III. Historical Impact: WOWYR, 60 Years of Plus-Minus

In the previous post in this series we introduced the idea of regressing WOWY data — game-by-game plus-minus data — to gauge player impact. In other words, if you looked at all of the activity of players moving in and out lineups over the years, whose team changed the most based on a given player’s presence?

Our previous regression was done using a standard Ordinary Least Squares method, which does a decent job estimating value, but not quite as good as “Ridge Regression” for this data. I don’t want to give you a math-ache, but we can improve this method in the same way that RAPM improved upon APM for regressed play-by-play data.

For the 50’s, 60’s and 70’s, the results are often similar to the OLS version, only this new model performs much better on held-out test data (when we leave a random chunk of data out of the regression and ask the model to predict it). Here are the improved 1954-1983 results using ridge:

PlayerWOWYRGP
Bird7.1355
Robertson..Oscar.6.5986
Moore..Otto.6.1350
Davis..Walter.6.0426
West..Jerry.5.7984
Kenon5.5426
Moore..Johnny.5.4175
Cunningham5.2665
Cartwright5.2326
McMillian..Jim.5.1519
Hill..Armond.4.9259
Schayes..Dolph.4.7551
Lanier4.6751
Thurmond4.6562
Russell..Bill.4.51097
Arizin4.4635
Abdul.Jabbar4.21041
Cheeks4.2535
Dawkins4.2343
Walton..Bill.4.2178
Frazier4.0629
Walk3.9361
Reid..Robert.3.9333
McMahon3.8330
Chamberlain3.71186
Free3.7608
Williams..Gus.3.6461
Jones..KC.3.6428
Toney3.6267
Johnson..Marques.3.6475
Silas..Paul.3.5790
Mix3.4424
Taylor..Brian.3.4238
Gilmore3.4560
Beaty3.3545
npArchibald3.3181
npHayes..Elvin.3.2240
Ray..Cliff.3.2682
McGinnis3.1504
May..Scott.3.1184
Neal..Lloyd.3.1217
Porter..Kevin.3.0489
Smith..Greg.3.0345
Erving2.9775
Robisch2.9196
Owens..Tom.2.9259
DeBusschere2.81026
Weiss2.8341
Barry..Rick.2.8754
Perry..Curtis.2.8416
Dukes2.7463
Hayes..Elvin.2.7934
Johnson..Dennis.2.6528
Counts2.6220
Cousy2.5852
Jones..Bobby.2.5701
Cleamons2.4407
Gola2.4602
Abdul.Aziz2.3256
Hawkins..Connie.2.3378
Marin2.3617
Corzine2.3258
Sloan2.2687
McGlocklin2.2595
Hazzard2.2492
Davis..Johnny.2.1345
Pettit2.1835
Barnett..Dick.2.1933
Jones..Sam.2.1744
Vandeweghe2.0227
Petrie2.0436
Hollins..Lionel.2.0550
Washington..Kermit.2.0334
Nichols2.0193
Yardley2.0452
Skoog2.0179
Baylor2.0934
Murphy..Calvin.1.9685
Carr..Kenny.1.9216
Howell1.9847
Unseld1.9945
Knight..Billy.1.9448
Chaney1.9529
Heinsohn1.8818
Shumate1.8200
Gale1.8331
Paultz1.8394
Havlicek1.71264
Boozer..Bob.1.7624
Brewer..Jim.1.7179
Ford..Chris.1.6681
Twyman1.6770
Parish1.6379
Williams..Ray.1.6402
Cowens1.5568
Thompson..Mychal.1.5254
Smith..Phil.1.5497
Jackson..Luke.1.5299
Sharman1.5585
Bing1.4821
Adams..Alvan.1.4742
Kojis1.4419
Bradley..Bill.1.4624
Attles1.4492
Moncrief1.4250
Smith..Elmore.1.4447
Kerr..Red.1.4863
Bellamy1.4951
Gross1.4440
Caldwell..Joe.1.4345
Issel1.4515
Green..Si.1.4268
Dantley1.3304
Buckner1.3384
Dunn1.3175
McCarthy1.3221
Roberson..Rick.1.3187
Dandridge1.3668
Van.Breda.Kolff1.2236
Johnson..Gus.1.2641
Monroe..Earl.1.2710
Johnson..John.1.2626
Paxson..Jim.1.2247
Mikkelsen1.2400
Sears1.2472
Edwards..James.1.2356
Martin..Slater.1.1461
Barnes..Jim.1.1211
Haywood..Spencer.1.1529
Drew..John.1.1533
Wilkes1.1675
Newlin1.1653
Brown..Fred.1.1670
Collins..Doug.1.1492
Mullins1.1506
Carr..Austin.1.1497
Jones..Dwight.1.0263
Archibald1.0232
Johnston1.0364
Jordon1.0250
Beard1.0249
Hawkins..Tom.1.0218
Chones1.0590
Sikma1.0428
Bridges0.9910
Siegfried0.9349
Benson0.9262
Boerwinkle0.9324
Gilliam..Herm.0.9292
Stokes..Maurice.0.9203
Embry0.9590
Washington..Jim.0.9571
Hagan0.9467
Roundfield0.8461
Robinson..Flynn.0.8268
White..Jo.Jo.0.8673
Smith..Bingo.0.8570
Walker..Chet.0.8938
Bianchi0.8228
Short0.8208
Carroll..Joe.Barry.0.7237
Bridgeman0.7478
Imhoff0.7378
Van.Arsdale..Dick.0.7837
Winters0.6450
Rule0.6305
Meriweather0.6259
Smith..Randy.0.6881
Riordan0.6328
Johnson..Eddie.0.6387
Hairston0.6655
Snyder..Dick.0.6641
Thompson..David.0.6413
Brooks..Michael.0.6246
Van.Lier0.6635
Davis..Brad.0.6217
Nelson..Don.0.5497
Loughery0.5672
Harrison..Bob.0.5228
Greer0.5893
Hetzel0.5193
Adams..Don.0.5330
King..George.0.5224
npCowens0.4192
Braun0.4489
Gray..Leonard.0.4175
Sobers0.4477
Heard0.4495
King..Bernard.0.4349
Guokas0.4268
Ramsey0.3460
Russell..Cazzie.0.3499
Scott..Ray.0.3687
Love..Bob.0.2584
Van.Arsdale..Tom.0.2742
Buse0.2431
Erickson0.2604
Westphal0.2493
Graboski0.2435
Rollins0.1344
Lovellette0.1555
Tyler0.1383
Chenier0.0558
Clark..Archie.0.0579
Grevey0.0274
Steele0.0226
Nixon0.0369
Trevsant-0.1251
Price..Jim.-0.1217
Hudson..Lou.-0.2745
Allen..Lucious.-0.2430
Reed..Willis.-0.3762
Gervin-0.3613
Meschery-0.3637
Scott..Charlie.-0.3418
Maravich-0.3591
Shue-0.4617
Mitchell..Mike.-0.4282
Robinson..Truck.-0.4724
Lacey-0.4215
Costello-0.4643
Richardson..Michael.-0.4278
Wilkens-0.41002
Lee..Clyde.-0.4400
Foust-0.4394
Henderson..Tom.-0.4402
Coleman..Jack.-0.4267
Webster..Marvin.-0.5226
Kelley..Rich.-0.5216
Bantom-0.5465
Malone..Moses.-0.5458
McGuire..Dick.-0.6287
Silas..James.-0.6255
Jones..Wali.-0.6480
Garmaker-0.6379
Natt-0.6316
Stallworth-0.7188
Guerin-0.7812
English-0.8353
Parker..Sonny.-0.8241
Dierking-0.8293
Block-0.9265
Lucas..John.-0.9376
Holland-0.9246
Charles..Ken.-0.9193
Komives-0.9535
Dischinger-0.9351
Smith..Adrian.-0.9318
Williamson..John.-1.0278
Maxwell..Cedric.-1.0453
Poquette-1.0238
Gallatin-1.0299
Goodrich-1.0768
Johnson..Mickey.-1.1608
Lantz-1.1317
Share-1.1405
Leonard..Slick.-1.2395
Lucas..Mo.-1.2594
McAdoo-1.2499
Wilkerson-1.2373
Davis..Jim.-1.2178
Rowe-1.2566
Ellis..Leroy.-1.2898
George..Jack.-1.3384
Greenwood-1.3331
Robinson..Cliff.-1.3178
Hawes..Steve.-1.3304
Shelton-1.3527
Russell..Campy.-1.4515
Theus-1.4334
Brewer..Ron.-1.4330
npGreer-1.4242
Naulls-1.4495
Sauldsberry-1.5279
Davis..Dwight.-1.6234
Nater-1.7278
Leavell-1.7227
Bristow-1.8322
Macauley-1.9379
Barnett..Jim.-1.9465
Adelman-1.9235
Lucas..Jerry.-1.9772
Money-1.9234
Smith..Larry.-2.0203
Kunnert-2.0314
Gianelli-2.1272
Coleman..EC.-2.1268
Neumann-2.2213
Strawder-2.2268
Green..Johnny.-2.2497
Miles..Eddie.-2.2521
Laimbeer-2.2190
Olberding-2.3328
DiGregorio-2.3220
Garrett..Dick.-2.5228
Lloyd..Earl.-2.6376
Carr..ML.-2.6217
Ohl-2.7771
Sanders..Tom.-2.7831
Bryant..Joe.-2.7318
Bibby..Henry.-2.7330
LaRusso-2.7721
Johnson..George.-2.7497
Tomjanovich-2.8687
Gambee-3.0306
Rodgers..Guy.-3.0784
Long..John.-3.4242
Haskins-3.7324
Fox..Jim.-3.8368
Watts-3.9179
Walker..Jimmy.-4.5380
Carter..Fred.-4.6453
Wicks-4.8683
Ballard-4.9316
Huston-5.0214
Jones..Caldwell.-5.6615
Chappell-5.9200
Bockhorn-6.0400
Kauffman-6.8231

Full WOWYR results

After 1984, basketball-reference provides minutes played for each player in every game. Instead of constructing “core lineups” based on season-long minutes per game averages, now we can create the lineups by using the actual minutes played in each game. If we combine all the seasons together and run our regression (with a few conditions discussed below) we can finally make a historical comparison across the last 60-plus seasons.

Below are the full WOWYR results of two models, one which carves out prime years for a player and another that does not. The prime model outperforms the career model, but it’s an interesting comparison nonetheless. (Note that this is not a true measurement of a player’s “prime” compared to his career.) The table is filtered for players with at least 400 qualifying games played.

PlayerPrime WOWYRPrime GPCareer WOWYRCareer GPPrime BeginPrime End
Magic.Johnson10.185710.088919801991
John.Stockton9.89216.5154819881997
David.Robinson9.19266.6107319902001
Michael.Jordan9.011028.2123919851998
Steve.Nash8.89446.0120420012011
Sidney.Moncrief8.65034.167519811986
Dikembe.Mutombo8.58977.1104319922002
LeBron.James8.511057.4118420052016
Robertson..Oscar.8.49868.598619611972
Yao.Ming7.54938.049320032011
West..Jerry.7.49847.398419611973
Paul.Pierce7.211815.7141320002013
LaMarcus.Aldridge7.16956.573620082016
Dirk.Nowitzki7.112565.1143720002014
Reggie.Lewis7.14134.041819891993
Don.Buse7.04736.043119841985
Anfernee.Hardaway6.84784.171519942000
Gary.Payton6.89464.0142419932003
Shaquille.O.Neal6.711245.2136919932006
Marin6.56176.061700
DeAndre.Jordan6.54791.651820112016
Kobe.Bryant6.513584.9148919982013
Dan.Majerle6.58525.796819902000
Russell..Bill.6.410976.2109719581969
Murphy..Calvin.6.36856.968500
Clyde.Drexler6.310525.9115219851997
Bruce.Bowen6.27243.682720012008
Russell.Westbrook6.24966.366120112016
Kareem.Abdul.Jabbar6.212384.1158819701985
Serge.Ibaka6.25508.955020102016
Kevin.Garnett6.213604.4149219972013
Greg.Ballard6.25664.856619841987
Julius.Erving6.110332.9109819721986
Darryl.Dawkins6.14955.549519841987
Barry..Rick.6.17545.275419661978
Bill.Laimbeer6.19386.0107819821991
Doc.Rivers6.06465.475519851994
Chamberlain6.011866.1118619601973
Rasheed.Wallace6.010575.2117119972009
Chris.Ford5.96815.168100
Amir.Johnson5.94285.642820072016
Jim.Paxson5.95323.160519811987
Schayes..Dolph.5.95516.155119541961
DeBusschere5.910265.5102600
McGinnis5.95046.850419761980
Chris.Paul5.88417.184120062016
McMillian..Jim.5.85195.251900
Vlade.Divac5.810615.4111119912004
Hakeem.Olajuwon5.711055.5132819851997
Chauncey.Billups5.79834.2106819992012
Tim.Duncan5.713634.7159519982013
Arizin5.66355.463500
Kevin.Durant5.66501.072820092016
Rasho.Nesterovic5.65236.553020002009
Deron.Williams5.65512.883020072013
Winters5.54504.645000
Larry.Johnson5.57505.075019922001
Alvan.Adams5.59694.5100919761987
Bob.Lanier5.48335.875119841984
Otis.Thorpe5.39143.3115119871997
T.R..Dunn5.35415.254119841991
B.J..Armstrong5.35063.556719911997
Dennis.Rodman5.38913.994519881998
Peja.Stojakovic5.37084.282620012010
npJohn.Stockton5.26270.0000
Jeff.Hornacek5.28974.0113719891998
Jones..KC.5.24284.842800
Larry.Nance5.19415.696919831993
Kenon5.14265.242600
Paul.Pressey5.14966.057919851991
Terry.Cummings5.17483.395619831992
Metta.World.Peace5.15901.896320022010
Patrick.Ewing5.010795.6123719861999
Thurmond5.05625.156219651974
Gus.Williams5.07064.770619841987
Charles.Barkley4.910624.1116719861999
Mark.Price4.95472.668919881995
Hersey.Hawkins4.99223.297519891999
Allen.Leavell4.94323.843219841989
Rashard.Lewis4.98505.396220012011
Marc.Gasol4.86124.161220092016
Ray..Cliff.4.76823.268200
Charles.Oakley4.612003.4129919872001
Tony.Parker4.611693.1125120032016
Frazier4.66294.362919681976
Isiah.Thomas4.69730.8102619831993
Eddie.Jones4.58924.396719952006
Cunningham4.56654.566519661975
McGlocklin4.55955.159500
Elden.Campbell4.56192.675419942002
Bryon.Russell4.55323.362619972003
Anthony.Parker4.44364.243620002012
Tracy.McGrady4.46912.484520002009
Theo.Ratliff4.44984.859619982006
Cousy4.48523.985200
Al.Horford4.46314.263120082016
Toni.Kukoc4.46463.474219942003
Chris.Bosh4.48144.196620062016
Chris.Webber4.47354.288319952006
Beaty4.35454.254500
Alonzo.Mourning4.36583.675719932002
Robert.Parish4.312632.6138919791993
Dennis.Johnson4.310883.1115519791989
Adrian.Dantley4.37923.383319771989
Scottie.Pippen4.311294.0131719892001
Zaza.Pachulia4.25153.451520042016
Bernard.King4.27854.479719781991
Raymond.Felton4.26682.374520062014
Antonio.Daniels4.26033.260319982009
Dwight.Howard4.27441.595320062014
Tony.Allen4.24994.549920052016
Artis.Gilmore4.28525.186319721987
Shane.Battier4.27794.596520022011
Jermaine.O.Neal4.16773.178320012010
Derrick.McKey4.17623.489619891998
Larry.Bird4.110455.8104519801992
Clifford.Robinson4.111363.2131219912004
Josh.Howard4.14414.949420052012
Lindsey.Hunter4.06013.264919942004
Nicolas.Batum4.05024.050220092016
Detlef.Schrempf4.08495.4102619891999
Steve.Smith4.07641.588319932002
Mitch.Richmond4.09243.293019892001
Kerry.Kittles3.95374.554419972004
Danny.Ainge3.97933.590619851993
J.R..Smith3.96963.177320072016
Andrew.Toney3.94704.447019841988
Porter..Kevin.3.94893.648900
Klay.Thompson3.94254.642520122016
Latrell.Sprewell3.98173.696519942004
Karl.Malone3.914263.1165319872002
Pettit3.88353.783500
Monta.Ellis3.87363.475320072016
Havlicek3.812643.2126419631976
Bill.Cartwright3.88493.492919801992
Petrie3.84364.043600
Roy.Hibbert3.84763.154020092015
Matt.Barnes3.86181.765720072016
Smith..Phil.3.84972.749700
Alton.Lister3.84704.847019841997
Charles.Smith3.75260.957059775992
Calvin.Natt3.75843.058419841990
Nate.McMillan3.76662.569619871996
Zydrunas.Ilgauskas3.77052.676319982009
Derek.Fisher3.710374.1116019982011
Trevor.Ariza3.76442.969820072016
Andrew.Lang3.74223.542219892000
Frank.Brickowski3.74343.843419851997
Mike.Gminski3.75952.160719811991
Jerome.Kersey3.75792.085019871993
Horace.Grant3.69884.0124919892000
Ben.Wallace3.67224.4101320012008
Billy.Knight3.65072.944819841985
James.Worthy3.67992.691619831992
Kevin.McHale3.67922.690219821991
Walt.Williams3.65474.154719932003
James.Posey3.66992.577520002009
Howell3.68473.784700
Dukes3.64633.446300
Mark.Aguirre3.57862.088019821991
Vince.Carter3.58452.7122220002010
Michael.Adams3.55222.857919881994
Ron.Harper3.55463.499619871994
Baron.Davis3.56962.879720012010
Jack.Sikma3.59933.8104919791990
Andre.Iguodala3.48924.197720062016
David.West3.47723.082820062015
Henderson..Tom.3.44023.640200
Greer3.48932.789300
Bobby.Jones3.48824.689439913994
Fat.Lever3.45070.965819851990
Jason.Kidd3.410472.9152319962008
Danny.Manning3.44492.272019891995
Steve.Francis3.45581.056420002007
Sloan3.46873.768700
Newlin3.46533.265300
Jones..Sam.3.47443.274400
Ray.Williams3.45483.954819841987
Sharman3.45853.158500
Rolando.Blackman3.49074.597419831992
Reggie.Miller3.411902.9148319892002
Jon.Koncak3.34544.145419861996
Ricky.Pierce3.36362.079019861994
Chaney3.35293.552900
Shawn.Kemp3.38005.190119912000
Lamar.Odom3.29113.698520002011
Stacey.Augmon3.26003.961319922004
Elvin.Hayes3.29342.893419691982
Tim.Hardaway3.27451.599040054017
Baylor3.29343.093400
Dale.Davis3.28652.699219932003
Ervin.Johnson3.24852.748519942005
Free3.26082.860800
Kojis3.24193.241900
George.Hill3.25154.454420102016
Kevin.Johnson3.16712.277419891997
Cliff.Levingston3.14494.444919841995
Glen.Rice3.17941.8101640054014
Chris.Dudley3.14263.242619882002
Beno.Udrih3.14162.641620052016
Hedo.Turkoglu3.17723.681220022012
Perry..Curtis.3.14162.641600
Rodney.Rogers3.16432.668119952005
Washington..Jim.3.15713.157100
Udonis.Haslem3.15583.167920052012
Erick.Dampier3.17243.275819982010
Sam.Cassell3.17683.596719962006
James.Donaldson3.17191.972619821992
Smith..Elmore.3.14473.044700
Charlie.Ward3.04512.945119962005
Tyson.Chandler3.07391.788820052015
Mike.Conley3.06602.866020082016
Joe.Johnson3.09802.7119820042015
Moses.Malone3.010162.2116519781990
Jameer.Nelson3.05882.469820062014
Embry3.05902.759000
Gola3.06022.960200
Reggie.Evans3.04402.944020032015
Brent.Barry3.06693.370419962007
Armen.Gilliam3.07241.276019881998
Manu.Ginobili3.05452.595420052011
Rik.Smits2.98063.580619892000
Dan.Roundfield2.96893.768919841987
Sears2.94722.747200
Joakim.Noah2.95172.453620082015
Jared.Dudley2.95042.350420082016
Bellamy2.99512.795100
Mehmet.Okur2.95273.856820042012
Mario.Elie2.96013.164419912000
P.J..Brown2.99474.3105419952006
Shawn.Marion2.911342.6120820012014
Danny.Granger2.94410.954020072012
Chenier2.95582.155800
Carmelo.Anthony2.97932.795820062016
Mike.Bibby2.98633.2104119992009
Marcin.Gortat2.94691.346920082016
Cuttino.Mobley2.97132.476020002009
Haywood..Spencer.2.95292.752900
Jeff.Teague2.84462.944620102016
Graboski2.84352.843500
Luol.Deng2.86444.786520072015
Anthony.Mason2.88441.891219922002
Terrell.Brandon2.84783.159419952002
Johnson..Gus.2.86412.664100
Hollins..Lionel.2.85502.155000
J.J..Redick2.85054.050520072016
Jason.Terry2.810050.4124020012012
Tree.Rollins2.76812.968119841995
Barnett..Dick.2.79332.793300
Mark.Jackson2.711322.4123819882001
Greg.Ostertag2.74122.041219962006
Anderson.Varejao2.74802.348120052015
Kerr..Red.2.78632.486300
Reggie.Williams2.74722.055339984010
Alex.English2.78844.0100519791989
Hazzard2.74922.549200
npGary.Payton2.64780.0000
Kendrick.Perkins2.65803.262120062014
Grant.Hill2.65541.8100819952005
Paul.Millsap2.66383.772920092016
Kenyon.Martin2.67032.778020012011
Mikkelsen2.64002.440000
Twyman2.67702.377000
Boozer..Bob.2.66242.462400
Alvin.Robertson2.65541.972719861992
Gilbert.Arenas2.54862.751920032011
Dennis.Scott2.54832.853619911998
Jalen.Rose2.56030.681319992006
Collins..Doug.2.54922.449200
Michael.Redd2.54872.355720032009
J.R..Reid2.54321.943219902000
Van.Arsdale..Dick.2.58372.283700
Terry.Porter2.57042.4109919871994
Bradley..Bill.2.56242.562400
Aaron.McKie2.55681.859619952004
Brendan.Haywood2.55661.956620022013
Hairston2.56552.365500
Wayne.Cooper2.54343.243419841991
White..Jo.Jo.2.56731.967300
Antonio.Davis2.48282.685119942005
Darren.Collison2.44490.744920102016
Kevin.Willis2.49351.7111919861999
Larry.Drew2.45050.251039994006
Pau.Gasol2.411551.9115520022016
Silas..Paul.2.47900.879000
Meschery2.46371.963700
Jamal.Mashburn2.46511.165119942004
Al.Harrington2.37542.183420022012
Darrell.Walker2.34911.852319851992
Elton.Brand2.36231.296120002008
Rudy.Gay2.36431.570220082016
Truck.Robinson2.37992.872419841985
James.Edwards2.37822.383619781991
Dan.Issel2.35852.164819711984
Yardley2.34522.345200
Kyle.Korver2.38081.982020052016
Lee..Clyde.2.34002.040000
A.C..Green2.39891.5115619871998
Andrew.Bogut2.35972.559720062016
Quentin.Richardson2.35622.661020012010
Brandon.Jennings2.24222.242220102016
Mark.West2.25252.053419851997
Marvin.Williams2.26802.274420072016
Carlos.Boozer2.27770.989520042014
Fred.Brown2.26941.367019841984
Dwyane.Wade2.28481.8100820052015
Love..Bob.2.25842.358400
Devin.Harris2.26052.562620062016
Robert.Horry2.28081.795419932003
Johnny.Davis2.24951.949519841986
Morris.Peterson2.15171.555620012008
Danny.Ferry2.14662.046619912003
npRon.Harper2.14500.0000
npAntonio.McDyess2.15320.0000
Larry.Smith2.16951.869519841993
Raja.Bell2.15761.559120032012
Kevin.Duckworth2.15443.456419881995
George.Gervin2.17573.381819741985
Snyder..Dick.2.06412.064100
Andrei.Kirilenko2.07211.474420022013
Tom.Chambers2.09043.5105119821992
Tony.Battie2.05002.050019982011
Van.Lier2.06351.963500
John.Long2.06192.061919841997
Nene.Hilario2.07192.974520032015
Sherman.Douglas2.05780.860719901999
Jeff.Foster2.04542.445420002011
Andre.Miller2.09242.2118620012011
Xavier.McDaniel2.06552.279319861993
Nick.Anderson1.96881.474019912000
Kyle.Lowry1.94860.360420102016
Boris.Diaw1.95013.089420062011
Mix1.94241.542400
Mullins1.95061.750600
Bo.Outlaw1.95481.155819942004
Walker..Chet.1.99382.093800
Mike.James1.94242.242420032013
Zach.Randolph1.99071.394620042016
Ty.Lawson1.94231.342320102016
Evan.Turner1.94342.343420112016
Carr..Austin.1.94972.049700
Buck.Williams1.911912.6130919821995
Bridges1.99102.191000
Dave.Corzine1.86361.263619841990
Cedric.Maxwell1.87451.874519841988
Bing1.88211.382100
Chones1.85901.659000
Mike.Miller1.85840.981720022010
Craig.Ehlo1.86382.565419871996
Tyreke.Evans1.84171.541720102016
Martin..Slater.1.84611.546100
Unseld1.89451.894500
Eddie.Johnson1.812650.5146839673979
Dale.Ellis1.88250.5102919871997
Heinsohn1.88181.881800
Glenn.Robinson1.86971.871140104020
Jason.Collins1.74612.046120022014
Smith..Bingo.1.75700.357000
Amar.e.Stoudemire1.75970.479420042012
Allen.Iverson1.79510.897819972009
Brevin.Knight1.75130.951319982009
Mychal.Thompson1.77961.681919791990
David.Thompson1.74130.341319761981
Luis.Scola1.75451.554520082016
Ricky.Sobers1.7623-0.462319841986
Kenny.Anderson1.76412.174319932002
Guerin1.78121.481200
Eric.Snow1.76572.769719992007
Mark.Olberding1.75631.356319841987
Stephen.Jackson1.66821.381120032011
Sam.Mitchell1.65901.260719902000
Smith..Randy.1.68811.688100
Luke.Ridnour1.65691.062420052013
Nick.Collison1.65090.551320052015
Loughery1.66721.367200
Stephon.Marbury1.67390.483919982007
Cowens1.65681.756800
Shaun.Livingston1.64050.140520052016
Paul.Westphal1.64933.249319761981
Byron.Scott1.67801.8100319851993
Keith.Van.Horn1.65531.655319982006
Tom.Gugliotta1.65290.764319932000
Anthony.Johnson1.54111.641119982010
Jeff.McInnis1.54301.243019992008
Chris.Mullin1.55380.995619881995
Damon.Stoudamire1.57451.883519962005
Rajon.Rondo1.56501.769720082016
Russell..Cazzie.1.54991.449900
Cleamons1.54071.740700
Brad.Daugherty1.55790.557919871994
Van.Arsdale..Tom.1.57421.474200
John.Starks1.57402.478819922001
Chris.Mills1.45030.550319942003
John.Salley1.45292.954519871995
Rowe1.45661.056600
Wayman.Tisdale1.46761.068919861996
Hagan1.44671.346700
Dana.Barros1.44941.349419902002
Heard1.44951.649500
Tyrone.Hill1.46201.869619932003
Sean.Elliott1.45341.876419911997
Nelson..Don.1.44971.249700
Goran.Dragic1.34081.041720102016
Charles.Jones1.3436-0.145659695986
David.Lee1.35761.363720072014
Joe.Dumars1.39783.4107719871998
Russell..Campy.1.35150.651500
Taj.Gibson1.34171.241720102016
Jarrett.Jack1.3654-0.669620072016
Rick.Mahorn1.37001.374219821991
Komives1.35351.153500
Brad.Davis1.36160.661619841992
Chris.Duhon1.34341.443420052013
Grant.Long1.36951.282719891999
Voshon.Lenard1.34892.048919962006
Tayshaun.Prince1.38651.5103620042013
Johnson..John.1.36260.462600
Gerald.Wallace1.36462.166520052014
Marco.Belinelli1.34001.140020082016
Cliff.Robinson1.35141.651419841989
Chris.Morris1.35441.054419891999
Reed..Willis.1.37620.976200
LaSalle.Thompson1.25081.056019841991
Billy.Owens1.25140.951419922001
Mark.Eaton1.27353.076319841992
Corliss.Williamson1.25230.156819972005
Dominique.Wilkins1.2868-0.2100719841994
Christian.Laettner1.25621.275019932000
John.Drew1.26061.153319841985
Johnny.Newman1.26621.185819891998
Channing.Frye1.24970.849720062016
Vladimir.Radmanovic1.24651.846520022013
Brandon.Bass1.24981.549820062016
Wesley.Person1.25501.859419952003
Richard.Jefferson1.27201.3100820032011
Chris.Childs1.14690.246919952003
Jerry.Stackhouse1.15861.689019962003
Chris.Kaman1.14671.556220052013
Monroe..Earl.1.17101.071000
Clark..Archie.1.15791.157900
Thabo.Sefolosha1.15130.351320072016
Antawn.Jamison1.19641.1104420002012
Robert.Reid1.17460.674619841991
Gerald.Wilkins1.16470.882819871994
Eric.Williams1.14810.648119962006
Mookie.Blaylock1.18430.789319912001
Winston.Garland1.14001.240019881995
Dell.Curry1.16411.171119881999
Sam.Perkins1.19941.2122219851996
George.McCloud1.0469-0.246919902002
Ray.Allen1.011800.9143819982012
Blake.Griffin1.04543.645420112016
Maurice.Cheeks1.011031.4120819801990
Marques.Johnson1.07162.071619841987
Bobby.Jackson1.05011.250119982009
Joe.Smith1.06340.480019962005
Ramsey1.04600.946000
Derek.Anderson1.05140.352019982007
Dandridge1.06681.066800
npChris.Mullin1.04180.0000
Jeff.Malone1.08210.389419851995
Kenny.Thomas1.04931.349320002010
Danny.Schayes1.04640.746419841999
Kirk.Hinrich0.97650.882820042014
Matt.Harpring0.95261.252819992008
Earl.Watson0.95321.053220022013
Purvis.Short0.96180.661819841990
Shandon.Anderson0.94460.144619972006
Rod.Strickland0.97621.094719902000
Shue0.96170.861700
Kiki.Vandeweghe0.97290.572919841993
Brian.Grant0.96490.367319952004
Rod.Higgins0.94351.643519841995
Mo.Williams0.97170.674920052015
npMike.Dunleavy0.98140.0000
George.Lynch0.95140.451419942005
Tim.Thomas0.9593-0.370020002008
Jason.Richardson0.96120.886620042011
Derrick.Coleman0.86500.773719912002
Hot.Rod.Williams0.86691.882519871995
Rickey.Green0.8582-0.258219841992
Scott..Charlie.0.84181.341800
Marcus.Camby0.88070.190419972010
Michael.Finley0.87841.6110519962005
Allen..Lucious.0.74301.543000
Jamaal.Wilkes0.77773.377719841986
Costello0.76430.464300
Raef.LaFrentz0.74591.745919992008
Calbert.Cheaney0.7607-0.363119942004
Vinny.Del.Negro0.74701.155019891998
Steve.Blake0.75050.160820062014
Attles0.74920.949200
Terry.Tyler0.76311.263119841989
Gross0.74401.844000
Lovellette0.75550.655500
George.Johnson0.6583-1.258339693970
Braun0.64890.648900
Chucky.Atkins0.6504-0.050420002010
Leandro.Barbosa0.64721.052320042012
Corey.Brewer0.65050.150520082016
Cedric.Ceballos0.64230.942319912001
Jay.Vincent0.64680.246819841990
James.Harden0.65181.657520112016
Arron.Afflalo0.64951.853620102016
Thaddeus.Young0.65981.664720092016
Antoine.Carr0.65161.252019851998
Richard.Hamilton0.58190.995620012010
Rodney.McCray0.56390.471219851992
John.Wall0.5439-0.243920112016
Kevin.Martin0.55351.062520072015
Kurt.Thomas0.56431.980219992008
Brad.Miller0.56771.172120012010
Josh.Smith0.5724-0.487120072015
Bantom0.54650.346500
Dave.Greenwood0.56910.369119841991
Kevin.Gamble0.54110.841119891997
npTiny.Archibald0.44130.341300
Corey.Maggette0.45970.166320022012
Tyrone.Corbin0.48190.884419871999
Bonzi.Wells0.44461.044620002008
Doug.Christie0.4675-1.377619962004
Erickson0.4604-0.260400
Jason.Williams0.4691-0.573319992008
Roy.Hinson0.4463-0.546319841991
Wally.Szczerbiak0.44981.360220002007
Hudson..Lou.0.4745-0.174500
Caron.Butler0.46710.484520032012
Sleepy.Floyd0.46620.570419841992
Naulls0.44950.049500
Maravich0.45910.359100
Kendall.Gill0.4667-0.487019922001
npManu.Ginobili0.44090.0000
Darrell.Griffith0.45370.853719841991
Darrell.Armstrong0.3548-0.358019972005
Ben.Gordon0.36010.761420052013
Trenton.Hassell0.34900.849020022010
LaRusso0.3721-0.472100
Michael.Cooper0.37670.576719801990
Lucious.Harris0.34180.641819942005
Ruben.Patterson0.2487-0.648719992008
Maurice.Lucas0.27412.886519761985
Derek.Harper0.2817-0.4119119871996
Howard.Eisley0.24380.343819952006
Greg.Anthony0.1422-0.442219922002
Rafer.Alston0.1548-0.456420032010
Bob.McAdoo0.1616-0.261619841986
DeMar.DeRozan0.14730.452120112016
Scott..Ray.0.1687-0.168700
Nick.Van.Exel0.1797-0.685519942004
Kenny.Smith0.16900.370519881996
Jrue.Holiday0.14240.442420102016
Randy.Foye0.1535-0.453520072016
Steve.Kerr0.14710.547119902003
Mike.Woodson0.15520.555219841991
Sedale.Threatt0.0561-0.364419861995
Wilkens0.01002-0.5100200
Jason.Thompson-0.0439-0.443920092016
Vin.Baker-0.04480.170619952000
Lucas..Jerry.-0.0772-0.677200
Vernon.Maxwell-0.0646-0.974119891997
Orlando.Woolridge-0.1643-1.764319831994
Vern.Fleming-0.1622-1.970319851993
Ellis..Leroy.-0.18980.289800
Shawn.Bradley-0.1528-0.354819942003
Isaiah.Rider-0.1509-1.650919942002
npJason.Kidd-0.14760.0000
Lou.Williams-0.1554-1.656320082016
Joe.Barry.Carroll-0.26550.365519841990
Courtney.Lee-0.25260.452620092016
Shelton-0.25270.852700
Junior.Bridgeman-0.26700.467019841987
Avery.Johnson-0.27400.978719922002
Dee.Brown-0.35170.452739984010
Rodney.Stuckey-0.3529-0.252920082016
Juwan.Howard-0.3732-0.198519952004
Lamond.Murray-0.3508-0.550819952006
Anthony.Peeler-0.36010.164819932003
Blue.Edwards-0.35840.358819901998
Ed.Pinckney-0.3412-0.641219861997
Jamal.Crawford-0.3952-0.7104620042016
Rony.Seikaly-0.4621-0.362219891998
Goodrich-0.4768-0.776800
Thurl.Bailey-0.4667-0.778519851992
Mario.Chalmers-0.4578-0.557820092016
Donyell.Marshall-0.4673-0.771019952006
Vinnie.Johnson-0.58230.882319831992
LaPhonso.Ellis-0.5517-0.853419932002
Spud.Webb-0.5537-1.053819861996
Drew.Gooden-0.55960.763420032012
Travis.Best-0.5442-1.244219962005
Jones..Wali.-0.5480-0.748000
David.Wesley-0.57670.486619972006
Sam.Bowie-0.5435-0.043519851995
Wilson.Chandler-0.5417-0.841720082015
Norm.Nixon-0.5593-1.963019781986
Spencer.Hawes-0.5423-1.042320082016
Barnett..Jim.-0.5465-0.846500
Al.Jefferson-0.66320.671820072015
Andrea.Bargnani-0.6451-0.845120072016
Allan.Houston-0.6771-1.781719952004
Samuel.Dalembert-0.6645-1.064620042015
Larry.Hughes-0.6599-1.866220002009
Eric.Gordon-0.6404-1.640420092016
Wesley.Matthews-0.6446-1.251720112016
Brook.Lopez-0.7479-0.947920092016
Brian.Shaw-0.7555-0.665319912001
Lorenzen.Wright-0.75060.052519972006
Willie.Anderson-0.74620.646919891996
Chuck.Person-0.85620.785419871993
Greg.Monroe-0.8439-0.443920112016
Ohl-0.8771-1.477100
Jim.Jackson-0.8791-0.682619942005
Mickey.Johnson-0.9763-0.876319841986
Loy.Vaught-0.9448-1.244819912001
Bryant.Stith-0.9483-0.448319932002
npGrant.Hill-0.94540.0000
Antoine.Walker-1.0815-1.389919972006
Quinn.Buckner-1.04191.238419841986
Bob.Sura-1.0439-1.443919962005
Johnny.Dawkins-1.0418-1.241819871995
Michael.Cage-1.0742-0.288219871996
Kenny.Carr-1.1434-0.743419841987
Shareef.Abdur.Rahim-1.16530.478119972005
Rex.Chapman-1.1565-1.158319891999
Kevin.Edwards-1.1440-0.844019892001
Olden.Polynice-1.1538-1.668119911999
Mike.Mitchell-1.2598-1.559819841988
Share-1.2405-1.340500
John.Bagley-1.2488-1.048819841992
Muggsy.Bogues-1.2667-0.974019881998
Desmond.Mason-1.2555-1.759020022009
Harvey.Grant-1.2459-0.655719901996
Jeff.Green-1.3555-2.862220092016
Rory.Sparrow-1.3673-2.767319841992
Walter.Davis-1.4908-2.892319781991
Rick.Fox-1.46570.774819942003
Hubert.Davis-1.4424-1.542419932003
Carter..Fred.-1.4453-2.345300
Pooh.Richardson-1.4472-1.853019901996
Reggie.Theus-1.4929-0.992919791991
DeShawn.Stevenson-1.4474-0.951820042013
Troy.Murphy-1.4499-1.656220032010
Herb.Williams-1.57720.380919831992
Ramon.Sessions-1.5452-2.045220082016
Caldwell.Jones-1.5885-0.288519841990
Bimbo.Coles-1.6549-1.657619922003
Miles..Eddie.-1.6521-1.552100
Jose.Calderon-1.6580-2.066020082016
Clarence.Weatherspoon-1.6733-1.576319932003
John.Salmons-1.7612-1.468920062015
Ken.Norman-1.7515-1.055719891996
Rasual.Butler-1.7447-2.444720032016
John.Paxson-1.7555-2.056619851993
Emeka.Okafor-1.8570-1.857020052013
Terry.Mills-1.8444-2.344419912000
Benoit.Benjamin-1.9628-1.563319861996
Rodgers..Guy.-2.0784-2.478400
Bill.Hanzlik-2.2406-2.040619841990
Ron.Anderson-2.34410.244119851994
Jay.Humphries-2.3713-2.771319851994
Green..Johnny.-2.5497-2.749700
Sanders..Tom.-2.5831-2.383100
Doug.West-2.5448-2.944819902001
Scott.Skiles-2.6424-3.142419871996
Kelly.Tripucka-2.7558-2.355819841991
Wicks-2.8683-3.268300
O.J..Mayo-3.0521-2.652120092016
Ricky.Davis-3.1575-3.659420022010
Martell.Webster-3.1410-2.041020062015
Mahmoud.Abdul.Rauf-3.5448-2.944819912001
Tomjanovich-4.5687-4.768700

We often talk about the “smell test” in these kinds of metrics, and seeing a collection of MVPs cluster at the top smells like Thanksgiving. Pretty much any tweaking of variables yields the same names at the top (although of the big names, Larry Bird moves around a bit). If we include players with only a few seasons of data, there’s the occasional Otto Moore among the legends, but that’s expected in any regression model, especially when the sample starts to become small.

There’s a lot to talk about here, and in a later post, I’ll dissect these numbers in greater detail. I caution you to hold off on reaching conclusions that are too strong until I lay out the historical nuances in these numbers, but for now, feel free to peruse them using the search function.

The rest of this post will include a lot of math/APBR stuff. A special thanks to the legendary Evan Z, who answered all of my questions related to running penalized regressions. In the next post, I’ll dive into all of these historical numbers and what they mean.

WOWYR Methodology

Lineups

Before 1984: To qualify for a lineup, players needed to play over 25 minutes per game for a team. When only four players on a team averaged over 25 mpg for the season, additional players were included in the “core lineup.” In such cases, players who clustered near 23-24 mpg completed the lineup for a team. (Yes, this means that some teams have lineups with 5 players and some with more.)

Players with fewer than 83 qualifying games in total were converted to “replacement” players. This is different than an RAPM replacement player, who represents someone on the end of the bench. Here, it’s someone who could not make other starting/core units for more than a year’s worth of games. Test-sample accuracy (measured by MSE) improved by converting these players to replacements, which removes a significant amount of noise from the model.

Note: Some early lineups from the 50’s and 60’s were manually constructed and may be missing lineups that only played a few games here and there.

After 1984: After 1984, we have the actual minutes played by each player in each gameTo qualify for a lineup, a player had to play at least 20 minutes in a game. Values ranging from 20-30 minutes were explored, and 20 minutes yielded the best test-sample results.

Most core players will play for 20 minutes in a given night, barring some kind of injury or rare situation in which they have extreme foul trouble. Furthermore, since this is not a per-possession metric, it’s assumed that it’s rare to impact a game by playing in under 40% of its possessions. This also means that when someone plays only a few minutes in a game, he is counted as missing that game.

Because of the change in qualifying criteria, a separate replacement player was created for this era. Test-sample accuracy improved with replacement players set at 82 games. (Again, all postseason games were included.)

Prime vs. Non-Prime Seasons: To improve the performance of the model, players with clear jumps in their play were split into two different players — “prime” and “non-prime” versions of themselves. For example, it treats Kobe Bryant differently in 1996, 2006 and 2016. There will always be a certain amount of “smoothing” across a player’s “regular” years; this is an attempt to trim the extremes on the edges. Young players usually take a year or two to develop, while aging veterans still log minutes despite being completely different versions of themselves (Kevin Garnett says hello).

This division should not be thought of as an attempt to carve out a players “best years.” Instead, the line is often drawn when there are clear jumps in minutes per game.

Players with smooth descents, like Garnett, are slightly harder to differentiate, where there might be a two or three-year period that could qualify as “he’s not the same guy anymore.” Either way, aging is always a tricky thing to control for in multi-year studies, but this is far better than telling the model to treat 37 year-old Vince Carter as the same guy who made eight consecutive All-Star games playing nearly 15 mpg more per night.

Point Differentials

Every unique lineup for a given season has (1) a number of games played and (2) a point differential. The point differential is calculated by taking the season-long SRS of all opponent’s for that lineup and using that as a strength of schedule adjuster, along with three points from home-court advantage.

(This means the “true” opponent quality will not always be captured, in instances where the opponent is fielding a lineup that differs greatly in performance from it’s season-long average SRS. Future versions of WOWYR could pit lineups directly against lineups in the traditional adjusted plus-minus manner.)

The Regression

The regression uses the lineups (as described above), the point differential of the lineup and the number of games played to weight the lineup. (The OLS version was technically Weighted Least Squares.) Weighting uses the inverse of the variance of the number of games played by the lineup.

Variance (based on number of games played by a lineup) was calculated by taking seasons from different consistent core lineups (the same group of players) and then randomly sampling differing numbers of games to create a power function that represents the standard deviation for any number of games.

Standard Deviation = 14.402x-0.6567 where x is the number of games.

Regression used 10-fold cross-validation. Best test results were found using 90% data to train the model and 10% for testing, with a test MSE of 3.0 and RMSE ratio of 1:1 between train and test data.

Future Directions

There are a few key areas to explore in the future. It’s possible using under 20 minutes per game at a game-by-game level might be better. Additionally, the difference in data resolution between pre-1984 and post-1984 (Orwellian data!) means that there might be better ways to blend the models. Additionally, areas like prime seasons could be tweaked.

 

II. Historical Impact: Introducing WOWYR – top players of the 50’s, 60’s & 70’s

So you want to compare the all-time greats but have limited historical data? Not sure what to make of players before the Databall era, when plus-minus wasn’t available and, depending on how far back you go, the box score wasn’t even complete? Don’t worry, you’ve come to the right place.

In the first post in this series, we looked at WOWY data – a simple concept that isolates a player in order to gauge his value by using game-by-game results. But we were left with a fundamental problem — how do we estimate impact for players who weren’t injured or traded? It’s clear Jerry West provided significant lift, but what about someone like Bill Russell? How do we measure his non-box impact?

The answer? Regression, the same statistical method used on play-by-play data in the last few years to create irreplaceable impact metrics like RAPM (Regularized Adjusted Plus-Minus). Since comprehensive play-by-play does not exist before the late ’90’s, WOWYR instead regresses WOWY data, or game-by-game plus-minus data. (It’s better than WOWY, so it’s “wowier,” and stands for “With or Without You Regressed.”)

Evidence Beyond Injuries

WOWY score is almost always predicated on injuries, isolating lineups with-and-without players. But there’s far more evidence in the data beyond that.

First, there is indirect evidence for a player when his teammates leave the lineup. Let’s say we wanted to know how much Scottie Pippen contributed to the Bulls +9 point-differential in the early ’90’s. In 1994, when Michael Jordan left the Bulls, we could infer something about Pippen based on the change caused by Jordan’s absence. How?

If Jordan left and the team remained a +9 team, then it would be fairly safe to infer that Jordan was not the reason the Bulls were +9…which tells us that key remaining players on the team, like Pippen and Horace Grant, were the ones responsible for the large point differential.

WOWY Regression Graphic

Conversely, if Jordan left the Bulls and they unraveled into a -5 team, not only does that say amazing things about MJ but it would mean that the players left behind, like Pippen and Grant, weren’t integral to that +9 differential. Thus, we can make inferences about other players, even when they don’t leave the game-by-game lineup. So while Bill Russell didn’t miss as much time as Jerry West, there’s a bevy of evidence about Russell left by his teammates and all of the time that they miss over the years.

Similarly, when two players leave the lineup, it’s not a pure WOWY instance. But again, we can gain valuable insight here too: If the combination of two players leaving caused a team to fall apart, then we can infer that (a) one of those players was making the team excel, or (b) both of them were. Even though it’s unclear who caused it, it’s yet another piece of evidence that can be incorporated with direct and indirect game-by-game information about a player.

Indeed, regression parses all of these scenarios and provides an answer to how much different players impact the game. The result is a single, points-per-game value that estimates a player’s impact over multiple years.

Introducing WOWYR

Much like the first generation of adjusted plus-minus stats used Ordinary Least Squares (OLS) regression, so does version 1.0 of WOWYR. Follow-up versions will refine the method, but I wanted to start with OLS both for simplicity and so we see standard errors for each player; a smaller standard error indicates less variability in the player’s estimate.

Below are the WOWYR values for every player from 1954-1983 who played at least 450 games. All data is from basketball-reference, however their data changes slightly after 1983, so I’ll be incorporating 1984-present in a future post.

PlayerWOWYRError
Robertson..Oscar.7.51.5
Abdul.Jabbar6.92.3
Russell..Bill.6.42.0
West..Jerry.6.11.2
Cunningham5.91.5
Thurmond5.81.7
Johnson..Marques.5.33.3
Schayes..Dolph.5.32.0
Ray..Cliff.5.32.7
Lanier5.21.2
Chamberlain5.11.3
McMillian..Jim.5.11.4
DeBusschere4.71.9
Arizin4.71.9
Free4.62.0
Hayes..Elvin.4.42.0
Frazier4.34.1
McGinnis4.21.9
Cheeks4.06.5
Jones..Bobby.3.93.1
Smith..Bingo.3.82.9
Gilmore3.72.9
Murphy..Calvin.3.72.1
Silas..Paul.3.51.1
Barry..Rick.3.51.2
Johnson..John.3.41.9
Sloan3.21.7
Barnett..Dick.3.21.3
Greer3.12.8
Porter..Kevin.3.11.2
Marin3.11.1
Erving3.13.0
Dukes3.02.2
Cousy2.91.5
Hazzard2.91.5
McGlocklin2.92.2
Howell2.81.5
Issel2.65.0
Beaty2.61.7
Gola2.61.5
Johnson..Dennis.2.67.2
Mullins2.52.4
Hagan2.52.3
Boozer..Bob.2.41.1
Unseld2.41.3
Pettit2.42.7
Drew..John.2.31.9
White..Jo.Jo.2.31.9
Hollins..Lionel.2.21.2
Jones..Sam.2.12.0
Heinsohn2.11.4
Bellamy2.11.2
Smith..Phil.2.02.2
Baylor2.01.1
Brown..Fred.2.02.1
Havlicek2.01.5
Adams..Alvan.2.02.0
Bing1.91.1
Chaney1.91.7
Haywood..Spencer.1.81.4
Sharman1.82.0
Smith..Randy.1.71.9
Kerr..Red.1.61.6
Yardley1.62.0
Sears1.61.8
Ford..Chris.1.61.5
Bradley..Bill.1.63.5
Van.Arsdale..Dick.1.51.4
Roundfield1.52.2
Newlin1.41.8
Collins..Doug.1.21.7
Johnson..Gus.1.11.2
Martin..Slater.1.11.7
Chones1.11.3
Westphal1.02.1
Carr..Austin.1.01.5
Bridges0.91.5
Cowens0.91.5
Loughery0.91.5
Embry0.82.6
Van.Arsdale..Tom.0.71.2
Braun0.72.1
Shue0.61.9
Nelson..Don.0.61.1
Monroe..Earl.0.61.5
Maravich0.61.3
Attles0.52.1
Snyder..Dick.0.51.3
Love..Bob.0.52.9
Meschery0.42.6
Dandridge0.41.7
Scott..Ray.0.41.1
Shelton0.42.6
Sobers0.31.7
Chenier0.31.8
Bridgeman0.22.0
Hairston0.21.1
Bantom0.11.4
Hudson..Lou.0.01.5
Van.Lier0.01.4
Ramsey-0.11.3
Washington..Jim.-0.12.1
Erickson-0.11.2
Rowe-0.21.8
Twyman-0.22.9
Winters-0.22.8
Heard-0.31.0
Ellis..Leroy.-0.31.2
Lovellette-0.52.0
Naulls-0.51.6
Wilkens-0.51.4
Russell..Cazzie.-0.51.3
Clark..Archie.-0.61.3
Goodrich-0.91.5
Malone..Moses.-0.92.3
Reed..Willis.-0.91.4
Walker..Chet.-1.02.3
Wilkes-1.04.0
Komives-1.11.6
Guerin-1.31.4
McAdoo-1.31.5
Miles..Eddie.-1.42.0
Robinson..Truck.-1.41.1
Maxwell..Cedric.-1.53.6
Russell..Campy.-1.51.7
Jones..Wali.-1.62.3
Johnson..Mickey.-1.61.9
Costello-1.81.8
Lucas..Mo.-1.91.9
Green..Johnny.-2.41.5
Ohl-3.21.3
Barnett..Jim.-3.21.6
Rodgers..Guy.-3.51.7
Tomjanovich-3.52.0
LaRusso-3.81.5
Johnson..George.-3.92.6
Sanders..Tom.-4.42.5
Lucas..Jerry.-4.51.4
Jones..Caldwell.-6.12.2
Carter..Fred.-6.42.2
Wicks-7.32.6
Gervin-9.38.7

Keep in mind that the only data fed into this statistical model is (a) who played in a game and (b) what the score of that game was. Yet, more than half of the MVP’s claimed during the time period fall in the top-11. A search of similar criteria for the time period produces a list of similar All-NBAers. Pretty cool, eh?

Despite filtering for players with a good five seasons or more of playing time, there are still instances where multicollinearity and uncertain rear their ugly heads. Fortunately, some of these ambiguities — for instance, the early 80’s 76ers, Bucks, Spurs and Sonics — will be ironed out when more seasons are added. Other players, like Walt Frazier, just have a fuzzier signal than most.

Detailed methodology for OLS WOWYR can be found below. I’ll go into more detail in the next post in this series when WOWYR is improved.


Method Summary

Lineups

  • ~25+ mpg to qualify for a lineup (aka ignore lower-minute players)
  • Exceptions: if 5th-highest minute player is below 25 mpg, will often take that player and any other in the same mpg range (usually 23-24 mpg) to complete the “lineup.”

Point Differential

  • Take the average, unadjusted strength of schedule (based on the full 82-game SRS value of a team)
  • Add a home-court advantage factor (3 points)
  • All postseason data is included

The Regression

  • Players who fail to qualify for more than 82 games worth of lineups are treated as a “replacement rotational” player
  • “Prime” and “non-prime” seasons are treated as separate players — more on this in the next post.
  • Technically, this is Weighted Least Squares (WLS), where weights are determined by games played (using the standard square-inverse of the variance).
  • Regression is performed on all lineups and their point differentials.

 

From the Vault: Brady vs. Manning, Superclutch

On the cusp of football season, a look back at a comparison of two of the all-time greats. This was the second post in a two-part series,  originally published on January 25, 2012. 

In the last post, we improved on the “game-winning drive” metric by looking at 4th quarter drives when the game was tied or within one score. That post examined drives starting between the 1:00 mark and the 15:00 mark of the 4th (and OT). Let’s define “Super Clutch” drives as those starting in the last five minutes. (Again, excluding desperation drives starting under a minute.)

Below are the Super Clutch results for Peyton Manning and Tom Brady. Included are the other MVP-level QB’s of this era, Drew Brees and Aaron Rodgers:

Super Clutch Years Drive Pts/Dr TD% Score% Avg. Yds Avg. Start Avg. Time TOL % at Home
Tom Brady 03-07, 10-11 19 3.95 47.4% 68.4% 47.6 33.0 02:29 1.68 26.3%
Peyton Manning 03-10 31 3.52 38.7% 64.5% 44.6 32.5 02:31 1.84 45.1%
Drew Brees 06-11 17 2.94 35.3% 47.1% 47.5 26.1 02:55 1.29 41.2%
Aaron Rodgers 08-11 16 1.63 18.8% 25.0% 28.3 27.8 02:57 1.94 25.0%

NB: If New Orlean’s placekicker had converted all of his field goals, Brees would boast a 64.7% score rate and 3.47 points per drive.

So Brady has been better — otherworldly, really — in the final moments of games. This, despite playing mostly on the road. Manning continues to look amazing as well, and so does Drew BreesAaron Rodgers has a long way to go in this regard.

And for those in the mood for some small-sampled data, here are the Big Three QB’s performances on regular clutch drives in the postseason:

Clutch Playoffs Years Pos Pts/Dr TD% Score% Avg. Yds Avg. Start Avg. Time TOL % at Home
Tom Brady 03-07, 10-11 9 2.89 22.2% 66.7% 37.3 33.3 07:06 2.78 11.1%
Peyton Manning 03-10 11 2.09 18.2% 45.6% 33.2 25.3 05:23 2.73 81.8%
Drew Brees 06-11 7 4.14 42.9% 71.4% 36.0 36.1 10:13 2.00 28.6%

And alas we see where Manning earned his (unjustified) reputation as coming up short in the postseason. It’s unjustified because, as anyone who has read this blog knows, the sample size is too small to conclude anything, and these figures don’t control for defensive strength. Brees has been magnificent, scoring on five of seven playoff clutch drives, and Brady has failed on only three postseason drives: early in the 4th against the Colts (2006), the Giants (2007) and in the final minute against Indianapolis again in the 2006 AFC championship.

One final note: After examining a number of clutch performances in basketball, it’s particularly interesting to observe that these quarterbacks seem to perform so well in clutch (and super clutch) situations. In basketball, shooting and scoring typically decline later in games. Yet, at least with Manning and Brady, they’ve performed as well (or better) than the best offenses in NFL history in these situations.

I. Historical Impact: WOWY Score Update

How valuable is a player? How many points per game is he worth? In sports, these are Holy Grail questions that play-by-play data has helped estimate. But how do we compare Magic and Bird when they played before play-by-play was available? How do we compare Russell and Chamberlain when they don’t even have a complete box score?

A few years ago, I circulated a method that takes a stab at these questions by using injuries, trades and free agent signings to compare teams with and without a given player. The result is an historical, (mostly) apples-to-apples comparison of value between players, called WOWY. (There’s a full primer on WOWY attached to the end of this post.) The lineup data — not from play-by-play, but from game-by-game — gives us the same insight into players for the last 60 years.

Take Bill Walton’s legendary rise and fall in Portland. All other things being equal, how did the team fare with and without him in the lineup? It turns out, Walton’s missed time from those years produces the best WOWY score in NBA history. (See the third tab, titled “Top WOWY Runs.”) In other words, Walton had the biggest observable impact of qualifying players (i.e. players who were injured or traded) on any team ever, his presence improving the Blazers by more than eight points per game.

In researching Thinking BasketballI examined hundreds of these WOWY runs. For those familiar with it, I also cleaned up the data, adding controls and incorporating postseason games for over 1,500 instances since the inception of the shot clock in 1954-55. And if we combine those instances for players — only focusing on what I’ve liberally called their “prime” — we can see who left a large impact when in and out of the lineup for an entire career.

Below are the top 10 prime WOWY scores of all-time, with a minimum sample of 20 games missed:

Top 10 WOWY Scores All Time

Indeed, the best combined numbers are from players often found in all-time top-10 or top-20 lists. You can see all the results in this spreadsheet of over 200 qualifying players.

The two outliers — Robertson and West — make most top-20 or top-15 lists. (ESPN had them at 11 and 13, respectively, in their recent top-100 rankings.) While Oscar is largely revered, most people don’t know that his impact was quantifiably enormous, dragging an otherwise inept team in Cincinnati to respectability, then later catapulting Kareem’s Bucks into the upper stratosphere.

Meanwhile, when West was healthy, many of his teams were elite, only overshadowed in history by the dynastic Celtics. Amazingly, West’s teams performed better with him in all 12 lineups that he missed time. Oscar did the same for 11 consecutive lineups. (Note that about one third of WOWY scores on that list are negative.)

538’s Benjamin Morris ran a limited version of this years ago to argue for the greatness of Dennis Rodman, although he only used a minimum of 15-game injury blocks. Rodman’s good, but he clocks in at 16th here. And yes, Kobe (26th) beats Jordan (32nd), but MJ’s number comes largely from 1986 when he broke his foot and missed most of the season. (His 22 missed games from 92, 93 and 95 respectively would elevate him to 25th on the list.)

While this is all valuable data, it’s still limited. It doesn’t help answer our original question for players who don’t miss much time, like Chamberlain and Russell (and even Jordan). We’ll address that issue in Part II of this series on historical impact. For now, I’ll leave you with a WOWY primer below…


What’s WOWY?

It stands for “With or Without You,” and compares the performance of a roster with a given player and without that given player over the course of an entire game. It is an attempt to isolate a player’s impact on that given roster.

I almost always control for players who played at least 25 minutes per game (noted in the control column of this spreadsheet). This typically yields five to seven-man rotations for most teams, depending on how they distribute the minutes. There are some instances where I’ll control for the entire starting 5, even if someone is below the 25-minute mark. Similarly, there are situations that call for including two players at around 23 to 24 minutes per game because there is no clear-cut fifth man on a team.

How is WOWY different from On/Off?

On/Off captures changes within a game. WOWY captures changes from game-to-game. One strength of WOWY is that multi-collinearity is not a problem; in other words, player values cannot be confounded by moving in and out of the game together. In that sense, it is an incredibly pure representation of a player’s value to a given roster, troubled by issues like sample size (major issue), team growth (minor issue), opponent unhealthy lineups (minor) and valuable bench cohorts (minor).

(Note that some lineups have synergistic effects where the whole is greater than the sum of the parts, and removing any player from that equation can disrupt the synergy.)

What’s a WOWY Score?

It’s an attempt to quantify how impressive a given WOWY run is. It takes into account sample size, the distribution of SRS scores in a given era and the quality of the player’s team.

What is “95% +/-?”

It is a confidence interval, based on the SRS-variance of a typical NBA team. For example, from 1977-1978 the Blazers were a -1.2 team in 26 controlled games without Bill Walton. A 95% +/- value of “3.5” means that 95% of the time, the actual full-season SRS of such a team will fall within 3.5 points of that value, or somewhere between -4.7 and +2.3 SRS. (Note: More consistent teams will be slightly penalized by this and more inconsistent teams with benefit from it.)

What is SIO?

It stands for “simple in/out,” and is a basic curving of impact based on the quality of a team. It means that taking a -10 team to -5 is given less value than taking a +5 team to +10.

When combining runs for a “prime score,” why is SIO different than WOWY score?

Uneven samples can provide extremely warped results due to some basic math illusions. Take Michael Jordan, who missed the majority of his games in 1986. His team’s “out” totals will then largely reflect the 1986 Bulls (who were below .500), but his “in” totals will be weighted heavily by the Bulls dynastic teams. So, even if his team performed the same with or without him, his out sample largely be from a -3 SRS team, while his in sample would be teams closer to 9 SRS.

WOWY score was designed to correct this problem — for multiple seasons, it takes the impact (SIO) from a given sample and weighs it accordingly. For instance, if a player makes a team 10 points better in a five-game sample, and then two points better in a 20-game sample, his weighted impact is 3.6 points (because 80% of the sample is from the two-point change).

The actual in and out values are included for posterity, but unless a player played on relatively consistent teams, the numbers won’t reflect the actual impact the player had on his lineups.

Why are there multiple entries for the sample player-season?

The controls are different. Players might miss games from one lineup and then, following a team trade, might play with and without a different lineup.

From the Vault: Are Role Players Worse on the Road

This post was originally published on June 3, 2012. 

On the ESPN pregame show before Game 4 of the Eastern Conference Finals between Boston and Miami, there was a long discussion about why peripheral players tend to struggle more on the road than at home. Which, of course, begs the question…do peripheral players really struggle more on the road than at home?

If we break down player importance by minutes played, we can stratify everyone in the NBA into six categories, ranging from guys who play under 15 minutes per game to those who play more than 35. This is what the results look like for free throw shooting:

Free Throw% Away Home Diff Away % of Home
Players Over 35 mpg .763 .757 -.006 100.8%
30-35 .796 .795 -.001 100.1%
25-30 .774 .768 -.005 100.7%
20-25 .712 .722 .011 98.5%
15-20 .707 .689 -.018 102.6%
Under 15 .677 .675 -.002 100.3%

This confirms another myth-buster we learned at the Sloan MIT Sports Conference this year: teams shoot free throws better on the road, not at home. Players over 35 minutes per game see a small improvement on the road, with home-cooking only reserved for players in the 20 to 25 minute bracket. Those players see a 1.1% decrease in free throw shooting on the road.

Obviously, free throw shooting isn’t a category that tells us much. Instead, let’s look at overall box score statistics that ballpark play based on the basic box stats. First, Game Score (similar to PER) and then Expected Value run only on the box score stats. Finally, points per game and True Shooting% are included.

Game Score Away Home Diff Away % of Home
Players Over 35 mpg 14.6 15.7 1.1 93.2%
30-35 11.1 12.0 0.9 92.5%
25-30 7.7 8.7 0.9 89.4%
20-25 5.9 6.1 0.2 96.8%
15-20 4.0 4.0 0.0 99.8%
Under 15 2.2 2.4 0.2 90.9%
Box EV Away Home Diff Away % of Home
Players Over 35 mpg 4.5 5.4 0.8 84.3%
30-35 3.8 4.4 0.6 87.4%
25-30 2.9 3.4 0.5 84.0%
20-25 2.3 2.5 0.2 92.6%
15-20 1.5 1.5 -0.3 102.2%
Under 15 0.6 0.7 0.1 85.9%
Points Per Game Away Home Diff Away % of Home
Players Over 35 mpg 18.95 19.62 0.7 96.6%
30-35 14.75 15.36 0.6 96.0%
25-30 10.79 11.17 0.4 96.6%
20-25 7.81 7.81 0.0 100.0%
15-20 5.43 5.31 -0.1 102.2%
Under 15 3.18 3.33 0.2 95.5%
True Shooting% Away Home Diff Away % of Home
Players Over 35 mpg .535 .556 .021 96.2%
30-35 .534 .554 .020 96.4%
25-30 .522 .534 .013 97.6%
20-25 .520 .519 -.001 100.2%
15-20 .506 .506 .000 100.0%
Under 15 .471 .485 .013 97.2%

Based on these measurements, lower minute players are actually more consistent on the road than they are away from home. Consider:

  • 25-30 minute players decrease the most on the road by Game Score and Box-based EV
  • 25-30 minute player see no decline in points per game and TS%
  • Under 15 minute players see a Road decline comparable to high minute players in points and efficiency

Otherwise, the players with the biggest drop-off in road performance are the high-minute players! Whether it’s composite box metrics or scoring and shooting, the biggest difference between road and home is typically seen in the key players. In the composite metrics especially, the high-minute players see a significantly larger decline on the road than the low-minute players do.

Keep in mind this is not a definitive study, but a broad examination. We could change the criteria to examine “only All-Stars” or “only All-Stars in the playoffs,” and it’s possible the results look different. But it’s important to note, that in general, it is not the role players who decline more on the road, but the stars.

The Best “Healthy” Offenses of All-Time

In the last post, we looked at the best point-differentials of all-time posted by teams that were “healthy” (when all 25-minute per game players were in action, minimum 41 games played together). But what about isolating the offensive side of the ball?

Since box scores aren’t readily available before 1984, we are limited to teams from the last 32 seasons. But that’s fine — 99 of the top 100 most efficient teams in NBA history played in 1984 or later. (The 1982 Nuggets are the exception.)

Before analyzing the list, a quick disclaimer to keep in mind: Offensive rating is not a perfect representation of offensive quality. Teams can choose offensive-centric lineups at the expense of defense for a net boost, such as crashing the offensive boards instead of retreating in transition defense. Below are the top offenses, relative to the defenses faced, based on these healthy lineup standards:

Healthy Offense Relative ORtg

The 2006 Suns played the second half of the season without Kurt Thomas after running out of big men. As a result, they played one of the most lopsided lineups in NBA history, starting Boris Diaw at center and three wings alongside Steve Nash. They had one big man (Brian Grant) off the bench. While they feasted on defenses, they were defensively compromised and posted an abysmal +6.6 defensive rating during these games. Given that, I wouldn’t rush to crown them the GOAT offense. Some of the Dallas teams on the list also suffer from this kind of lineup tradeoff, slotting Dirk Nowitzki at center next to an offensively-leaning forward.

Offensive rebounding has declined drastically over the last two decades as teams have sacrificed crashing the glass in order to defend transition. Some teams still crash the glass hard, but sometimes individuals are just great offensive rebounders. Dennis Rodman is the ultimate example example of this — he’ll jump a team two tiers by himself. For example, in 37 games without Rodman, the ’96 and ’97 Bulls — with Longley, Kukoc, Jordan and Pippen playing — saw a 5.1% drop in their offensive rebounding rate, which is about the difference between the best offensive rebounding team in the league and an average one.

So let’s expand the list to include components that help place a team’s offensive rating in perspective, such as offensive rebounding rate and turnover percentage. Let’s also include the raw offensive rating and true shooting percentage (TS%) of the team:

Healthy Offense Expanded

First, the 2004 Kings number is shocking because they did it without Chris Webber; they smoked the league with Brad Miller starting in place of him, a phenomenon I discuss in Thinking Basketball.

The ’96 Magic and ’16 Warriors certainly jump out as candidates for the best offenses ever. If you’re eyes thought you’d never seen anything like Golden State this year, you were right; the Warriors shooting efficiency yielded an unheard of 1.19 points per scoring attempt. The ’96 Magic were amazing too, but aided by a shortened 3-point line.

There’s a dark horse in there: The 2016 Cavs, the team that beat the Warriors. Injuries have masked an all-time level offense, led by LeBron JamesKyrie Irving and even Kevin Love. They are not in the upper stratosphere of shooting efficiency, but are a low-turnover offense (11.5%) that benefits from player-specific offensive rebounding by Tristian Thompson.

But how good is an offense that can only take advantage of a fundamentally poor defense? While most offenses perform better against weaker defenses, Cleveland has no correlation between an opponent’s defensive strength and its own offensive production. A linear regression predicts that the Cavs offense will actually perform better against elite defenses than almost every team on this list, including Golden State. Given the small samples, I wouldn’t put too much stock in this, but it is worth noting nonetheless.

Of course, there’s an elephant in the room. Where will Kevin Durant, Steph Curry and the 2017 Warriors place on this list?

 

 

From the Vault: Observations from a season of Stat-Tracking

This post was originally published on April 13, 2011. It is a summary of findings after one year of stat-tracking basketball games in attempt to extend the box score. SportsVU now captures similar data. 

If one spends enough time watching NBA games with a DVR, trends start to jump out. Unfortunately, there’s no way the human brain can accurately catalog all that information. Perhaps Data from Star Trek should be assigned to finding trends in basketball games. In the meantime, here are some statistical observations from roughly 23,000 possessions of stat-tracking in 2011:

Creation

  • 16% of all field goals came off of an Opportunity Created (OC).
  • 46% of 3-pointers came off of an OC.
  • The average player shot 40% on 3-point shots off of an OC.
  • The Spurs led the league in OC’s (23.5 per 100 possessions), with the Hawks second at 23.4.
  • The Jazz needed the most help on defense — which means their opponents create the most opportunities (23.7 OC per 100).
    • The Jazz had the lowest Defensive Rating in the sample by far (118.7).

Fouling

  • The Lakers committed the fewest shooting fouls in the league (16.5 free throws/100).
  • Someone takes an offensive foul every 88 possessions…or a little more than once per game.
  • Phoenix takes more offensive fouls than any other team – 2.2 per 100 possessions.

Defense

  • In guarded situations, the most successful teams are the best defensive teams: The four leaders in guarded field goal percentage are in the top-5 in defensive rating (and Milwaukee’s sample was too small):
    1. Miami (36.6%)
    2. Chicago (36.6%)
    3. Boston (36.9%)
    4. LA Lakers (37.7%)
  • The Lakers make the most defensive errors…but give up the fewest points per error (1.50 points/error), a credit to Andrew Bynum and Pau Gasol protecting the paint.
  • Every 172 possessions there is a forced turnover not counted as a steal (eg slapped off a leg out of bounds. That means the NBA doesn’t track about 1700 “steals” during the season.
  • Teams shoot the worst in unguarded situations against the Lakers (56.6% eFG%), which suggests that LA does well closing out shots and fighting through screens…or they’re just lucky.

Top “Healthy” Teams in NBA History

Who are the best teams in NBA history? We often answer this question by looking at a team’s entire body of work, lumping in the good, the bad and the injured. Most teams have key players miss games and some even trade for key players, changing the chemistry of a given lineup. So who were the best teams when all of the key actors were on stage?

Below I’ve indexed the top “healthy” teams — when all 25-minute per game players were in action for a game — since the shot clock (1955) by SRS (adjusted margin of victory). Using this criteria, 51 teams have posted at least an 8.0 SRS when healthy.  Just 29 teams have eclipsed the 9.0 mark. (10 of those teams failed to win a title — well inline with what is predicted by the variability of a 7-game series.) The best are below, playoffs included:

Top Healthy Offenses

Disclaimers: SRS, while a better predictor of results than win percentage, is not a de facto team-ranker. First, it’s subject to the usual variance seen in the NBA (detailed in Chapter 4 of Thinking Basketball), so it’s not a perfect representation of team strength. Second, some teams are more resilient in makeup — they are better equipped at handling a variety of opponents while still remaining efficient, boosting their odds of winning from series to series. Finally, SRS is a measure of within-season dominance, so it cannot allow for perfect comparisons across seasons. A 10 SRS in 1986 is probably more impressive than one in 1972.

With that said, it is by far the single best metric for evaluating the performance of a team against its competition. The teams listed above were manhandling opponents, which is why many went on to win a title.

While this year’s Warriors were the most dominant single-season team ever, their SRS is influenced by a league that was incredibly top-heavy. Four of the top-40 healthy teams ever played in 2016 (Golden State, San Antonio, Oklahoma City and Cleveland), which is either an unlikely coincidence, or a reflection of inflated numbers from a lopsided league.

The other top four seasons are from expansion eras, when teams could pick up an additional point or two by facing expansion squads a few times a year and padding their numbers with blowouts. All of those teams are in the conversation for “greatest ever,” but their statistical dominance here should be slightly curved.

As mentioned, we see the usual suspects: Jordan’s first three-peat Bulls. Jordan’s second three-peat Bulls. Kareem’s Bucks and the early 70’s Lakers. This is all line with in-depth analysis of the greatest teams ever.

So who are the most impressive teams of all-time that you probably didn’t know about:

  1. 2014 Spurs. When healthy, they posted an amazing 11.8 SRS. That team is basketball’s Sistine Chapel and Gregg Popovich its Michelangelo.
  2. 2004 Pistons. Absolutely impregnable after the Rasheed Wallace trade in ways that reminded everyone it was time for a rule change.
  3. 2008-09 Lakers and Celtics. These teams were fantastic in an incredibly competitive league. The Celtics were +8.8 and +9.3 when healthy, and the Lakers +9.7 and +9.0 once Pau Gasol joined. Kevin Garnett’s injury robbed us of possibly the NBA’s greatest trilogy.
  4. 1996 Magic. Yes, they were worthy of a documentary.

Amazingly, of the top 40 healthy teams of all-time, seven are Pop’s Spurs teams. Five are Jordan’s Bulls. Four are Laker teams with Kobe Bryant.

Remember this list the next time you construct an all-time list or you look ahead to the 2016 season.

Edit: This post was updated to include the postseason totals for the 2016 Warriors, and 96-97 Bulls. 

From the Vault: Exploring the Spacing Effect

This post was originally published on November 26, 2011. It examines a concept mentioned in my new book, Thinking Basketball

One of the more dominant themes of this summer’s Online Hoops Summit of Nerdness was the “Spacing Effect” that good shooters provide for an offense. By being a threat to score from all over the floor, shooters pull out defenders who could otherwise help on penetration or flood the paint for defense and rebounding. For example, in the last post we combed over five years of raw on/off data — how well a team performed with a player in the lineup versus when he was on the bench — and some of the biggest impacts were made by great shooters.

Of the 21 players who added at least six points of efficiency to a 107 offense (teams averaging 107 points or more per 100 possessions without the player), seven are on the all-time top-100 list of 3-point percentage leaders (minimum 500 attempts). 17 of the 21 (81%) used the 3-point shot regularly, with only Brad Miller (2004), Shaquille O’Neal (2005), Kevin Garnett (2008) and Tyson Chandler (2008) operating primarily inside the arc. The average 3-point percentage from that group was a whopping 38.2%. (League average 35.7% over that time.)

Below are the 21 player seasons, with their 3-point percentage:

Player Year Net Change Ortg On Court Ortg Off Court Season 3 pt %
Josh Howard 2004 6 117.6 111.6 .303
Radmanovic 2008 8.6 119.5 110.9 .406
Williams 2008 6.1 116 109.9 .395
Nowitzki 2004 6.2 115.6 109.4 .341
Bryant 2008 6.5 115.4 108.9 .361
Lewis 2005 7.3 116 108.7 .400
Joe Johnson 2005 8.4 117 108.6 .478
Josh Howard 2007 6.5 114.9 108.4 .385
Allen 2005 7 115.2 108.2 .376
Marion 2007 8.6 116.8 108.2 .317
Radmanovic 2005 11.7 119.8 108.1 .389
Chandler 2008 6.9 114.5 107.6
O’Neal 2005 7.6 114.9 107.3
Christie 2004 6.7 114 107.3 .345
Finley 2005 6.8 114 107.2 .407
Posey 2006 6.2 113.4 107.2 .403
B. Miller 2004 7.5 114.6 107.1
Billups 2008 8 115.1 107.1 .401
Terry 2006 8.5 115.5 107 .411
Garnett 2008 8 115 107

Also from that five-year chunk of data, there were 55 instances of players boasting an on/off of 9.0 or better on offense (minimum 1000 minutes played). Again, this means their teams offense scored at least nine more points per 100 possessions with them on the court that year. Only ten of those seasons saw a player attempt less than one 3-point shot per game. We see the same results: the other 45 (82% of the group) averaged 38.4% from behind the arc.

Of particular interest are the shooting specialists. Who we classify as one-dimensional shooters is somewhat subjective, but it’s a mighty coincidence that Vladimir Radmanovic appears on the above list twice, with two different teams. And that Peja Stojakovic does the same, in two different situations, in his two best 3-point shooting seasons (43.3% in 2004, 44.1% in 2008). And that Damon Jones seemed to help Miami so much in 2005 with a career-best 43.2% from downtown. And that Fred Hoiberg led the league in 3-point percentage in 2005 at a staggering 48.3% and booted Minnesota’s offense while on the court.

Of course, making so many 3′s is also part of the reason these players are helping so much, but perhaps not quite as much as one would think. In Hoiberg’s case, he attempted 4.1 3′s every 36 minutes, which means the difference between 48.3% and league average was roughly 1.6 points per 36 minutes, or about 2.3 points/100 at Minnesota’s 2005 pace. Radmanovic launched 5.7 3′s every 36 minutes in 2008, and if he converted at league average the Lakers would have scored about 1.8 fewer points in his games.

So while greater accuracy translates directly to more points, something else is happening here indirectly. It’s possible these shooters are repeatedly the beneficiary of coming in and out of the lineup with their team’s superstars. Although that seems unlikely, we can look at long-term adjusted plus-minus (APM) data and see the same pattern.

In Joe Ilardi’s 2003-2009 APM model, the best offensive players in the league are names we’d expect: Steve NashLeBron JamesKobe BryantChris Paul and Dwyane Wade. It’s also littered with resident shooters, like Antawn Jamison (“stretch” power forward) at No. 7, Michael Redd (12th), Ray Allen (13th), Jason Terry (19th), Anthony Morrow (21st), Peja Stojakovic (22nd), Rashard Lewis (23rd), Danilo Gallinari (26th), Anthony Parker (40th), Mike Bibby (45th) and Sasha Vujacic (48th). Below are how the top-50 3-pooint shooters (500 attempts) by percentage scored in Ilardi’s APM study:

Player 3P% Off APM
Jason Kapono .454 -1.36
Steve Nash .439 8.84
Anthony Parker .424 2.55
Ben Gordon .415 2.37
Raja Bell .414 -1.22
Daniel Gibson .412 1.40
Bobby Simmons .410 -0.61
Brent Barry .409 0.32
Matt Bonner .409 1.00
Peja Stojakovic .409 4.15
Bruce Bowen .408 -4.99
Wally Szczerbiak .406 1.08
Leandro Barbosa .404 0.51
Kyle Korver .404 -0.20
Eddie House .403 -1.88
Mike Miller .402 1.21
Chauncey Billups .401 5.32
Matt Carroll .400 0.39
Troy Murphy .398 0.41
Roger Mason .395 -0.58
Brian Cook .394 -2.41
Danny Granger .393 1.40
James Jones .393 1.80
Ray Allen .392 5.33
Steve Blake .392 -0.08
Luther Head .392 -1.21
Shane Battier .391 0.33
Rashard Lewis .390 3.91
Michael Finley .389 -1.58
Kevin Martin .389 1.10
Jameer Nelson .389 0.14
Hedo Turkoglu .389 1.89
Jason Terry .387 4.41
Mo Williams .386 1.39
Tyronn Lue .384 -0.47
Jose Calderon .383 0.71
Vladimir Radmanovic .381 1.84
Michael Redd .381 5.46
Kirk Hinrich .380 -0.88
Mike Bibby .379 2.31
Joe Johnson .379 1.40
Dirk Nowitzki .379 4.71
Mike James .378 -0.80
Delonte West .378 -0.39
Andrea Bargnani .377 -1.24
Maurice Evans .377 0.26
Mehmet Okur .377 -0.48
Sasha Vujacic .377 2.24
Manu Ginobili .376 4.94
J.R. Smith .376 1.98
Derek Fisher .375 -1.60

The average Offensive APM in the entire study was -0.45. The average Offensive APM of the top-50 3-point shooters on the list is +1.08. 32 of the 50 were positive-impact players. The glaring outlier, Bruce Bowen, can be explained away quite nicely. We’re using the 3-point shot to approximate outside shooting ability (or the threat of outside shooting), and Bowen isn’t a very good outside shooter. Using available data, he took about one deep jumper a game from 2007-2009 converting at 38%. He shot 57.5% from the free throw line during the period, the worst of anyone of the list by nearly 8%.

We could further define “good outside shooters” by looking at floor data on shooting from 16-23 feet if we wanted to. Although, despite the presence of someone like Bowen, 3-point shooting is sufficient for now to demonstrate the presence of the Spacing Effect.

Thinking Basketball Now Available on Amazon

Excited to announce that my new book, Thinking Basketball, is now available on Amazon in paperback.

The book is largely a culmination of the ideas on this blog over the years, using our own cognition to explore misconceptions about the NBA. It’s built on the concepts that have been presented on this blog (some of which I’ll try and re-upload this summer), as well as new research that was developed specifically for the book.

It would not exist without you, the reader, supporting this blog over the years and constantly participating to improve the ideas shared in this space. Thanks for reading and I hope you enjoy it!

Some core topics:

  • Averaging 50 points per game is rarely better than averaging 20
  • Why “Chokers” aren’t always chokers
  • How winning warps our memories, and thus our narratives about players and teams
  • The value of clutch play and closers
  • Building championship teams and the value of one-on-one play