For all your fancy-pants statistical needs.

Praise for The Basketball Distribution:

"...confusing." - CBS
"...quite the pun master." - ESPN

Recent Tw-happenings

I've been posting all kinds of nonsense to twitter lately. Here are some of the more informative tweets:

1) Lineup stuff:


2) Jason Kidd has played the best defense (of Miami & Dallas players) during the playoffs.

3) Nick Collison is not represented well by box-score or advanced box-score statistics.

4) I put together Lebron James' year-by-year Statistical and Actual Regularized +/- numbers since '08.

Most (& Least) Valuable Players in the 2011 Playoffs, Pre-Finals Edition


EDIT: I have also posted the most & least efficient players to Google Docs (as many of the poor performances don't make it into the bottom 25 as such players lost their series).


Here are the top & bottom 25, respectively. (These are not adjusted for opponent quality).

The numbers are based on my statistical plus-minus numbers, which I convert to wins via the "Pythagorean" formula. (Although I give each player the same baseline "team" value here for simplicity).

PlayerTmwin% added per gameplayoff wins added
1LeBron JamesMIA18.9%2.84
2Kevin DurantOKC16.5%2.80
3Dirk NowitzkiDAL14.5%2.17
4Dwyane WadeMIA12.3%1.85
5Jason KiddDAL10.7%1.60
6James HardenOKC9.2%1.56
7Derrick RoseCHI9.6%1.54
8Chris BoshMIA8.3%1.25
9Joakim NoahCHI6.8%1.09
10Chris PaulNOH17.7%1.06
11Zach RandolphMEM7.7%1.00
12Jason TerryDAL6.3%0.95
13Kevin GarnettBOS10.4%0.94
14Ray AllenBOS10.2%0.91
15Luol DengCHI5.0%0.80
16Russell WestbrookOKC4.2%0.71
17Marc GasolMEM4.8%0.62
18Nick CollisonOKC3.3%0.57
19Shawn MarionDAL3.4%0.51
20Paul PierceBOS5.4%0.48
21Rajon RondoBOS5.3%0.48
22Marcus CambyPOR7.2%0.43
23Dwight HowardORL7.1%0.43
24Danny GrangerIND8.4%0.42
25Tyson ChandlerDAL2.8%0.42

And the worst:

PlayerTmwin% added per gameplayoff wins added
1Mike BibbyMIA-6.1%-0.92
2Kendrick PerkinsOKC-5.1%-0.86
3DeShawn StevensonDAL-3.9%-0.58
4Amare StoudemireNYK-12.8%-0.51
5Marco BelinelliNOH-8.5%-0.51
6Sam YoungMEM-3.6%-0.47
7Richard JeffersonSAS-7.1%-0.43
8J.J. RedickORL-7.1%-0.42
9Joe JohnsonATL-3.5%-0.42
10Glen DavisBOS-4.4%-0.39
11Joel AnthonyMIA-2.4%-0.36
12Emeka OkaforNOH-5.9%-0.35
13Jarrett JackNOH-5.6%-0.34
14Tyler HansbroughIND-6.7%-0.34
15Wilson ChandlerDEN-6.6%-0.33
16Marvin WilliamsATL-2.7%-0.33
17Landry FieldsNYK-7.6%-0.30
18Jason CollinsATL-2.4%-0.28
19Raymond FeltonDEN-5.7%-0.28
20Willie GreenNOH-4.6%-0.28
21Arron AfflaloDEN-9.2%-0.28
22Lamar OdomLAL-2.7%-0.27
23J.R. SmithDEN-5.5%-0.27
24Bill WalkerNYK-6.5%-0.26
25Antonio McDyessSAS-4.1%-0.25

NBA PLAYOFF PLAYER RATINGS as of 5/24

Earlier today, I made a prediction formula (regression) that predicts a player's Adjusted Plus-Minus based only on the advanced stats which Basketball-Reference spits out*

The following is their estimated Adjusted Plus-Minus, their total (pace-adjusted) personal point differential, and their total value to their team per 100 possessions (eRAPM * ~Min%).


PlayerTm~poss. playedeRAPMtotal valuevalue per 100
LeBron JamesMIA11836.982.16.2
Kevin DurantOKC13086.281.65.4
Dwyane WadeMIA10715.761.54.6
Dirk NowitzkiDAL10485.759.74.5
Derrick RoseCHI11704.451.93.7
Jason KiddDAL9374.441.73.2
James HardenOKC9673.938.22.5
Chris BoshMIA10703.133.52.5
Jason TerryDAL8833.833.42.5
Chris PaulNOH4826.732.15.7
Zach RandolphMEM9922.929.12.4
Kevin GarnettBOS6324.427.53.2
Joakim NoahCHI9672.827.51.9
Ray AllenBOS6963.926.83.2
Luol DengCHI12551.923.81.7
Marc GasolMEM10001.818.11.5
Russell WestbrookOKC11451.415.71.0
Paul PierceBOS6612.114.01.6
Tyson ChandlerDAL8331.713.91.0
Rajon RondoBOS6652.113.81.6
Marcus CambyPOR3223.912.62.2
Dwight HowardORL4972.512.52.2
Danny GrangerIND3533.512.22.6
Jameer NelsonORL4162.911.92.1
Nick CollisonOKC7231.611.70.8
Manu GinobiliSAS3353.311.22.4
Gerald WallacePOR4362.410.61.9
Kobe BryantLAL6821.510.61.1
Shawn MarionDAL8401.19.20.7
Serge IbakaOKC9171.09.10.6
LaMarcus AldridgePOR4971.89.01.6
Ronnie BrewerCHI4511.88.00.6
Andrew BynumLAL6171.27.60.8
Ron ArtestLAL5531.26.80.8
Taj GibsonCHI5011.36.60.5
Carlos BoozerCHI9270.76.60.5
Eric MaynorOKC3831.76.50.4
Ty LawsonDEN3221.85.91.2
Kirk HinrichATL3331.85.91.0
Jose BareaDAL4631.25.70.4
Jrue HolidayPHI3621.55.61.2
Carmelo AnthonyNYK2991.64.81.3
Jeff TeagueATL4591.04.60.6
Greivis VasquezMEM2741.74.50.4
Nene HilarioDEN3121.34.20.9
Pau GasolLAL6900.64.10.4
Trevor ArizaNOH4640.83.70.6
Andre MillerPOR3740.93.20.6
Brandon RoyPOR2661.02.50.4
James JonesMIA5240.52.50.2
Elton BrandPHI3570.72.50.5
Derek FisherLAL6260.42.30.2
George HillSAS3640.51.90.3
Thabo SefoloshaOKC6360.31.80.1
Ryan AndersonORL2830.51.50.3
Josh SmithATL8440.10.70.1
Peja StojakovicDAL6070.10.50.0
Al HorfordATL9020.00.30.0
Matt BarnesLAL2520.10.20.0
Darrell ArthurMEM3870.00.20.0
Brendan HaywoodDAL4510.00.10.0
Jermaine O'NealBOS3800.00.10.0
Jamal CrawfordATL690-0.1-0.40.0
Matt BonnerSAS237-0.2-0.5-0.1
Jason RichardsonORL295-0.2-0.7-0.1
Shawne WilliamsNYK195-0.5-0.9-0.2
Shannon BrownLAL320-0.4-1.3-0.1
Mario ChalmersMIA613-0.3-1.6-0.1
Keith BogansCHI553-0.3-1.7-0.1
Steve BlakeLAL279-0.8-2.2-0.3
Andre IguodalaPHI351-0.6-2.2-0.5
C.J. WatsonCHI251-0.9-2.3-0.2
O.J. MayoMEM698-0.4-2.7-0.2
Louis WilliamsPHI251-1.2-3.1-0.7
Tony ParkerSAS426-0.7-3.1-0.6
Brandon BassORL268-1.2-3.3-0.6
Kenyon MartinDEN285-1.2-3.3-0.7
Jodie MeeksPHI241-1.4-3.3-0.7
Paul GeorgeIND256-1.5-3.8-0.8
Darren CollisonIND281-1.5-4.3-0.9
Daequan CookOKC368-1.2-4.4-0.3
Nazr MohammedOKC285-1.6-4.5-0.3
Nicolas BatumPOR291-1.5-4.5-0.8
Tony AllenMEM674-0.7-4.6-0.4
Carl LandryNOH410-1.2-4.8-0.8
Gary NealSAS214-2.3-4.8-0.9
Toney DouglasNYK216-2.3-4.9-1.3
Zydrunas IlgauskasMIA200-2.5-5.0-0.6
Danilo GallinariDEN285-1.8-5.1-1.1
Wesley MatthewsPOR389-1.4-5.6-1.0
Mike ConleyMEM977-0.6-5.8-0.5
Tim DuncanSAS409-1.4-5.8-1.0
Shane BattierMEM653-0.9-5.8-0.5
Omer AsikCHI285-2.1-5.9-0.4
Zaza PachuliaATL376-1.6-6.0-0.6
Thaddeus YoungPHI245-2.5-6.0-1.3
Kyle KorverCHI507-1.2-6.1-0.4
Delonte WestBOS328-2.0-6.4-0.8
Hedo TurkogluORL403-1.6-6.6-1.2
Roy HibbertIND254-2.6-6.6-1.4
Jeff GreenBOS333-2.1-7.1-0.8
Antonio McDyessSAS279-2.6-7.2-1.3
Lamar OdomLAL551-1.4-7.9-0.8
Raymond FeltonDEN293-2.8-8.2-1.7
Jason CollinsATL304-2.7-8.2-0.7
Marvin WilliamsATL416-2.3-9.5-0.8
Wilson ChandlerDEN222-4.3-9.5-2.0
Jarrett JackNOH214-4.6-9.8-1.7
Tyler HansbroughIND316-3.1-9.8-2.1
Emeka OkaforNOH362-2.8-10.3-1.8
Glen DavisBOS368-3.1-11.4-1.3
Joe JohnsonATL958-1.3-12.0-1.1
Joel AnthonyMIA817-1.5-12.1-0.9
J.J. RedickORL231-5.3-12.3-2.2
Richard JeffersonSAS339-3.7-12.4-2.2
Sam YoungMEM493-2.7-13.5-1.1
DeShawn StevensonDAL395-3.7-14.6-1.1
Marco BelinelliNOH333-4.5-14.8-2.6
Amare StoudemireNYK258-5.9-15.2-4.0
Mike BibbyMIA601-4.0-24.2-1.8
Kendrick PerkinsOKC869-2.9-25.3-1.7

I also found the relative team ratings during the playoffs according to this system:



TmEst. Efficiency Margin
DAL11.31
MIA10.15
OKC8.59
CHI7.65
BOS6.74
POR4.92
LAL2.18
MEM1.59
ORL0.51
NOH-0.70
PHI-1.38
ATL-1.49
IND-2.63
SAS-3.25
DEN-3.40
NYK-4.29


MATH:
 *I used Basketball Reference's '07-'11 career advanced stats and Engalmann's Regularized three-year offensive and defensive +/-, for all players with >1000 minutes played. I made a regression (with no intercept), gradually weaning out variables with a P-value of >.05, and the following is the result:

(Offense has an R^2 of ~.6, Defense of ~.4)

coefficientvalue
TRB%3.282424852
ORB%-1.704972232
DRB%-1.550130287
STL%1.12274153
ORTGxUsg1.062903376
USG%-0.945778193
TS% out of 100-0.361792241
BLK%0.247314245
eFG% out of 1000.135585541
ORTG0.085543135
TOV%0.078829447
DRTG-0.036343776


Win Shares per 48 Minutes versus Easy Player Ratings


Since Win-Shares per 48 minutes and my Easy Player Ratings use the exact same data (although EPR also adds minutes per game) to calculate player "efficiency," I thought I would compare the two.

I took all NBA players from in the 3-point era who played more than 1000 minutes and looked at their WS/48 and EPR values. From there, I just had a look at the top 100 in Win-Shares per 48.

Most notably, David Robinson (3.36 EPR) beats out Michael Jordan (3.27 EPR), barely -- this is somewhat intuitive, as Jordan's old years in Washington significantly decrease his "average," likely from his poor defensive numbers.




Now here are the 10 players in the top 100 who WS/48 comparatively likes the most:
PlayerFromToUSG%ORtgPoints Prod Per 100DRtgMPWS/48(rk)EPR(rk)difference
1Leon Powe2007201120.411523.4610313.90.174331.1788-55
2Steve Mix1980198321.711324.52110317.20.168391.1887-48
3Marcin Gortat2008201115.311617.74810217.20.162461.1789-43
4Steve Nash1997201121.211925.22811031.30.168391.2280-41
5Kevin Love2009201122.111725.85710929.80.163451.1986-41
6Mark Price1987199822.811626.44810929.90.158521.1493-41
7Ryan Anderson2009201120.711523.80510518.90.157531.0894-41
8Amir Johnson2006201114.312217.44610717.80.154610.8099-38
9Carl Landry2008201120.511723.98510824.90.155601.0495-35
10Todd MacCulloch2000200317.711320.00110015.40.166431.3274-31

Unfortunately, Steve Nash's lower usage and nearly non-existent defensive stats underrate him in EPR. Personally, I think Nash is in the top 5 offensive players of all time, which his usage and Offensive Rating do not capture well. Not sure where the rest of these guys fall - it could be because of low minutes-played, but that term is not worth all that much.


Here is a look at the players in the top 100 who the EPR system likes more than WS/48:



PlayerFromToUSG%ORtgPoints Prod Per 100DRtgMPWS/48(rk)EPR(rk)difference
1Patrick Ewing*198620022810629.689934.30.15771.832849
2Jack Sikma1980199120.911022.9910233.70.149821.584438
3Scottie Pippen*1988200422.510824.310234.90.146941.495737
4Eddie Jones1995200820.111122.31110334.40.147891.525336
5Dennis Rodman*1987200011.411412.99610031.70.15771.594235
6Horace Grant1988200415.211717.78410433.20.147891.515435
7Dikembe Mutombo199220091511116.659930.80.153691.723534
8Jeff Ruland1982199322.310924.30710233.40.149821.535131
9Dominique Wilkins*1983199930.311233.93610835.50.148851.456025
10Peja Stojakovic1999201121.511424.5110633.50.147891.416623

EPR likes moderately high usage at average offensive rating, which explains Ewing near the top. In my regression, Ewing's efficiency + usage is above the threshold of having negative (relative) impact. Not quite sure what to make of the rest.



At any rate, here is the entire list of the top 100 players by WS/48

PlayerFromToUSG%ORtgPoints Prod Per 100DRtgMPWS/48(rk)EPR(rk)
David Robinson*1990200326.211630.399634.7
0.251
3.361
Michael Jordan*1985200333.311839.2910338.3
0.251
3.272
LeBron James2004201131.811536.5710240.1
0.2274
2.943
Tim Duncan1998201127.811030.589535.8
0.2166
2.924
Larry Bird*1980199226.511530.4810138.4
0.20313
2.695
Chris Paul2006201123.812128.8010437.1
0.2333
2.676
Dirk Nowitzki199920112711731.5910336.5
0.2148
2.617
Karl Malone*1986200429.411333.2210137.2
0.20512
2.588
Magic Johnson*1980199622.312126.9810436.7
0.2255
2.539
Manu Ginobili2003201125.111528.879928.1
0.2148
2.5210
Shaquille O'Neal1993201129.511333.3410134.7
0.20811
2.4911
Yao Ming2003201126.811230.029932.5
0.214
2.4312
Dwight Howard2005201123.211125.759836
0.18819
2.4213
Charles Barkley*1985200024.811929.5110536.7
0.2166
2.3914
Kevin Garnett1996201125.211127.979936.7
0.19118
2.3915
Hakeem Olajuwon*1985200227.110829.279835.7
0.17730
2.2316
Arvydas Sabonis*1996200322.911225.659724.2
0.214
2.2317
Julius Erving*1980198726.911230.1310234.1
0.18222
2.0818
Dwyane Wade2004201132.511136.0810437.6
0.19316
2.0619
John Stockton*1985200318.912122.8710431.8
0.20910
2.0520
PlayerFromToUSG%ORtgPoints Prod Per 100DRtgMP
WS/48(rk)
EPR(rk)
Kareem Abdul-Jabbar*1980198924.211628.0710432.6
0.18222
2.0321
Pau Gasol2002201123.611527.1410435.9
0.17926
2.0022
Kobe Bryant1997201131.511235.2810536.4
0.18720
1.9723
Adrian Dantley*1980199126.812032.1611036
0.19217
1.9524
Shawn Marion2000201121.111123.4210136.3
0.16246
1.9125
Paul Pierce1999201127.811030.5810337
0.16741
1.8426
Sidney Moncrief1980199120.611924.5110530.2
0.18720
1.8327
Patrick Ewing*198620022810629.689934.3
0.1577
1.8328
Clyde Drexler*1984199825.411428.9610534.6
0.17334
1.8229
Moses Malone*198019952611429.6410533.5
0.17926
1.8230
Larry Nance1982199420.611623.9010433.4
0.17136
1.8131
Amare Stoudemire2003201126.911430.6710634.6
0.17730
1.7732
Kevin McHale*1981199322.411826.4310631
0.1824
1.7733
Alonzo Mourning1993200825.610827.6510031
0.16643
1.7434
Dikembe Mutombo199220091511116.659930.8
0.15369
1.7235
Brad Daugherty1987199422.211425.3110536.5
0.15656
1.7036
Reggie Miller1988200521.612126.1410934.3
0.17632
1.6837
Elton Brand200020112411126.6410436.9
0.15656
1.6438
Chauncey Billups199820112211825.9610732.3
0.17926
1.6439
Carlos Boozer2003201123.911126.5310332.6
0.15951
1.6340
PlayerFromToUSG%ORtgPoints Prod Per 100DRtgMP
WS/48(rk)
EPR(rk)
Chris Bosh2004201124.811328.0210636.9
0.1649
1.6241
Dennis Rodman*1987200011.411413.0010031.7
0.1577
1.5942
Greg Oden2009201019.711723.0510322.1
0.1824
1.5843
Jack Sikma1980199120.911022.9910233.7
0.14982
1.5844
Andrew Bynum2006201118.511721.6510324.3
0.17235
1.5745
Bob Lanier*198019842111223.5210228.1
0.16148
1.5746
Robert Parish*1980199721.211323.9610329
0.15753
1.5647
Andrei Kirilenko2002201118.911221.1710230.8
0.15656
1.5648
Artis Gilmore*1980198818.411921.9010630.9
0.16741
1.5449
Bobby Jones1980198617.111619.8410224.2
0.1737
1.5450
Jeff Ruland1982199322.310924.3110233.4
0.14982
1.5351
Kevin Durant2008201129.811133.0810738
0.15461
1.5352
Eddie Jones1995200820.111122.3110334.4
0.14789
1.5253
Horace Grant1988200415.211717.7810433.2
0.14789
1.5154
Dan Issel*1980198524.911829.3810929.9
0.1737
1.5055
Kermit Washington1980198815.911418.1310229.3
0.15461
1.5056
Scottie Pippen*1988200422.510824.3010234.9
0.14694
1.4957
Al Horford2008201117.511620.3010533.8
0.15461
1.4858
Kevin Johnson1988200022.611826.6710934.1
0.17829
1.4759
Dominique Wilkins*1983199930.311233.9410835.5
0.14885
1.4560
PlayerFromToUSG%ORtgPoints Prod Per 100DRtgMP
WS/48(rk)
EPR(rk)
Bill Laimbeer1981199416.911519.4410431.8
0.14982
1.4361
Ray Allen1997201124.511427.9310837
0.15461
1.4362
Joakim Noah2008201115.411517.7110226.2
0.1649
1.4263
Nene Hilario2003201118.111320.4510329.6
0.15272
1.4264
Blake Griffin2011201127.311130.3010738
0.15272
1.4165
Peja Stojakovic1999201121.511424.5110633.5
0.14789
1.4166
Tracy McGrady1998201129.610831.9710433.7
0.15461
1.4067
Shawn Kemp199020032510626.5010027.9
0.14789
1.3968
Brandon Roy2007201125.411629.4611035.6
0.15753
1.3769
Marques Johnson198019902411226.8810634
0.1577
1.3770
PlayerFromToUSG%ORtgPoints Prod Per 100DRtgMP
WS/48(rk)
EPR(rk)
Detlef Schrempf1986200120.311723.7510729.6
0.15656
1.3371
Paul Millsap2007201119.711422.4610426
0.15174
1.3272
Vince Carter199920112910931.6110636.4
0.14694
1.3273
Todd MacCulloch2000200317.711320.0010015.4
0.16643
1.3274
Mehmet Okur2003201121.611324.4110529.1
0.14694
1.3175
Scot Pollard1998200812.511414.259916.5
0.15369
1.2776
Cedric Maxwell1980198816.911819.9410628.7
0.15461
1.2777
Anderson Varejao2005201113.711515.7610224.7
0.15174
1.2678
Gary Payton1991200722.511124.9810635.3
0.14885
1.2479
Steve Nash1997201121.211925.2311031.3
0.16839
1.2280
PlayerFromToUSG%ORtgPoints Prod Per 100DRtgMP
WS/48(rk)
EPR(rk)
Jeff Hornacek1987200019.711723.0510831.5
0.15461
1.2181
Brad Miller1999201118.411420.9810528.6
0.1577
1.2082
Serge Ibaka2010201115.911518.2910322.8
0.15369
1.2083
Maurice Cheeks1980199315.411718.0210631.8
0.14694
1.1984
Calvin Natt1980199021.311424.2810731.4
0.14694
1.1985
Kevin Love2009201122.111725.8610929.8
0.16345
1.1986
Steve Mix1980198321.711324.5210317.2
0.16839
1.1887
Leon Powe2007201120.411523.4610313.9
0.17433
1.1788
Marcin Gortat2008201115.311617.7510217.2
0.16246
1.1789
Terrell Brandon1992200223.911026.2910529.8
0.14789
1.1590
David Lee200620111911722.2310831
0.14885
1.1491
Kevin Martin2005201124.711728.9011131.2
0.15174
1.1492
Mark Price1987199822.811626.4510929.9
0.15852
1.1493
Ryan Anderson2009201120.711523.8110518.9
0.15753
1.0894
Carl Landry2008201120.511723.9910824.9
0.15560
1.0495
Terry Porter1986200219.111521.9710727.8
0.1577
1.0196
Ricky Pierce198319982511629.0011024.4
0.14694
0.9697
Kiki Vandeweghe1981199323.611928.0811330.3
0.14885
0.9698
Amir Johnson2006201114.312217.4510717.8
0.15461
0.8099
Ty Lawson201020111911822.4211023.6
0.14694
0.69100

Easy Player Rating System!

As a basketball statistician, I am thoroughly obsessed with Jeremias Engalmann's Adjusted Plus-Minus numbers.
As a basketball fan, I realize that most people are hesitant to even attempt to understand what's going on in Adjusted Plus-Minus.

To combine the two worlds, I have looked at the latest four individual seasons of data, and I have compared advanced basketball stats with the Adjusted Plus-Minus numbers. By using four advanced stats (easily found at Basketball-Reference.com: per game, per season, or per-career), we can estimate how much a player impacts their team, per possession.

Here are the four statistics:

-Minutes per Game
-Offensive Rating (ORTG)
-Usage% (Possessions used)
-Defensive Rating (DRTG)

I made a regression of values to predict the Adjusted Plus-Minus, and averaged each season from 2008-2011 (with players having 500 minutes or more). The result is the following:

=(0.035 x Minutes/Game) + (0.43 x (Usage%/100) x Offensive Rating) - (0.14 x Defensive Rating) - (0.44 x Usage%) + 13.8

For Dwight Howard, this season, we get:
37.6 Minutes per game
27.2% Usage
113 Offensive Rating
94 Defensive Rating

=(0.035 x 37.6) + (0.43 x 0.272 x 113) - (0.14 x 94) - (0.44 x 27.2) + 13.8
=1.316 + 13.21648 - 13.16 - 11.968 + 13.8
=3.2        --- (although it's 3.45 if you use the more precise numbers below)

[For stat-heads, the actual coefficients are:  Min/G: 0.034853, ORTG*Usg/100: 0.434141, DRTG: -0.13995, USG%: -0.43613]


So for the 2010-2011 regular season, I have calculated the predicted "Net Efficiency." This is simply our estimate of how much a player adds to his team's point differential per 100 possessions of offense & 100 possessions of defense. Also, I have calculated the estimated "Wins Added" by multiplying their efficiency by the % of minutes they played, and converting that number into a wins estimate (how many wins an average team would have gained from their performance).

Here are the results for 2010-2011 (Regular Season - players with 500 or more minutes).

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