><tr><td>Isaiah Cousins</td><td>Oklahoma</td><td>2016</td><td>0.01</td><td>0.411</td></tr><tr><td>Sviatoslav Mykhailiuk</td><td>Kansas</td><td>2018</td><td>0.01</td><td>0.444</td></tr><tr><td>TJ Leaf</td><td>UCLA</td><td>2017</td><td>0.01</td><td>0.466</td></tr><tr><td>Donte DiVincenzo</td><td>Villanova</td><td>2018</td><td>0.01</td><td>0.401</td></tr><tr><td>Darius Johnson-Odom</td><td>Marquette</td><td>2010</td><td>0.009</td><td>0.474</td></tr><tr><td>Isaiah Canaan</td><td>Murray State</td><td>2012</td><td>0.009</td><td>0.456</td></tr><tr><td>John Jenkins</td><td>Vanderbilt</td><td>2012</td><td>0.009</td><td>0.439</td></tr><tr><td>Jimmy Butler</td><td>Marquette</td><td>2010</td><td>0.009</td><td>0.5</td></tr><tr><td>Sterling Brown</td><td>SMU</td><td>2016</td><td>0.009</td><td>0.536</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Nikola Vucevic</td><td>USC</td><td>2010</td><td>-0.004</td><td>0.222</td></tr><tr><td>Kyle OQuinn</td><td>Norfolk State</td><td>2010</td><td>-0.004</td><td>0.239</td></tr><tr><td>Glen Rice</td><td>Georgia Tech</td><td>2011</td><td>-0.004</td><td>0.302</td></tr><tr><td>Iman Shumpert</td><td>Georgia Tech</td><td>2011</td><td>-0.005</td><td>0.278</td></tr><tr><td>Erick Green</td><td>Virginia Tech</td><td>2010</td><td>-0.005</td><td>0.275</td></tr><tr><td>Tyrone Wallace</td><td>California</td><td>2013</td><td>-0.005</td><td>0.224</td></tr><tr><td>Kawhi Leonard</td><td>San Diego State</td><td>2010</td><td>-0.005</td><td>0.205</td></tr><tr><td>Jarrett Allen</td><td>Texas</td><td>2017</td><td>-0.005</td><td>0</td></tr><tr><td>Dominique Jones</td><td>South Florida</td><td>2010</td><td>-0.005</td><td>0.311</td></tr><tr><td>Ray McCallum</td><td>Detroit</td><td>2012</td><td>-0.005</td><td>0.24</td></tr><tr><td>Maurice Harkless</td><td>St. Johns (NY)</td><td>2012</td><td>-0.005</td><td>0.215</td></tr><tr><td>SirDominic Pointer</td><td>St. Johns (NY)</td><td>2012</td><td>-0.006</td><td>0.189</td></tr><tr><td>Josh Richardson</td><td>Tennessee</td><td>2013</td><td>-0.006</td><td>0.214</td></tr><tr><td>Wesley Iwundu</td><td>Kansas State</td><td>2016</td><td>-0.007</td><td>0.2</td></tr><tr><td>Lance Stephenson</td><td>Cincinnati</td><td>2010</td><td>-0.007</td><td>0.219</td></tr></tbody>',
"aDFG3P": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aDFG3P</th></tr></thead><tbody><tr><td>Norris Cole</td><td>Cleveland State</td><td>2010</td><td>0.005</td></tr><tr><td>Demetrius Jackson</td><td>Notre Dame</td><td>2014</td><td>0.005</td></tr><tr><td>JaJuan Johnson</td><td>Purdue</td><td>2010</td><td>0.005</td></tr><tr><td>Darrun Hilliard</td><td>Villanova</td><td>2013</td><td>0.005</td></tr><tr><td>Jared Cunningham</td><td>Oregon State</td><td>2012</td><td>0.005</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2012</td><td>0.005</td></tr><tr><td>Nate Wolters</td><td>South Dakota State</td><td>2011</td><td>0.005</td></tr><tr><td>Mike Scott</td><td>Virginia</td><td>2011</td><td>0.005</td></tr><tr><td>Josh Okogie</td><td>Georgia Tech</td><td>2018</td><td>0.004</td></tr><tr><td>Kay Felder</td><td>Oakland</td><td>2014</td><td>0.004</td></tr><tr><td>Pat Connaughton</td><td>Notre Dame</td><td>2014</td><td>0.004</td></tr><tr><td>Jordan Bell</td><td>Oregon</td><td>2016</td><td>0.004</td></tr><tr><td>James Ennis</td><td>Long Beach State</td><td>2013</td><td>0.004</td></tr><tr><td>Tyler Harvey</td><td>Eastern Washington</td><td>2015</td><td>0.004</td></tr><tr><td>Melvin Frazier</td><td>Tulane</td><td>2017</td><td>0.004</td></tr><tr><td>...</td><td></td><td></td><td></td></tr><tr><td>Otto Porter</td><td>Georgetown</td><td>2012</td><td>-0.006</td></tr><tr><td>Wade Baldwin</td><td>Vanderbilt</td><td>2016</td><td>-0.006</td></tr><tr><td>Branden Dawson</td><td>Michigan State</td><td>2015</td><td>-0.006</td></tr><tr><td>Jawun Evans</td><td>Oklahoma State</td><td>2016</td><td>-0.006</td></tr><tr><td>Frank Jackson</td><td>Duke</td><td>2017</td><td>-0.006</td></tr><tr><td>Bam Adebayo</td><td>Kentucky</td><td>2017</td><td>-0.006</td></tr><tr><td>Landry Shamet</td><td>Wichita State</td><td>2017</td><td>-0.006</td></tr><tr><td>DeAaron Fox</td><td>Kentucky</td><td>2017</td><td>-0.006</td></tr><tr><td>Willie Cauley-Stein</td><td>Kentucky</td><td>2015</td><td>-0.006</td></tr><tr><td>K.J. McDaniels</td><td>Clemson</td><td>2014</td><td>-0.007</td></tr><tr><td>Nigel Williams-Goss</td><td>Gonzaga</td><td>2017</td><td>-0.007</td></tr><tr><td>Donovan Mitchell</td><td>Louisville</td><td>2017</td><td>-0.007</td></tr><tr><td>Lavoy Allen</td><td>Temple</td><td>2010</td><td>-0.007</td></tr><tr><td>Fab Melo</td><td>Syracuse</td><td>2012</td><td>-0.007</td></tr><tr><td>Shai Gilgeous-Alexander</td><td>Kentucky</td><td>2018</td><td>-0.007</td></tr></tbody>',
"aEFG": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aEFG</th><th>eFG%</th></tr></thead><tbody><tr><td>Donte DiVincenzo</td><td>Villanova</td><td>2018</td><td>0.035</td><td>0.59</td></tr><tr><td>TJ Leaf</td><td>UCLA</td><td>2017</td><td>0.034</td><td>0.652</td></tr><tr><td>Georges Niang</td><td>Iowa State</td><td>2013</td><td>0.032</td><td>0.577</td></tr><tr><td>Terrence Ross</td><td>Washington</td><td>2011</td><td>0.029</td><td>0.539</td></tr><tr><td>Jakob Poeltl</td><td>Utah</td><td>2015</td><td>0.029</td><td>0.681</td></tr><tr><td>Georges Niang</td><td>Iowa State</td><td>2016</td><td>0.029</td><td>0.6</td></tr><tr><td>Doug McDermott</td><td>Creighton</td><td>2012</td><td>0.028</td><td>0.654</td></tr><tr><td>John Jenkins</td><td>Vanderbilt</td><td>2012</td><td>0.028</td><td>0.62</td></tr><tr><td>Will Barton</td><td>Memphis</td><td>2012</td><td>0.027</td><td>0.55</td></tr><tr><td>Devonte Graham</td><td>Kansas</td><td>2017</td><td>0.027</td><td>0.556</td></tr><tr><td>Marcus Morris</td><td>Kansas</td><td>2011</td><td>0.027</td><td>0.601</td></tr><tr><td>Kim English</td><td>Missouri</td><td>2012</td><td>0.027</td><td>0.64</td></tr><tr><td>Jalen Brunson</td><td>Villanova</td><td>2018</td><td>0.027</td><td>0.604</td></tr><tr><td>Justise Winslow</td><td>Duke</td><td>2015</td><td>0.027</td><td>0.551</td></tr><tr><td>Sam Dekker</td><td>Wisconsin</td><td>2015</td><td>0.027</td><td>0.586</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Cory Jefferson</td><td>Baylor</td><td>2012</td><td>-0.007</td><td>0.522</td></tr><tr><td>Sindarius Thornwell</td><td>South Carolina</td><td>2015</td><td>-0.007</td><td>0.397</td></tr><tr><td>Josh Selby</td><td>Kansas</td><td>2011</td><td>-0.007</td><td>0.461</td></tr><tr><td>Nate Wolters</td><td>South Dakota State</td><td>2010</td><td>-0.008</td><td>0.426</td></tr><tr><td>George King</td><td>Colorado</td><td>2014</td><td>-0.009</td><td>0.333</td></tr><tr><td>John Henson</td><td>UNC</td><td>2011</td><td>-0.009</td><td>0.501</td></tr><tr><td>Tony Carr</td><td>Penn State</td><td>2017</td><td>-0.01</td><td>0.421</td></tr><tr><td>Erick Green</td><td>Virginia Tech</td><td>2010</td><td>-0.01</td><td>0.348</td></tr><tr><td>Melvin Frazier</td><td>Tulane</td><td>2016</td><td>-0.01</td><td>0.459</td></tr><tr><td>George King</td><td>Colorado</td><td>2016</td><td>-0.01</td><td>0.545</td></tr><tr><td>Josh Richardson</td><td>Tennessee</td><td>2012</td><td>-0.012</td><td>0.397</td></tr><tr><td>Isaiah Cousins</td><td>Oklahoma</td><td>2013</td><td>-0.013</td><td>0.324</td></tr><tr><td>Johnny OBryant</td><td>LSU</td><td>2012</td><td>-0.015</td><td>0.404</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2012</td><td>-0.015</td><td>0.39</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2013</td><td>-0.018</td><td>0.386</td></tr></tbody>',
"aDEFG": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aDEFG</th></tr></thead><tbody><tr><td>Mike Scott</td><td>Virginia</td><td>2011</td><td>0.017</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2012</td><td>0.014</td></tr><tr><td>Tyler Harvey</td><td>Eastern Washington</td><td>2015</td><td>0.013</td></tr><tr><td>Melvin Frazier</td><td>Tulane</td><td>2017</td><td>0.013</td></tr><tr><td>Jared Cunningham</td><td>Oregon State</td><td>2011</td><td>0.011</td></tr><tr><td>Royce White</td><td>Iowa State</td><td>2012</td><td>0.011</td></tr><tr><td>Marcus Thornton</td><td>William & Mary</td><td>2014</td><td>0.011</td></tr><tr><td>Damian Lillard</td><td>Weber State</td><td>2011</td><td>0.01</td></tr><tr><td>Jerome Robinson</td><td>Boston College</td><td>2017</td><td>0.01</td></tr><tr><td>Khyri Thomas</td><td>Creighton</td><td>2018</td><td>0.01</td></tr><tr><td>Kay Felder</td><td>Oakland</td><td>2014</td><td>0.01</td></tr><tr><td>Kevin Murphy</td><td>Tennessee Tech</td><td>2010</td><td>0.009</td></tr><tr><td>Taurean Prince</td><td>Baylor</td><td>2016</td><td>0.009</td></tr><tr><td>Erik Murphy</td><td>Florida</td><td>2010</td><td>0.009</td></tr><tr><td>C.J. McCollum</td><td>Lehigh</td><td>2010</td><td>0.008</td></tr><tr><td>...</td><td></td><td></td><td></td></tr><tr><td>Al-Farouq Aminu</td><td>Wake Forest</td><td>2010</td><td>-0.022</td></tr><tr><td>Kemba Walker</td><td>UConn</td><td>2011</td><td>-0.023</td></tr><tr><td>Ekpe Udoh</td><td>Baylor</td><td>2010</td><td>-0.023</td></tr><tr><td>Dion Waiters</td><td>Syracuse</td><td>2012</td><td>-0.023</td></tr><tr><td>Caleb Swanigan</td><td>Purdue</td><td>2016</td><td>-0.023</td></tr><tr><td>Donovan Mitchell</td><td>Louisville</td><td>2017</td><td>-0.024</td></tr><tr><td>Tyshawn Taylor</td><td>Kansas</td><td>2010</td><td>-0.024</td></tr><tr><td>Rondae Hollis-Jefferson</td><td>Arizona</td><td>2015</td><td>-0.024</td></tr><tr><td>Mason Plumlee</td><td>Duke</td><td>2011</td><td>-0.024</td></tr><tr><td>Deyonta Davis</td><td>Michigan State</td><td>2016</td><td>-0.024</td></tr><tr><td>Chris Singleton</td><td>Florida State</td><td>2010</td><td>-0.025</td></tr><tr><td>K.J. McDaniels</td><td>Clemson</td><td>2014</td><td>-0.026</td></tr><tr><td>Keita Bates-Diop</td><td>Ohio State</td><td>2018</td><td>-0.027</td></tr><tr><td>Jaren Jackson Jr.</td><td>Michigan State</td><td>2018</td><td>-0.027</td></tr><tr><td>Jeff Withey</td><td>Kansas</td><td>2012</td><td>-0.032</td></tr></tbody>',
"a3PAr": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>a3PAr</th><th>3PAr</th></tr></thead><tbody><tr><td>Denzel Valentine</td><td>Michigan State</td><td>2016</td><td>5.312</td><td>0.527</td></tr><tr><td>John Jenkins</td><td>Vanderbilt</td><td>2012</td><td>5.24</td><td>0.666</td></tr><tr><td>Grayson Allen</td><td>Duke</td><td>2017</td><td>5.212</td><td>0.622</td></tr><tr><td>P.J. Hairston</td><td>UNC</td><td>2012</td><td>4.457</td><td>0.702</td></tr><tr><td>P.J. Hairston</td><td>UNC</td><td>2013</td><td>4.36</td><td>0.61</td></tr><tr><td>Anthony Brown</td><td>Stanford</td><td>2011</td><td>4.166</td><td>0.551</td></tr><tr><td>Luke Kennard</td><td>Duke</td><td>2016</td><td>4.159</td><td>0.513</td></tr><tr><td>Marcus Thornton</td><td>William & Mary</td><td>2015</td><td>4.029</td><td>0.538</td></tr><tr><td>C.J. Wilcox</td><td>Washington</td><td>2011</td><td>3.706</td><td>0.73</td></tr><tr><td>Jordan Hamilton</td><td>Texas</td><td>2010</td><td>3.661</td><td>0.53</td></tr><tr><td>Terrence Ross</td><td>Washington</td><td>2011</td><td>3.532</td><td>0.543</td></tr><tr><td>Tim Hardaway</td><td>Michigan</td><td>2011</td><td>3.463</td><td>0.546</td></tr><tr><td>Pat Connaughton</td><td>Notre Dame</td><td>2015</td><td>3.322</td><td>0.618</td></tr><tr><td>Elliot Williams</td><td>Memphis</td><td>2010</td><td>3.287</td><td>0.423</td></tr><tr><td>Marcus Denmon</td><td>Missouri</td><td>2010</td><td>3.284</td><td>0.612</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Wesley Iwundu</td><td>Kansas State</td><td>2015</td><td>-4.851</td><td>0.122</td></tr><tr><td>Damian Jones</td><td>Vanderbilt</td><td>2015</td><td>-4.935</td><td>0.015</td></tr><tr><td>Branden Dawson</td><td>Michigan State</td><td>2014</td><td>-5.027</td><td>0.005</td></tr><tr><td>Dexter Pittman</td><td>Texas</td><td>2010</td><td>-5.051</td><td>0</td></tr><tr><td>John Henson</td><td>UNC</td><td>2010</td><td>-5.091</td><td>0.099</td></tr><tr><td>Skal Labissiere</td><td>Kentucky</td><td>2016</td><td>-5.127</td><td>0.011</td></tr><tr><td>T.J. Warren</td><td>NC State</td><td>2014</td><td>-5.211</td><td>0.178</td></tr><tr><td>Branden Dawson</td><td>Michigan State</td><td>2015</td><td>-5.32</td><td>0</td></tr><tr><td>Travis Leslie</td><td>Georgia</td><td>2010</td><td>-5.45</td><td>0.032</td></tr><tr><td>Tyler Zeller</td><td>UNC</td><td>2011</td><td>-5.547</td><td>0</td></tr><tr><td>Brice Johnson</td><td>UNC</td><td>2016</td><td>-5.551</td><td>0</td></tr><tr><td>Cody Zeller</td><td>Indiana</td><td>2013</td><td>-5.707</td><td>0.006</td></tr><tr><td>Branden Dawson</td><td>Michigan State</td><td>2012</td><td>-5.736</td><td>0.016</td></tr><tr><td>Brice Johnson</td><td>UNC</td><td>2013</td><td>-5.876</td><td>0</td></tr><tr><td>Diamond Stone</td><td>Maryland</td><td>2016</td><td>-6.286</td><td>0</td></tr></tbody>',
"aD3PAr": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aD3PAr</th></tr></thead><tbody><tr><td>Sterling Brown</td><td>SMU</td><td>2017</td><td>3.517</td></tr><tr><td>Denzel Valentine</td><td>Michigan State</td><td>2014</td><td>3.392</td></tr><tr><td>Devon Hall</td><td>Virginia</td><td>2016</td><td>3.308</td></tr><tr><td>Colton Iverson</td><td>Minnesota</td><td>2011</td><td>3.269</td></tr><tr><td>Zach LaVine</td><td>UCLA</td><td>2014</td><td>3.254</td></tr><tr><td>Shake Milton</td><td>SMU</td><td>2018</td><td>3.161</td></tr><tr><td>Peyton Siva</td><td>Louisville</td><td>2012</td><td>3.118</td></tr><tr><td>Paul George</td><td>Fresno State</td><td>2010</td><td>2.966</td></tr><tr><td>Andre Roberson</td><td>Colorado</td><td>2013</td><td>2.915</td></tr><tr><td>Jawun Evans</td><td>Oklahoma State</td><td>2016</td><td>2.908</td></tr><tr><td>Thomas Welsh</td><td>UCLA</td><td>2018</td><td>2.896</td></tr><tr><td>Sterling Brown</td><td>SMU</td><td>2014</td><td>2.822</td></tr><tr><td>Darius Miller</td><td>Kentucky</td><td>2010</td><td>2.801</td></tr><tr><td>Shabazz Napier</td><td>UConn</td><td>2012</td><td>2.759</td></tr><tr><td>Tim Hardaway</td><td>Michigan</td><td>2013</td><td>2.741</td></tr><tr><td>...</td><td></td><td></td><td></td></tr><tr><td>Mason Plumlee</td><td>Duke</td><td>2012</td><td>-2.612</td></tr><tr><td>Richaun Holmes</td><td>Bowling Green State</td><td>2013</td><td>-2.64</td></tr><tr><td>Patrick McCaw</td><td>UNLV</td><td>2015</td><td>-2.649</td></tr><tr><td>Sam Dekker</td><td>Wisconsin</td><td>2013</td><td>-2.789</td></tr><tr><td>Frank Kaminsky</td><td>Wisconsin</td><td>2015</td><td>-2.8</td></tr><tr><td>Tyler Ulis</td><td>Kentucky</td><td>2015</td><td>-2.808</td></tr><tr><td>Roy Devyn Marble</td><td>Iowa</td><td>2011</td><td>-2.936</td></tr><tr><td>Elfrid Payton</td><td>Louisiana</td><td>2014</td><td>-2.981</td></tr><tr><td>Jordan Clarkson</td><td>Tulsa</td><td>2012</td><td>-3.006</td></tr><tr><td>Josh Okogie</td><td>Georgia Tech</td><td>2018</td><td>-3.301</td></tr><tr><td>Malcolm Lee</td><td>UCLA</td><td>2011</td><td>-3.335</td></tr><tr><td>Nolan Smith</td><td>Duke</td><td>2011</td><td>-3.337</td></tr><tr><td>Jabari Bird</td><td>California</td><td>2016</td><td>-3.568</td></tr><tr><td>Doron Lamb</td><td>Kentucky</td><td>2012</td><td>-3.862</td></tr><tr><td>Sam Dekker</td><td>Wisconsin</td><td>2015</td><td>-4.469</td></tr></tbody>',
"aFTr": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aFTr</th><th>FTr</th></tr></thead><tbody><tr><td>Andrew Harrison</td><td>Kentucky</td><td>2015</td><td>6.594</td><td>0.596</td></tr><tr><td>Devonte Graham</td><td>Kansas</td><td>2015</td><td>6.112</td><td>0.65</td></tr><tr><td>Victor Oladipo</td><td>Indiana</td><td>2011</td><td>6.089</td><td>0.528</td></tr><tr><td>Arsalan Kazemi</td><td>Rice</td><td>2012</td><td>5.906</td><td>0.808</td></tr><tr><td>Tony Wroten</td><td>Washington</td><td>2012</td><td>5.897</td><td>0.591</td></tr><tr><td>Nate Wolters</td><td>South Dakota State</td><td>2010</td><td>5.794</td><td>0.648</td></tr><tr><td>Cameron Bairstow</td><td>New Mexico</td><td>2013</td><td>5.754</td><td>0.709</td></tr><tr><td>Shabazz Napier</td><td>UConn</td><td>2011</td><td>5.664</td><td>0.356</td></tr><tr><td>Joel Embiid</td><td>Kansas</td><td>2014</td><td>5.604</td><td>0.836</td></tr><tr><td>Joel Bolomboy</td><td>Weber State</td><td>2013</td><td>5.587</td><td>0.871</td></tr><tr><td>Derrick Williams</td><td>Arizona</td><td>2010</td><td>5.491</td><td>0.823</td></tr><tr><td>Roy Devyn Marble</td><td>Iowa</td><td>2014</td><td>5.46</td><td>0.456</td></tr><tr><td>Dwight Powell</td><td>Stanford</td><td>2014</td><td>5.34</td><td>0.557</td></tr><tr><td>Robert Sacre</td><td>Gonzaga</td><td>2011</td><td>5.329</td><td>0.7</td></tr><tr><td>Aaron White</td><td>Iowa</td><td>2013</td><td>5.324</td><td>0.863</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Josh Harrellson</td><td>Kentucky</td><td>2011</td><td>-3.073</td><td>0.269</td></tr><tr><td>Jalen Brunson</td><td>Villanova</td><td>2018</td><td>-3.15</td><td>0.313</td></tr><tr><td>Olivier Hanlan</td><td>Boston College</td><td>2015</td><td>-3.246</td><td>0.292</td></tr><tr><td>Thomas Welsh</td><td>UCLA</td><td>2017</td><td>-3.247</td><td>0.182</td></tr><tr><td>Erik Murphy</td><td>Florida</td><td>2011</td><td>-3.274</td><td>0.267</td></tr><tr><td>Andrew Goudelock</td><td>College of Charleston</td><td>2011</td><td>-3.306</td><td>0.192</td></tr><tr><td>Ryan Kelly</td><td>Duke</td><td>2011</td><td>-3.442</td><td>0.223</td></tr><tr><td>Thomas Welsh</td><td>UCLA</td><td>2015</td><td>-3.488</td><td>0.174</td></tr><tr><td>Chinanu Onuaku</td><td>Louisville</td><td>2016</td><td>-3.605</td><td>0.253</td></tr><tr><td>Dion Waiters</td><td>Syracuse</td><td>2011</td><td>-3.892</td><td>0.253</td></tr><tr><td>Derrick Caracter</td><td>UTEP</td><td>2010</td><td>-3.929</td><td>0.456</td></tr><tr><td>Fab Melo</td><td>Syracuse</td><td>2011</td><td>-3.955</td><td>0.446</td></tr><tr><td>Erik Murphy</td><td>Florida</td><td>2013</td><td>-4.134</td><td>0.16</td></tr><tr><td>Erik Murphy</td><td>Florida</td><td>2010</td><td>-4.618</td><td>0.375</td></tr><tr><td>Erik Murphy</td><td>Florida</td><td>2012</td><td>-4.753</td><td>0.159</td></tr></tbody>',
"aDFTr": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aDFTr</th><th>PF%</th></tr></thead><tbody><tr><td>Jevon Carter</td><td>West Virginia</td><td>2015</td><td>8.645</td><td>4.8</td></tr><tr><td>Markel Brown</td><td>Oklahoma State</td><td>2011</td><td>4.977</td><td>4.5</td></tr><tr><td>Josh Selby</td><td>Kansas</td><td>2011</td><td>4.385</td><td>5.1</td></tr><tr><td>Michael Gbinije</td><td>Duke</td><td>2012</td><td>3.642</td><td>10.1</td></tr><tr><td>Dejounte Murray</td><td>Washington</td><td>2016</td><td>3.529</td><td>4.2</td></tr><tr><td>Anthony Brown</td><td>Stanford</td><td>2011</td><td>3.423</td><td>3.5</td></tr><tr><td>Norris Cole</td><td>Cleveland State</td><td>2010</td><td>3.396</td><td>4.6</td></tr><tr><td>Isaiah Thomas</td><td>Washington</td><td>2011</td><td>3.385</td><td>4</td></tr><tr><td>Sindarius Thornwell</td><td>South Carolina</td><td>2015</td><td>3.383</td><td>5.4</td></tr><tr><td>Cleanthony Early</td><td>Wichita State</td><td>2013</td><td>3.346</td><td>6.4</td></tr><tr><td>Zach LaVine</td><td>UCLA</td><td>2014</td><td>3.303</td><td>4.9</td></tr><tr><td>Frank Mason</td><td>Kansas</td><td>2014</td><td>3.291</td><td>7.1</td></tr><tr><td>Kyle OQuinn</td><td>Norfolk State</td><td>2010</td><td>3.056</td><td>6.5</td></tr><tr><td>Raymond Spalding</td><td>Louisville</td><td>2016</td><td>2.971</td><td>7.7</td></tr><tr><td>Taurean Prince</td><td>Baylor</td><td>2014</td><td>2.919</td><td>9.6</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Alex Oriakhi</td><td>UConn</td><td>2011</td><td>-4.69</td><td>5.5</td></tr><tr><td>Perry Jones</td><td>Baylor</td><td>2012</td><td>-4.815</td><td>4.8</td></tr><tr><td>Cory Jefferson</td><td>Baylor</td><td>2013</td><td>-5.054</td><td>5</td></tr><tr><td>Willie Cauley-Stein</td><td>Kentucky</td><td>2014</td><td>-5.284</td><td>7</td></tr><tr><td>Jakob Poeltl</td><td>Utah</td><td>2015</td><td>-5.29</td><td>6.8</td></tr><tr><td>Wesley Iwundu</td><td>Kansas State</td><td>2014</td><td>-5.3</td><td>5.8</td></tr><tr><td>Justin Hamilton</td><td>Iowa State</td><td>2010</td><td>-5.418</td><td>6.5</td></tr><tr><td>Jacob Evans</td><td>Cincinnati</td><td>2017</td><td>-5.434</td><td>4.4</td></tr><tr><td>Larry Sanders</td><td>VCU</td><td>2010</td><td>-5.437</td><td>6.8</td></tr><tr><td>Damian Jones</td><td>Vanderbilt</td><td>2016</td><td>-5.469</td><td>7.5</td></tr><tr><td>Alex Oriakhi</td><td>Missouri</td><td>2013</td><td>-5.581</td><td>5.6</td></tr><tr><td>Montrezl Harrell</td><td>Louisville</td><td>2014</td><td>-5.697</td><td>5.1</td></tr><tr><td>Ben Simmons</td><td>LSU</td><td>2016</td><td>-5.699</td><td>4.6</td></tr><tr><td>Chinanu Onuaku</td><td>Louisville</td><td>2016</td><td>-5.762</td><td>7.7</td></tr><tr><td>Jeff Withey</td><td>Kansas</td><td>2012</td><td>-6.143</td><td>6</td></tr></tbody>',
"aOPACE": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aOPACE</th></tr></thead><tbody><tr><td>Russ Smith</td><td>Louisville</td><td>2012</td><td>0.108</td></tr><tr><td>Marshon Brooks</td><td>Providence</td><td>2010</td><td>0.1</td></tr><tr><td>Isaiah Whitehead</td><td>Seton Hall</td><td>2016</td><td>0.092</td></tr><tr><td>Kyrie Irving</td><td>Duke</td><td>2011</td><td>0.089</td></tr><tr><td>Trae Young</td><td>Oklahoma</td><td>2018</td><td>0.082</td></tr><tr><td>Cady Lalanne</td><td>UMass</td><td>2012</td><td>0.077</td></tr><tr><td>Russ Smith</td><td>Louisville</td><td>2013</td><td>0.076</td></tr><tr><td>Kim English</td><td>Missouri</td><td>2010</td><td>0.072</td></tr><tr><td>Cleanthony Early</td><td>Wichita State</td><td>2014</td><td>0.071</td></tr><tr><td>Patrick McCaw</td><td>UNLV</td><td>2016</td><td>0.07</td></tr><tr><td>Tyler Zeller</td><td>UNC</td><td>2010</td><td>0.069</td></tr><tr><td>C.J. McCollum</td><td>Lehigh</td><td>2012</td><td>0.067</td></tr><tr><td>Russ Smith</td><td>Louisville</td><td>2014</td><td>0.067</td></tr><tr><td>Justin Jackson</td><td>UNC</td><td>2015</td><td>0.066</td></tr><tr><td>Lorenzo Brown</td><td>NC State</td><td>2012</td><td>0.064</td></tr><tr><td>...</td><td></td><td></td><td></td></tr><tr><td>Perry Jones</td><td>Baylor</td><td>2012</td><td>-0.059</td></tr><tr><td>Festus Ezeli</td><td>Vanderbilt</td><td>2010</td><td>-0.059</td></tr><tr><td>Ivan Rabb</td><td>California</td><td>2016</td><td>-0.059</td></tr><tr><td>Montrezl Harrell</td><td>Louisville</td><td>2015</td><td>-0.059</td></tr><tr><td>Tyler Honeycutt</td><td>UCLA</td><td>2010</td><td>-0.059</td></tr><tr><td>Larry Nance</td><td>Wyoming</td><td>2014</td><td>-0.06</td></tr><tr><td>Devon Hall</td><td>Virginia</td><td>2018</td><td>-0.064</td></tr><tr><td>Cameron Bairstow</td><td>New Mexico</td><td>2012</td><td>-0.064</td></tr><tr><td>Larry Nance</td><td>Wyoming</td><td>2015</td><td>-0.066</td></tr><tr><td>Jerami Grant</td><td>Syracuse</td><td>2014</td><td>-0.067</td></tr><tr><td>Gorgui Dieng</td><td>Louisville</td><td>2013</td><td>-0.068</td></tr><tr><td>Jordan Bell</td><td>Oregon</td><td>2015</td><td>-0.068</td></tr><tr><td>Robert Williams</td><td>Texas A&M</td><td>2017</td><td>-0.069</td></tr><tr><td>Jakob Poeltl</td><td>Utah</td><td>2015</td><td>-0.073</td></tr><tr><td>Jordan Bell</td><td>Oregon</td><td>2016</td><td>-0.073</td></tr></tbody>',
"aDPACE": '<thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aDPACE</th></tr></thead><tbody><tr><td>Russ Smith</td><td>Louisville</td><td>2012</td><td>0.116</td></tr><tr><td>Devonte Graham</td><td>Kansas</td><td>2015</td><td>0.096</td></tr><tr><td>Marshon Brooks</td><td>Providence</td><td>2010</td><td>0.09</td></tr><tr><td>Peyton Siva</td><td>Louisville</td><td>2010</td><td>0.079</td></tr><tr><td>Kyrie Irving</td><td>Duke</td><td>2011</td><td>0.074</td></tr><tr><td>Russ Smith</td><td>Louisville</td><td>2014</td><td>0.066</td></tr><tr><td>Patrick McCaw</td><td>UNLV</td><td>2016</td><td>0.064</td></tr><tr><td>Trae Young</td><td>Oklahoma</td><td>2018</td><td>0.062</td></tr><tr><td>Ryan Kelly</td><td>Duke</td><td>2010</td><td>0.059</td></tr><tr><td>Thomas Robinson</td><td>Kansas</td><td>2010</td><td>0.058</td></tr><tr><td>Nigel Williams-Goss</td><td>Washington</td><td>2014</td><td>0.056</td></tr><tr><td>Russ Smith</td><td>Louisville</td><td>2013</td><td>0.054</td></tr><tr><td>Luke Harangody</td><td>Notre Dame</td><td>2010</td><td>0.052</td></tr><tr><td>Kim English</td><td>Missouri</td><td>2010</td><td>0.052</td></tr><tr><td>Markelle Fultz</td><td>Washington</td><td>2017</td><td>0.052</td></tr><tr><td>...</td><td></td><td></td><td></td></tr><tr><td>Cory Jefferson</td><td>Baylor</td><td>2013</td><td>-0.072</td></tr><tr><td>Cady Lalanne</td><td>UMass</td><td>2014</td><td>-0.072</td></tr><tr><td>Jakob Poeltl</td><td>Utah</td><td>2015</td><td>-0.073</td></tr><tr><td>Sam Dekker</td><td>Wisconsin</td><td>2015</td><td>-0.073</td></tr><tr><td>Jahlil Okafor</td><td>Duke</td><td>2015</td><td>-0.075</td></tr><tr><td>Steven Adams</td><td>Pitt</td><td>2013</td><td>-0.075</td></tr><tr><td>Peyton Siva</td><td>Louisville</td><td>2012</td><td>-0.075</td></tr><tr><td>Moritz Wagner</td><td>Michigan</td><td>2018</td><td>-0.076</td></tr><tr><td>Deyonta Davis</td><td>Michigan State</td><td>2016</td><td>-0.081</td></tr><tr><td>Malcolm Brogdon</td><td>Virginia</td><td>2016</td><td>-0.083</td></tr><tr><td>Vernon Macklin</td><td>Florida</td><td>2010</td><td>-0.086</td></tr><tr><td>Lazar Hayward</td><td>Marquette</td><td>2010</td><td>-0.088</td></tr><tr><td>Richaun Holmes</td><td>Bowling Green State</td><td>2015</td><td>-0.093</td></tr><tr><td>Justin Harper</td><td>Richmond</td><td>2010</td><td>-0.095</td></tr><tr><td>Larry Nance</td><td>Wyoming</td><td>2015</td><td>-0.1</td></tr></tbody>',
"null": null
};
</script>
<p>In my <a href="/2019/05/26/estimated-advanced-stats.html">previous post</a>, I took a look at how NCAA play-by-play stint data can give more accurate advanced stats. This post will take that a step further by applying RAPM to other stats beyond just points. Doing so unlocks unique insight which may not show up in traditional advanced stats. We can use this innovative data to better understand the impact that players have on team performance and playing style.</p>
<h2 id="player-impact-stats">Player Impact Stats</h2>
<p>By performing RAPM-like calculations, we are able to control for opposing players and teammates on the floor, isolating the true impact of an individual player. The primary usage of the RAPM framework is to determine how much each player impacts team and opponent points per possession (ORAPM and DRAPM). However, the amount of interesting and valuable information we can learn by applying RAPM to other box score counting stats (ast, blk, reb, etc.) is limitless. For example, we can better understand how well a player attacks the rim (e.g. blocks against, personal fouls drawn) or how a player impacts the game on defense (e.g. opponent pace impact, defensive eFG%). These insights can be used by NBA draft models to better project NBA potential.</p>
<p>Below you can find descriptions of all the innovative stats I am currently calculating. Let me know if you have additional ideas!</p>
<table>
<thead>
<tr>
<th style="text-align: center">Stat</th>
<th>Description</th>
<th>What measuring?</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: center">aFGP | aDFGP</td>
<td>Adjusted (Defensive) Field Goal Percentage</td>
<td>Player impact to team/opponent FG%</td>
</tr>
<tr>
<td style="text-align: center">aFG3P | aDFG3P</td>
<td>Adjusted (Defensive) Three Point Percentage</td>
<td>Player impact to team/opponent 3P%</td>
</tr>
<tr>
<td style="text-align: center">aEFG | aDEFG</td>
<td>Adjusted (Defensive) Effective Field Goal Percentage</td>
<td>Player impact to team/opponent EFG%</td>
</tr>
<tr>
<td style="text-align: center">a3PAr | aD3PAr</td>
<td>Adjusted (Defensive) Three Point Attempt Rate</td>
<td>Player impact to team/opponent 3PAr</td>
</tr>
<tr>
<td style="text-align: center">aFTr | aDFTr</td>
<td>Adjusted (Defensive) Free Throw Rate</td>
<td>Player impact to team/opponent FTr</td>
</tr>
<tr>
<td style="text-align: center">aORB | aDRB</td>
<td>Adjusted Offensive|Defensive Rebounds</td>
<td>Player impact to team ORB%/DRB%</td>
</tr>
<tr>
<td style="text-align: center">aAST | aASTA</td>
<td>Adjusted Assists (Against)</td>
<td>Player impact to team/opponent AST%</td>
</tr>
<tr>
<td style="text-align: center">aSTL | aSTLA</td>
<td>Adjusted Steals (Against)</td>
<td>Player impact to team/opponent STL%</td>
</tr>
<tr>
<td style="text-align: center">aBLK | aBLKA</td>
<td>Adjusted Blocks (Against)</td>
<td>Player impact to team/opponent BLK%</td>
</tr>
<tr>
<td style="text-align: center">aTOV | aTOVA</td>
<td>Adjusted Turnovers (Against)</td>
<td>Player impact to team/opponent TOV%</td>
</tr>
<tr>
<td style="text-align: center">aPF | aPFD</td>
<td>Adjusted Personal Fouls (Drawn)</td>
<td>Player impact to team/opponent PF%</td>
</tr>
<tr>
<td style="text-align: center">aOPACE | aDPACE</td>
<td>Adjusted Offensive|Defensive Pace</td>
<td>Player impact to team/opponent PACE</td>
</tr>
</tbody>
</table>
<h2 id="bayesian-prior">Bayesian Prior</h2>
<p>Similar to <a href="/2019/05/03/ncaaw-rapm.html">Bayesian RAPM</a>, I incorporated Bayesian priors to improve reliability, stability, and general performance. The RAPM-style calculations being performed all include an offensive and defensive component (e.g. ORB|DRB, BLK|BLKA, 3PAr|D3PAr). Many of the components have an obvious prior that you can assign for each player (e.g. ORB%, DRB%, 3PAr), however others don't have readily available statistics (e.g. BLKA, D3PAr). Typically, each RAPM calculation is able to utilize a prior for at least one of the two components. PACE is the only calculation which doesn't utilize any prior. Below you can see a list of the priors being used (coefficients based on results from corresponding "vanilla" RAPM-style calculation).</p>
<table>
<thead>
<tr>
<th>Stat</th>
<th>Prior</th>
<th>Coefficient</th>
<th>Intercept</th>
</tr>
</thead>
<tbody>
<tr>
<td>aFGP</td>
<td>FGP%</td>
<td>0.029391</td>
<td>-0.011547</td>
</tr>
<tr>
<td>aFG3P</td>
<td>3P%</td>
<td>0.01857</td>
<td>-0.00603</td>
</tr>
<tr>
<td>aEFG</td>
<td>eFG%</td>
<td>0.037284</td>
<td>-0.017261</td>
</tr>
<tr>
<td>a3PAr</td>
<td>3PAr%</td>
<td>4.907318</td>
<td>-1.696262</td>
</tr>
<tr>
<td>aFTr</td>
<td>FTr%</td>
<td>3.729186</td>
<td>-1.297644</td>
</tr>
<tr>
<td>aORB</td>
<td>ORB%</td>
<td>0.083874</td>
<td>-0.394939</td>
</tr>
<tr>
<td>aDRB</td>
<td>DRB%</td>
<td>0.028404</td>
<td>-0.262161</td>
</tr>
<tr>
<td>aAST</td>
<td>AST%</td>
<td>0.024444</td>
<td>-0.295840</td>
</tr>
<tr>
<td>aSTL</td>
<td>STL%</td>
<td>0.206034</td>
<td>-0.372796</td>
</tr>
<tr>
<td>aBLK</td>
<td>BLK%</td>
<td>0.080668</td>
<td>-0.128338</td>
</tr>
<tr>
<td>aTOV</td>
<td>TOV%</td>
<td>0.041269</td>
<td>-0.827779</td>
</tr>
<tr>
<td>aPF</td>
<td>PF%</td>
<td>0.058135</td>
<td>-0.353120</td>
</tr>
</tbody>
</table>
<h2 id="results">Results</h2>
<p>Below you can view players with the highest and lowest values across the different stats (going back to 2010). These results are currently filtered only to players who were selected in a NBA draft. Leading up to the 2019 draft, I will hope to share similar insight on 2019 draftees from these innovative stats - follow me on <a href="https://twitter.com/jessefischer33">Twitter</a> to hear more. Lastly, I am very excited to incorporate these innovative stats into my NBA draft model (results coming soon!).</p>
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<p><select id="stat_type" onchange="document.getElementById('stat').innerHTML = table_text[this.value]">
<option value="aFGP">aFGP (Adjusted Field Goal Percentage)</option><option value="aDFGP">aDFGP (Adjusted Defensive Field Goal Percentage)</option>
<option value="aFG3P">aFG3P (Adjusted Three Point Percentage)</option><option value="aDFG3P">aDFG3P (Adjusted Defensive Three Point Percentage)</option>
<option value="aEFG">aEFG (Adjusted Effective Field Goal Percentage)</option><option value="aDEFG">aDEFG (Adjusted Defensive Effective Field Goal Percentage)</option>
<option value="a3PAr">a3PAr (Adjusted Three Point Attempt Rate)</option><option value="aD3PAr">aD3PAr (Adjusted Defensive Three Point Attempt Rate)</option>
<option value="aFTr">aFTr (Adjusted Free Throw Rate)</option><option value="aDFTr">aDFTr (Adjusted Defensive Free Throw Rate)</option>
<option value="aORB">aORB (Adjusted Offensive Rebounds)</option><option value="aDRB">aDRB (Adjusted Defensive Rebounds)</option>
<option value="aAST">aAST (Adjusted Assists)</option><option value="aASTA">aASTA (Adjusted Assists Against)</option>
<option value="aSTL">aSTL (Adjusted Steals)</option><option value="aSTLA">aSTLA (Adjusted Steals Against)</option>
<option value="aBLK">aBLK (Adjusted Blocks)</option><option value="aBLKA">aBLKA (Adjusted Blocks Against)</option>
<option value="aTOV">aTOV (Adjusted Turnovers)</option><option value="aTOVA">aTOVA (Adjusted Turnovers Against)</option>
<option value="aPF">aPF (Adjusted Personal Fouls)</option><option value="aPFD">aPFD (Adjusted Personal Fouls Drawn)</option>
<option value="aOPACE">aOPACE (Adjusted Offensive Pace)</option><option value="aDPACE">aDPACE (Adjusted Defensive Pace)</option>
</select></p>
<table id="stat" class="stats"><thead><tr style="text-align: right;"><th>Name</th><th>College</th><th>Year</th><th>aFGP</th><th>FG%</th></tr></thead><tbody><tr><td>TJ Leaf</td><td>UCLA</td><td>2017</td><td>0.035</td><td>0.617</td></tr><tr><td>Georges Niang</td><td>Iowa State</td><td>2013</td><td>0.033</td><td>0.515</td></tr><tr><td>Georges Niang</td><td>Iowa State</td><td>2016</td><td>0.033</td><td>0.546</td></tr><tr><td>Donte DiVincenzo</td><td>Villanova</td><td>2018</td><td>0.031</td><td>0.481</td></tr><tr><td>Jakob Poeltl</td><td>Utah</td><td>2015</td><td>0.031</td><td>0.681</td></tr><tr><td>Will Barton</td><td>Memphis</td><td>2012</td><td>0.031</td><td>0.509</td></tr><tr><td>Larry Nance</td><td>Wyoming</td><td>2014</td><td>0.03</td><td>0.544</td></tr><tr><td>T.J. Warren</td><td>NC State</td><td>2013</td><td>0.03</td><td>0.622</td></tr><tr><td>Justise Winslow</td><td>Duke</td><td>2015</td><td>0.03</td><td>0.486</td></tr><tr><td>Anthony Davis</td><td>Kentucky</td><td>2012</td><td>0.029</td><td>0.623</td></tr><tr><td>Marcus Morris</td><td>Kansas</td><td>2011</td><td>0.029</td><td>0.57</td></tr><tr><td>Doug McDermott</td><td>Creighton</td><td>2012</td><td>0.029</td><td>0.601</td></tr><tr><td>Rondae Hollis-Jefferson</td><td>Arizona</td><td>2015</td><td>0.029</td><td>0.502</td></tr><tr><td>Justin Patton</td><td>Creighton</td><td>2017</td><td>0.028</td><td>0.676</td></tr><tr><td>Robert Williams</td><td>Texas A&M</td><td>2018</td><td>0.028</td><td>0.632</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td></tr><tr><td>Kentavious Caldwell-Pope</td><td>Georgia</td><td>2012</td><td>-0.007</td><td>0.396</td></tr><tr><td>Sindarius Thornwell</td><td>South Carolina</td><td>2015</td><td>-0.007</td><td>0.34</td></tr><tr><td>George King</td><td>Colorado</td><td>2014</td><td>-0.007</td><td>0.282</td></tr><tr><td>Tony Carr</td><td>Penn State</td><td>2017</td><td>-0.008</td><td>0.377</td></tr><tr><td>Melvin Frazier</td><td>Tulane</td><td>2016</td><td>-0.008</td><td>0.401</td></tr><tr><td>Nate Wolters</td><td>South Dakota State</td><td>2010</td><td>-0.008</td><td>0.381</td></tr><tr><td>Isaiah Cousins</td><td>Oklahoma</td><td>2013</td><td>-0.009</td><td>0.279</td></tr><tr><td>Josh Richardson</td><td>Tennessee</td><td>2012</td><td>-0.009</td><td>0.353</td></tr><tr><td>Josh Selby</td><td>Kansas</td><td>2011</td><td>-0.009</td><td>0.373</td></tr><tr><td>Grant Jerrett</td><td>Arizona</td><td>2013</td><td>-0.01</td><td>0.409</td></tr><tr><td>Frank Kaminsky</td><td>Wisconsin</td><td>2012</td><td>-0.01</td><td>0.411</td></tr><tr><td>Johnny OBryant</td><td>LSU</td><td>2012</td><td>-0.013</td><td>0.399</td></tr><tr><td>George King</td><td>Colorado</td><td>2016</td><td>-0.013</td><td>0.446</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2012</td><td>-0.014</td><td>0.337</td></tr><tr><td>Abdel Nader</td><td>Northern Illinois</td><td>2013</td><td>-0.018</td><td>0.337</td></tr></tbody></table>
How accurate are advanced stat estimates?http://tothemean.com/2019/05/26/estimated-advanced-stats.html2019-05-26T00:00:00Z2019-05-27T23:59:04-07:00Jesse Fischer<script>
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<p><em>Who was a better shot blocker in 2019 - <a href="https://www.sports-reference.com/cbb/players/tacko-fall-1.html">Tacko Fall</a> or <a href="https://www.sports-reference.com/cbb/players/tariq-owens-1.html">Tariq Owens</a>?</em></p>
<p>If you look at total blocks, then you might say Tariq was better (85 vs. 92). However, if you instead looked at BPG (2.6 vs. 2.4) or BLK/40 (4.1 vs. 3.8), then you might say Tacko was better.</p>
<p>As an advanced stat geek you know those numbers have caveats and you will likely check out block percentage instead. After visiting your <a href="https://www.sports-reference.com/cbb/play-index/psl_finder.cgi?request=1&amp;match=single&amp;year_min=2019&amp;class_is_fr=Y&amp;class_is_so=Y&amp;class_is_jr=Y&amp;class_is_sr=Y&amp;pos_is_g=Y&amp;pos_is_gf=Y&amp;pos_is_f=Y&amp;pos_is_fg=Y&amp;pos_is_fc=Y&amp;pos_is_c=Y&amp;pos_is_cf=Y&amp;games_type=A&amp;c1stat=mp&amp;c1comp=gt&amp;c1val=100&amp;order_by=blk_pct">favorite NCAA stats site</a> will see that Tacko had a BLK% of 11.5% compared to 12.1% for Tariq. At this point you can now authoritatively declare Tariq Owens as the better shot blocker in 2019!</p>
<p><em>But wait…I'm now here to tell you that there is a bit more to this story…</em></p>
<p>It turns out that many NCAA and NBA advanced stats are actually <em>estimates</em> and not true calculations.</p>
<hr />
<h2 id="how-to-calculate-actual-advanced-stats">How to calculate "actual" advanced stats?</h2>
<p>The grueling process of <a href="/2018/10/05/ncaa-rapm.html">converting play-by-play data into "stint data"</a> is hugely valuable. Beyond enabling <a href="/2019/04/27/ncaa-rapm.html">RAPM to be calculated</a>, this data can also be used to authoritatively calculate common advanced stats (i.e. ORB%, BLK%, AST%) instead of <a href="https://www.basketball-reference.com/about/glossary.html">relying on estimates</a>.</p>
<p>Having already <a href="/2019/04/27/ncaa-rapm.html">done the hard part</a>, I thought it would be interesting to compare how close the estimated versions of these metrics align with actual calculations.</p>
<hr />
<h2 id="how-much-do-estimated-advanced-stats-differ">How much do "estimated" advanced stats differ?</h2>
<p>Generally speaking, the estimated versions of these statistics align quite closely with the actual measurements<sup id="fnref:1"><a href="#fn:1" class="footnote">1</a></sup>. As you can see below, the <a href="https://en.wikipedia.org/wiki/Pearson_correlation_coefficient">correlation</a> between <a href="https://www.basketball-reference.com/about/glossary.html">estimated</a> and actual is > 0.98 across all metrics<sup id="fnref:2"><a href="#fn:2" class="footnote">2</a></sup>.</p>
<p><select id="stat_type" onchange="document.getElementById('stat').src = stat_images[document.getElementById('stat_type').value]; document.getElementById('stat_a').href = stat_images[document.getElementById('stat_type').value]">
<option value="ast">ast</option>
<option value="blk">blk</option>
<option value="drb">drb</option>
<option value="orb">orb</option>
<option value="stl">stl</option>
<option value="usg">usg</option>
</select></p>
<p><a href="/images/estimated_stats/estimated_actual_ast.png" id="stat_a"><img src="/images/estimated_stats/estimated_actual_ast.png" id="stat" /></a></p>
<table>
<thead>
<tr>
<th>Stat</th>
<th style="text-align: center">Correlation</th>
</tr>
</thead>
<tbody>
<tr>
<td>AST% </td>
<td style="text-align: center">0.992</td>
</tr>
<tr>
<td>BLK%</td>
<td style="text-align: center">0.996</td>
</tr>
<tr>
<td>DRB%</td>
<td style="text-align: center">0.982</td>
</tr>
<tr>
<td>ORB%</td>
<td style="text-align: center">0.995</td>
</tr>
<tr>
<td>STL%</td>
<td style="text-align: center">0.995</td>
</tr>
<tr>
<td>USG%</td>
<td style="text-align: center">0.992</td>
</tr>
</tbody>
</table>
<hr />
<h2 id="when-do-estimated-statistics-differ-from-actual">When do "estimated" statistics differ from "actual"?</h2>
<p>After digging into discrepancies, a handful of common patterns showed up. Before sharing these insights, let me first refresh your memory on the definitions for these advanced stats.</p>
<table>
<thead>
<tr>
<th>Stat</th>
<th>Definition</th>
</tr>
</thead>
<tbody>
<tr>
<td>AST% </td>
<td><small><font face="monospace">100 * AST / (((MP / (Tm MP / 5)) * Tm FG) - FG)</font></small></td>
</tr>
<tr>
<td>BLK%</td>
<td><small><font face="monospace">100 * (BLK * (Tm MP / 5)) / (MP * (Opp FGA - Opp 3PA))</font></small></td>
</tr>
<tr>
<td>DRB%</td>
<td><small><font face="monospace">100 * (DRB * (Tm MP / 5)) / (MP * (Tm DRB + Opp ORB))</font></small></td>
</tr>
<tr>
<td>ORB%</td>
<td><small><font face="monospace">100 * (ORB * (Tm MP / 5)) / (MP * (Tm ORB + Opp DRB))</font></small></td>
</tr>
<tr>
<td>STL%</td>
<td><small><font face="monospace">100 * (STL * (Tm MP / 5)) / (MP * Opp Poss)</font></small></td>
</tr>
<tr>
<td>USG%</td>
<td><small><font face="monospace">100 * ((FGA + 0.44 * FTA + TOV) * (Tm MP / 5)) / (MP * (Tm FGA + 0.44 * Tm FTA + Tm TOV))</font></small></td>
</tr>
</tbody>
</table>
<hr />
<h3 id="individual-players-impact-team-pace">1. Individual players impact team pace</h3>
<p>As you can see above, the denominator of these metrics all include overall team statistics weighted by the portion of minutes a player played. This assumes that team statistics are distributed evenly over time, which isn't always the case.</p>
<p>Bench players are often asked to milk the clock in a blowout. The coach might ask a specific player to push the pace. When a talented big man enters the game, the offense may slow down and work the ball inside.</p>
<p>An individual player can impact the pace on the defensive side as well. Dynamic defenders can speed up the game with turnovers and fast break points. On the other hand, a top tier defender or shot blocker can slow the game down by making it more difficult on the offense to find a good shot. It turns out that Tacko is one of those players!</p>
<p>Using stint data, I was able to calculate the average length of possession for all possessions that a player was on the court for. Below shows possession stats for the <a href="https://www.sports-reference.com/cbb/schools/central-florida/2019.html">2019 UCF Knights</a> (sorted by minutes played):</p>
<table>
<thead>
<tr>
<th>Player</th>
<th style="text-align: center">Off Poss (sec) </th>
<th style="text-align: center">Def Poss (sec) </th>
<th style="text-align: center">Off Pace </th>
<th style="text-align: center">Def Pace</th>
</tr>
</thead>
<tbody>
<tr>
<td>B.J. Taylor</td>
<td style="text-align: center">18.1</td>
<td style="text-align: center">18.1</td>
<td style="text-align: center">66.3</td>
<td style="text-align: center">66.3</td>
</tr>
<tr>
<td>Aubrey Dawkins</td>
<td style="text-align: center">18.1</td>
<td style="text-align: center">18.1</td>
<td style="text-align: center">66.3</td>
<td style="text-align: center">66.3</td>
</tr>
<tr>
<td>Terrell Allen</td>
<td style="text-align: center">18.2</td>
<td style="text-align: center">18.2</td>
<td style="text-align: center">65.9</td>
<td style="text-align: center">65.9</td>
</tr>
<tr>
<td>Tacko Fall</td>
<td style="text-align: center"><strong>18.7</strong></td>
<td style="text-align: center"><strong>18.8</strong></td>
<td style="text-align: center"><strong>64.2</strong></td>
<td style="text-align: center"><strong>63.8</strong></td>
</tr>
<tr>
<td>Collin Smith</td>
<td style="text-align: center">18.3</td>
<td style="text-align: center">18.3</td>
<td style="text-align: center">65.6</td>
<td style="text-align: center">65.6</td>
</tr>
<tr>
<td>Chad Brown</td>
<td style="text-align: center">18.0</td>
<td style="text-align: center">17.9</td>
<td style="text-align: center">66.7</td>
<td style="text-align: center">67.0</td>
</tr>
<tr>
<td>Dayon Griffin</td>
<td style="text-align: center">17.6</td>
<td style="text-align: center">18.0</td>
<td style="text-align: center">68.2</td>
<td style="text-align: center">66.7</td>
</tr>
<tr>
<td>Frank Bertz</td>
<td style="text-align: center">17.5</td>
<td style="text-align: center">17.4</td>
<td style="text-align: center">68.6</td>
<td style="text-align: center">69.0</td>
</tr>
<tr>
<td>Ceasar DeJesus</td>
<td style="text-align: center">17.5</td>
<td style="text-align: center">17.5</td>
<td style="text-align: center">68.6</td>
<td style="text-align: center">68.6</td>
</tr>
</tbody>
</table>
<p><br />As you can see, when Tacko was in the game the UCF pace slowed greatly on both ends of the court. This means that advanced stats that rely on possession estimates (based on minutes played) will credit Tacko for being on the court for more possessions than he actually was. This in turn will artificially lower statistics like BLK%, since shot block opportunities will be overstated.</p>
<hr />
<h3 id="individual-players-change-team-dynamics">2. Individual players change team dynamics</h3>
<p>Beyond just pace, individual players can have a large impact on team strategy and style of play. As you can see below, Tacko also has a huge impact on the opposing team's ability to take and make shots inside the three-point line.</p>
<table>
<thead>
<tr>
<th>Player</th>
<th style="text-align: center">Opp 2PA/FGA </th>
<th style="text-align: center">Opp FG%</th>
</tr>
</thead>
<tbody>
<tr>
<td>B.J. Taylor</td>
<td style="text-align: center">60.8%</td>
<td style="text-align: center">39.8%</td>
</tr>
<tr>
<td>Aubrey Dawkins</td>
<td style="text-align: center">62.3%</td>
<td style="text-align: center">39.4%</td>
</tr>
<tr>
<td>Terrell Allen</td>
<td style="text-align: center">62.3%</td>
<td style="text-align: center">38.7%</td>
</tr>
<tr>
<td>Tacko Fall</td>
<td style="text-align: center"><strong>58.6%</strong></td>
<td style="text-align: center"><strong>37.5%</strong></td>
</tr>
<tr>
<td>Collin Smith</td>
<td style="text-align: center">62.9%</td>
<td style="text-align: center">40.2%</td>
</tr>
<tr>
<td>Chad Brown</td>
<td style="text-align: center">62.8%</td>
<td style="text-align: center">39.1%</td>
</tr>
<tr>
<td>Dayon Griffin</td>
<td style="text-align: center">63.3%</td>
<td style="text-align: center">40.0%</td>
</tr>
<tr>
<td>Frank Bertz</td>
<td style="text-align: center">60.4%</td>
<td style="text-align: center">41.2%</td>
</tr>
<tr>
<td>Ceasar DeJesus</td>
<td style="text-align: center">62.5%</td>
<td style="text-align: center">43.7%</td>
</tr>
</tbody>
</table>
<p><br />With opponents having a lower proportion of 2PA with Tacko on the court, it is incorrect to distribute UCF's total opponent 2PA evenly by minutes played. This credits Tacko for a higher number of opponents 2PA than actuality, which will artificially lower his BLK%. Not all players will have as large of an impact on the game as Tacko, but any shift in team dynamics can result in unrealized biases in estimated advanced stats.</p>
<hr />
<h3 id="players-with-less-playing-time-have-less-influence-on-team-totals">3. Players with less playing time have less influence on team totals</h3>
<p>In the examples above, we can see that statistical totals for a team are not always reflective of team statistics during the time that a player was on the court. This is especially true for bench players who have less playing time. This is also true for players who suffer injuries during the season. A great example of this is <a href="https://www.sports-reference.com/cbb/players/kyrie-irving-1/gamelog/2011">Kyrie Irving</a> who played in only 11 out of 37 of games for the <a href="https://www.sports-reference.com/cbb/schools/duke/2011.html">2011 Duke Blue Devils</a>. Kyrie is a high impact player so this is an especially interesting use case to examine. In particular, Kyrie's estimated AST% was noticeably lower than his actual AST%.</p>
<p>With a high usage rate (26.4%), the number of FGM/40 by Kyrie's teammates was much lower when he was on the court (i.e. 24.3 FGM/game when he played vs. 27.6 when he didn't). This is partly due to Kyrie contributing lots of scoring himself (5 FGM/game). With Kyrie missing a large portion of the season, his teammates FGM/40 across the season more closely matched the latter. Kyrie's estimated AST% was impacted by this discrepancy because it is assuming a larger number of assist opportunities (teammate FGM) than he had in reality.</p>
<table>
<thead>
<tr>
<th>Kyrie</th>
<th style="text-align: center"># Games </th>
<th style="text-align: center">Kyrie FGM </th>
<th style="text-align: center">Teammate FGM </th>
<th style="text-align: center">Team AST%</th>
</tr>
</thead>
<tbody>
<tr>
<td>Kyrie Played </td>
<td style="text-align: center">11</td>
<td style="text-align: center">5.0</td>
<td style="text-align: center">24.3</td>
<td style="text-align: center">53.3%</td>
</tr>
<tr>
<td>Kyrie DNP</td>
<td style="text-align: center">26</td>
<td style="text-align: center">0.0</td>
<td style="text-align: center">27.6</td>
<td style="text-align: center">49.0%</td>
</tr>
</tbody>
</table>
<p><br />As hinted at, Kyrie's actual AST% was higher than his estimated AST%:</p>
<table>
<thead>
<tr>
<th>Player</th>
<th style="text-align: center">AST% (actual) </th>
<th style="text-align: center">AST% (estimated) </th>
<th style="text-align: center">Diff</th>
</tr>
</thead>
<tbody>
<tr>
<td>Kyrie Irving</td>
<td style="text-align: center">32.4%</td>
<td style="text-align: center">29.8%</td>
<td style="text-align: center">2.6</td>
</tr>
</tbody>
</table>
<p><br />We must remember that overall team statistics may not generalize as well for players with less playing time. Low-minute but high-impact players are ones to be especially mindful of.</p>
<hr />
<h3 id="efficiency-impacts-opportunities">4. Efficiency impacts opportunities</h3>
<p>More effective defensive players will create more defensive rebound opportunities (i.e. more missed shots). If we look at the <a href="https://www.sports-reference.com/cbb/schools/michigan/2018.html">2018 Michigan Wolverines</a>, we can see <a href="https://www.sports-reference.com/cbb/players/jon-teske-1.html">Jon Teske</a> and <a href="https://www.sports-reference.com/cbb/players/moritz-wagner-1.html">Moritz Wagner</a> on different ends of the spectrum. When Teske was on the court, opponents were held to a 37.8%(!) FG%. While on the other hand, opponents shot 45.4% when Wagner was on the court. These differences in efficiency have a non-trivial impact on the number of DRB opportunities. The more-efficient Teske actually has an overstated estimated DRB% because he had more opportunities for defensive rebounds that his estimated numbers would suggest, with the inverse being true for Wagner.</p>
<table>
<thead>
<tr>
<th>Player</th>
<th style="text-align: center">Opp FG% </th>
<th style="text-align: center">DRB% (actual) </th>
<th style="text-align: center">DRB% (estimated) </th>
<th style="text-align: center">Diff</th>
</tr>
</thead>
<tbody>
<tr>
<td>Moritz Wagner</td>
<td style="text-align: center"><strong>45.4%</strong></td>
<td style="text-align: center"><strong>26.9%</strong></td>
<td style="text-align: center"><strong>24.7%</strong></td>
<td style="text-align: center"><strong>2.2</strong></td>
</tr>
<tr>
<td>Isaiah Livers</td>
<td style="text-align: center">45.1%</td>
<td style="text-align: center">12.4%</td>
<td style="text-align: center">11.4%</td>
<td style="text-align: center">1.0</td>
</tr>
<tr>
<td>Zavier Simpson</td>
<td style="text-align: center">44.3%</td>
<td style="text-align: center">13.6%</td>
<td style="text-align: center">12.8%</td>
<td style="text-align: center">0.8</td>
</tr>
<tr>
<td>Charles Matthews</td>
<td style="text-align: center">43.3%</td>
<td style="text-align: center">18.1%</td>
<td style="text-align: center">17.0%</td>
<td style="text-align: center">1.1</td>
</tr>
<tr>
<td>Muhammad-Ali Abdur-Rahkman</td>
<td style="text-align: center">43.1%</td>
<td style="text-align: center">11.7%</td>
<td style="text-align: center">11.0%</td>
<td style="text-align: center">0.7</td>
</tr>
<tr>
<td>Duncan Robinson</td>
<td style="text-align: center">41.3%</td>
<td style="text-align: center">9.0%</td>
<td style="text-align: center">9.2%</td>
<td style="text-align: center">-0.2</td>
</tr>
<tr>
<td>Jordan Poole</td>
<td style="text-align: center">40.5%</td>
<td style="text-align: center">12.3%</td>
<td style="text-align: center">12.7%</td>
<td style="text-align: center">-0.4</td>
</tr>
<tr>
<td>Eli Brooks</td>
<td style="text-align: center">39.5%</td>
<td style="text-align: center">9.8%</td>
<td style="text-align: center">9.3%</td>
<td style="text-align: center">0.5</td>
</tr>
<tr>
<td>Ibi Watson</td>
<td style="text-align: center">38.3%</td>
<td style="text-align: center">8.3%</td>
<td style="text-align: center">8.9%</td>
<td style="text-align: center">-0.6</td>
</tr>
<tr>
<td>Jaaron Simmons</td>
<td style="text-align: center">38.0%</td>
<td style="text-align: center">8.4%</td>
<td style="text-align: center">9.1%</td>
<td style="text-align: center">-0.7</td>
</tr>
<tr>
<td>Jon Teske</td>
<td style="text-align: center"><strong>37.8%</strong></td>
<td style="text-align: center"><strong>16.6%</strong></td>
<td style="text-align: center"><strong>18.6%</strong></td>
<td style="text-align: center"><strong>-2.0</strong></td>
</tr>
</tbody>
</table>
<p><br />On offense, more efficient offensive players will create less offensive rebound opportunities (i.e. less missed shots). This was apparent for <a href="https://%20https//www.sports-reference.com/cbb/schools/kentucky/2010.html">2010 Kentucky Wildcat</a> starters <a href="https://www.sports-reference.com/cbb/players/patrick-patterson-1.html">Patrick Patterson</a> and <a href="https://www.sports-reference.com/cbb/players/demarcus-cousins-1.html">DeMarcus Cousins</a>. As seen below, Patterson's positive impact on team FG% translates to less ORB opportunities, causing his estimated ORB% to understate his value on the offensive glass.</p>
<table>
<thead>
<tr>
<th>Player</th>
<th style="text-align: center">Team FG% </th>
<th style="text-align: center">ORB% (actual) </th>
<th style="text-align: center">ORB% (estimated) </th>
<th style="text-align: center">Diff</th>
</tr>
</thead>
<tbody>
<tr>
<td>Daniel Orton</td>
<td style="text-align: center">49.4%</td>
<td style="text-align: center">10.6%</td>
<td style="text-align: center">10.3%</td>
<td style="text-align: center">0.3</td>
</tr>
<tr>
<td>Patrick Patterson</td>
<td style="text-align: center"><strong>49.0%</strong></td>
<td style="text-align: center"><strong>11.3%</strong></td>
<td style="text-align: center"><strong>10.6%</strong></td>
<td style="text-align: center"><strong>0.7</strong></td>
</tr>
<tr>
<td>Darius Miller</td>
<td style="text-align: center">48.9%</td>
<td style="text-align: center">5.0%</td>
<td style="text-align: center">4.7%</td>
<td style="text-align: center">0.3</td>
</tr>
<tr>
<td>John Wall</td>
<td style="text-align: center">48.7%</td>
<td style="text-align: center">2.7%</td>
<td style="text-align: center">2.7%</td>
<td style="text-align: center">0.0</td>
</tr>
<tr>
<td>Eric Bledsoe</td>
<td style="text-align: center">48.5%</td>
<td style="text-align: center">2.0%</td>
<td style="text-align: center">1.9%</td>
<td style="text-align: center">0.1</td>
</tr>
<tr>
<td>DeMarcus Cousins</td>
<td style="text-align: center"><strong>47.3%</strong></td>
<td style="text-align: center"><strong>19.0%</strong></td>
<td style="text-align: center"><strong>19.8%</strong></td>
<td style="text-align: center"><strong>-0.8</strong></td>
</tr>
<tr>
<td>Darnell Dodson</td>
<td style="text-align: center">46.8%</td>
<td style="text-align: center">3.4%</td>
<td style="text-align: center">3.6%</td>
<td style="text-align: center">-0.2</td>
</tr>
<tr>
<td>DeAndre Liggins</td>
<td style="text-align: center">44.9%</td>
<td style="text-align: center">4.6%</td>
<td style="text-align: center">4.6%</td>
<td style="text-align: center">-0.0</td>
</tr>
</tbody>
</table>
<p><br />Every player has their own unique impact on offensive and defensive FG%. If there are significant efficiency differences within a team, this can have noticeable impact on rebound opportunities which can throw off rebound percentage estimates.</p>
<hr />
<h2 id="how-much-does-this-matter">How much does this matter?</h2>
<p>While it is interesting to analyze differences between estimated and actual advanced stats, typically the deltas are small and the estimate advanced stats are "good enough". That is unless you need to <em>authoritatively</em> know whether Tacko or Tariq had a better BLK%.</p>
<p>To help you gauge how much this matters, here are observed differences between estimated and actual advanced stats. To help interpret, this is saying: <em>98% of the time a player's actual AST% will be between 'estimated AST% - 1.72' and 'estimated AST% + 3.66'</em>.</p>
<table>
<thead>
<tr>
<th>Stat (actual vs. estimated)</th>
<th style="text-align: center">p1</th>
<th style="text-align: center">p99</th>
</tr>
</thead>
<tbody>
<tr>
<td>AST% Difference</td>
<td style="text-align: center">-1.72% </td>
<td style="text-align: center">3.66%</td>
</tr>
<tr>
<td>BLK% Difference</td>
<td style="text-align: center">-0.47% </td>
<td style="text-align: center">0.85%</td>
</tr>
<tr>
<td>DRB% Difference</td>
<td style="text-align: center">-2.63% </td>
<td style="text-align: center">2.56%</td>
</tr>
<tr>
<td>ORB% Difference</td>
<td style="text-align: center">-0.91% </td>
<td style="text-align: center">1.40%</td>
</tr>
<tr>
<td>STL% Difference</td>
<td style="text-align: center">-0.16% </td>
<td style="text-align: center">0.35%</td>
</tr>
<tr>
<td>USG% Difference</td>
<td style="text-align: center">-0.99% </td>
<td style="text-align: center">2.50%</td>
</tr>
</tbody>
</table>
<p><br />You can be the judge as to whether or not these differences are large enough for you to care but either way <strong>it is always good to understand weaknesses of your data!</strong></p>
<p>Oh, and in case you were wondering - contrary to popular belief, it turns out that in 2019 Tacko did have a higher <em>actual</em> BLK%!</p>
<table>
<thead>
<tr>
<th>Player</th>
<th style="text-align: center">BLK% (actual) </th>
<th style="text-align: center">BLK% (estimated)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Tacko Fall</td>
<td style="text-align: center">12.6%</td>
<td style="text-align: center">11.5%</td>
</tr>
<tr>
<td>Tariq Owens</td>
<td style="text-align: center">11.7%</td>
<td style="text-align: center">12.1%</td>
</tr>
</tbody>
</table>
<p><br /></p>
<div class="footnotes">
<ol>
<li id="fn:1">
<p>It is worth pointing out that play-by-play data is messy and not always accurate, which means that "stint data" is imperfect as well. Additionally, determining which players are not on the court is not as easy as it sounds, so it is quite possible there are some edge cases which are not handled correctly. However, the fact that the estimated and actual statistics align so closely gives me confidence that data quality is not a major problem and my logic/heuristics are generally correct. It is also worth mentioning that some small differences are due to me the filtering out "garbage time" possessions (which also happens to be the messiest portions of play-by-play data). This filtering is minimal and mostly impacts low minute bench players. <a href="#fnref:1" class="reversefootnote">↩</a></p>
</li>
<li id="fn:2">
<p>This data spans 10 seasons (2010-2019) filtering to all players who played >100 minutes in a season. <a href="#fnref:2" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>