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Playoff RAPM Power Rankings

Posted by Neil Paine on April 21, 2011

What happens if you create power rankings using Jeremias Engelmann's 4-year Regularized Plus-Minus ratings (the most predictive version of APM) and each playoff team's distribution of minutes through two games?

Take a look:

Team MP Offense Defense Overall
MIA 479 11.0 6.2 17.0
LAL 482 6.9 6.9 13.9
BOS 479 4.1 9.0 13.2
POR 479 6.3 6.6 13.1
ORL 482 7.7 5.3 12.9
DAL 480 6.7 5.9 12.6
SAS 480 6.3 5.9 11.9
DEN 480 5.8 4.9 10.6
CHI 478 3.8 6.5 10.3
OKC 481 4.0 5.4 9.3
MEM 480 3.0 5.4 8.2
NYK 482 7.3 -1.0 6.4
PHI 479 2.1 3.5 5.5
NOH 480 2.7 2.7 5.4
ATL 481 2.1 3.3 5.3
IND 479 1.7 2.9 4.7

Those rankings are based on these rosters:

Player Tm G MP Off Def Ovr Player Tm G MP Off Def Ovr
Joe Johnson ATL 2 88 3.9 -0.7 3.2 Dwight Howard ORL 2 94 3.6 4.0 7.6
Al Horford ATL 2 71 0.1 1.4 1.4 Hedo Turkoglu ORL 2 78 2.9 -0.1 2.7
Josh Smith ATL 2 68 0.2 4.1 4.3 Jameer Nelson ORL 2 74 0.4 1.7 2.1
Jamal Crawford ATL 2 62 3.4 -2.1 1.2 Jason Richardson ORL 2 70 1.5 -1.8 -0.3
Kirk Hinrich ATL 2 58 -1.1 0.4 -0.8 Ryan Anderson ORL 2 52 1.7 1.8 3.4
Jason Collins ATL 2 37 -4.3 2.8 -1.5 Brandon Bass ORL 2 38 -1.2 1.2 0.0
Marvin Williams ATL 2 36 -0.8 0.4 -0.4 J.J. Redick ORL 2 38 0.6 -1.1 -0.5
Zaza Pachulia ATL 2 28 -1.0 1.1 0.1 Quentin Richardson ORL 2 20 -0.4 1.1 0.8
Josh Powell ATL 2 16 -2.8 -2.2 -5.1 Gilbert Arenas ORL 2 18 -0.8 1.4 0.6
Hilton Armstrong ATL 1 7 -3.2 1.0 -2.2
Etan Thomas ATL 1 7 -2.1 -0.9 -3.0
Damien Wilkins ATL 1 3 -2.7 -1.0 -3.7
Player Tm G MP Off Def Ovr Player Tm G MP Off Def Ovr
Rajon Rondo BOS 2 85 0.9 0.0 0.9 Carmelo Anthony NYK 2 78 3.5 -1.7 1.9
Paul Pierce BOS 2 84 2.8 2.5 5.2 Toney Douglas NYK 2 60 0.8 -0.5 0.2
Ray Allen BOS 2 80 3.2 0.7 4.0 Amare Stoudemire NYK 2 56 2.6 -0.9 1.8
Kevin Garnett BOS 2 70 1.1 6.4 7.5 Ronny Turiaf NYK 2 52 0.4 0.9 1.3
Glen Davis BOS 2 52 -2.0 0.9 -1.1 Bill Walker NYK 2 50 1.1 0.4 1.5
Jermaine O'Neal BOS 2 43 -1.6 2.1 0.5 Jared Jeffries NYK 2 45 0.5 1.8 2.4
Jeff Green BOS 2 29 -1.5 -2.1 -3.5 Chauncey Billups NYK 1 35 3.7 -0.3 3.4
Delonte West BOS 2 28 -0.9 2.2 1.3 Landry Fields NYK 2 35 1.8 -0.4 1.4
Nenad Krstic BOS 2 8 -1.2 1.6 0.4 Shawne Williams NYK 2 32 -0.3 0.1 -0.2
Anthony Carter NYK 2 21 -1.7 -0.5 -2.2
Roger Mason NYK 1 18 -0.4 -0.1 -0.5
Player Tm G MP Off Def Ovr Player Tm G MP Off Def Ovr
Luol Deng CHI 2 80 0.8 3.0 3.8 Danny Granger IND 2 75 2.7 -0.2 2.5
Derrick Rose CHI 2 78 1.9 0.0 1.9 Tyler Hansbrough IND 2 75 -1.3 0.1 -1.1
Carlos Boozer CHI 2 68 2.8 -0.7 2.2 Paul George IND 2 58 0.5 0.4 0.9
Joakim Noah CHI 2 60 0.6 1.8 2.4 Roy Hibbert IND 2 54 0.2 3.0 3.2
Kyle Korver CHI 2 43 0.7 1.9 2.5 Darren Collison IND 2 49 -0.4 -1.5 -1.9
Keith Bogans CHI 2 36 0.1 0.1 0.2 A.J. Price IND 2 38 0.7 0.9 1.6
Kurt Thomas CHI 2 34 -1.6 2.6 1.0 Jeff Foster IND 2 33 1.0 2.2 3.2
Ronnie Brewer CHI 2 32 -1.0 1.9 0.9 Brandon Rush IND 2 31 -1.8 -0.2 -2.0
Taj Gibson CHI 2 24 -0.8 1.6 0.8 Josh McRoberts IND 2 29 0.9 0.9 1.8
C.J. Watson CHI 2 18 -0.1 1.4 1.2 Mike Dunleavy IND 2 28 0.4 1.5 1.8
Omer Asik CHI 2 5 0.2 3.8 4.0 T.J. Ford IND 1 9 -0.3 0.8 0.4
Player Tm G MP Off Def Ovr Player Tm G MP Off Def Ovr
LeBron James MIA 2 82 6.6 3.7 10.2 Jrue Holiday PHI 2 73 2.0 -0.2 1.8
Chris Bosh MIA 2 74 2.8 2.1 4.9 Andre Iguodala PHI 2 73 -0.1 2.1 2.0
Dwyane Wade MIA 2 69 6.2 0.5 6.7 Elton Brand PHI 2 70 -0.8 1.7 0.9
Mike Bibby MIA 2 54 1.6 -1.3 0.3 Thaddeus Young PHI 2 57 1.9 2.5 4.3
Joel Anthony MIA 2 53 -3.6 1.5 -2.2 Jodie Meeks PHI 2 53 2.0 0.4 2.4
James Jones MIA 2 49 0.3 0.1 0.4 Louis Williams PHI 2 47 0.8 -1.9 -1.1
Mario Chalmers MIA 2 44 -1.1 1.2 0.1 Evan Turner PHI 2 35 -1.9 1.8 -0.1
Zydrunas Ilgauskas MIA 2 36 0.4 1.1 1.5 Spencer Hawes PHI 2 26 -1.4 -1.2 -2.6
Eddie House MIA 1 6 -0.1 0.6 0.5 Marreese Speights PHI 2 21 -0.2 -2.3 -2.5
Mike Miller MIA 2 6 1.0 -1.9 -0.9 Tony Battie PHI 2 14 -2.6 2.2 -0.3
Juwan Howard MIA 1 3 -1.8 -0.9 -2.6 Andres Nocioni PHI 1 10 0.9 -1.1 -0.2
Jamaal Magloire MIA 1 3 -0.9 1.6 0.7
Player Tm G MP Off Def Ovr Player Tm G MP Off Def Ovr
Dirk Nowitzki DAL 2 77 5.0 2.8 7.8 LaMarcus Aldridge POR 2 84 2.4 2.6 5.1
Jason Kidd DAL 2 68 0.7 1.2 1.9 Gerald Wallace POR 2 77 0.4 3.0 3.5
Shawn Marion DAL 2 61 -0.7 1.5 0.8 Andre Miller POR 2 72 2.5 0.5 3.0
Tyson Chandler DAL 2 60 0.0 2.6 2.6 Marcus Camby POR 2 65 -0.1 2.9 2.8
Jason Terry DAL 2 60 2.5 -0.6 1.9 Nicolas Batum POR 2 59 2.1 -1.2 0.9
Peja Stojakovic DAL 2 46 3.2 0.2 3.5 Wesley Matthews POR 2 55 -0.9 0.2 -0.6
Brendan Haywood DAL 2 36 -0.5 1.9 1.4 Brandon Roy POR 2 34 3.5 -0.1 3.4
Jose Barea DAL 2 35 -0.8 -0.9 -1.7 Rudy Fernandez POR 2 29 0.4 1.0 1.4
DeShawn Stevenson DAL 2 32 0.1 0.3 0.4 Patrick Mills POR 1 4 -2.1 -1.7 -3.8
Corey Brewer DAL 1 4 -1.2 1.0 -0.3 Armon Johnson POR 1 0 -1.4 1.1 -0.3
Brian Cardinal DAL 2 1 1.1 0.0 1.1
Player Tm G MP Off Def Ovr Player Tm G MP Off Def Ovr
Ty Lawson DEN 2 71 2.7 -1.0 1.7 Kevin Durant OKC 2 82 1.9 -0.8 1.1
Raymond Felton DEN 2 69 0.5 1.0 1.5 Russell Westbrook OKC 2 70 2.6 1.5 4.1
Danilo Gallinari DEN 2 69 1.4 0.5 1.9 James Harden OKC 2 54 2.3 1.8 4.0
Nene Hilario DEN 2 69 1.8 2.8 4.5 Kendrick Perkins OKC 2 53 -0.4 1.0 0.6
Wilson Chandler DEN 2 61 -0.4 1.2 0.9 Nick Collison OKC 2 51 0.4 2.3 2.7
Kenyon Martin DEN 2 56 0.0 2.1 2.1 Serge Ibaka OKC 2 48 -0.5 1.1 0.5
Al Harrington DEN 2 37 1.8 -0.1 1.6 Thabo Sefolosha OKC 2 45 -0.3 2.5 2.2
J.R. Smith DEN 2 24 3.1 0.4 3.5 Nazr Mohammed OKC 2 29 -0.9 -1.0 -1.9
Chris Andersen DEN 2 20 -0.1 2.5 2.5 Eric Maynor OKC 2 27 -0.1 2.8 2.8
Gary Forbes DEN 1 2 -0.3 -1.9 -2.2 Daequan Cook OKC 2 22 -0.4 0.0 -0.4
Kosta Koufos DEN 1 2 -1.8 -0.9 -2.7
Player Tm G MP Off Def Ovr Player Tm G MP Off Def Ovr
Kobe Bryant LAL 2 77 4.7 0.1 4.8 Chris Paul NOH 2 84 5.5 1.7 7.3
Pau Gasol LAL 2 74 2.9 1.5 4.4 Trevor Ariza NOH 2 81 -1.6 1.6 0.0
Ron Artest LAL 2 69 -0.1 3.5 3.5 Carl Landry NOH 2 69 0.8 -1.1 -0.4
Derek Fisher LAL 2 69 1.0 -0.2 0.8 Marco Belinelli NOH 2 52 0.4 -0.1 0.3
Lamar Odom LAL 2 59 1.5 3.4 4.9 Jarrett Jack NOH 2 48 0.1 -1.1 -1.0
Andrew Bynum LAL 2 58 -0.1 2.3 2.2 Emeka Okafor NOH 2 46 -1.4 1.2 -0.2
Shannon Brown LAL 2 30 -3.4 0.3 -3.1 Aaron Gray NOH 2 43 -0.2 0.7 0.5
Matt Barnes LAL 2 20 1.5 -1.0 0.5 Willie Green NOH 2 25 -1.1 -0.1 -1.1
Steve Blake LAL 1 18 1.4 -0.1 1.2 Jason Smith NOH 2 23 -1.5 0.9 -0.5
Trey Johnson LAL 1 6 -0.5 -0.1 -0.6 Didier Ilunga-Mbenga NOH 2 9 -2.5 1.5 -1.0
Theo Ratliff LAL 1 1 -0.8 -0.2 -1.0
Joe Smith LAL 1 1 -1.2 0.4 -0.9
Player Tm G MP Off Def Ovr Player Tm G MP Off Def Ovr
Mike Conley MEM 2 85 2.9 0.2 3.1 Tony Parker SAS 2 76 1.5 1.1 2.6
Marc Gasol MEM 2 83 0.7 1.6 2.2 Tim Duncan SAS 2 71 1.5 3.9 5.3
Zach Randolph MEM 2 68 0.9 1.5 2.4 Richard Jefferson SAS 2 71 0.7 0.7 1.4
Shane Battier MEM 2 53 1.9 1.7 3.6 George Hill SAS 2 64 0.3 0.7 0.9
Tony Allen MEM 2 52 -1.6 3.6 2.0 Matt Bonner SAS 2 44 2.3 1.8 4.0
O.J. Mayo MEM 2 49 1.4 -1.8 -0.5 Gary Neal SAS 2 44 0.9 -1.6 -0.7
Sam Young MEM 2 42 -1.1 0.0 -1.1 Antonio McDyess SAS 2 40 0.8 1.3 2.0
Darrell Arthur MEM 2 36 -3.1 2.1 -1.0 DeJuan Blair SAS 2 35 -0.1 -0.5 -0.7
Greivis Vasquez MEM 2 7 -0.8 -0.5 -1.4 Manu Ginobili SAS 1 34 4.3 1.9 6.2
Leon Powe MEM 1 3 0.1 1.1 1.1 Danny Green SAS 2 1 -0.2 0.2 0.0
Hamed Haddadi MEM 1 1 0.2 1.1 1.4
Ishmael Smith MEM 1 1 -0.9 -0.4 -1.3

Some notes:

  • I checked with Jeremias to make sure I was correctly computing the team power rankings as 5 * the minute-weighted average of a team's RAPM ratings. He said that was correct -- on-court efficiency is basically predicted by the sum of the ratings for each 5-man unit.
  • Even so, the team ratings look incredibly high by efficiency differential standards. Here is what Jeremias thinks causes this effect:

    "The shift comes from the the part that makes ridge regression different from ordinary least squares regression, the part where we penalize for extreme player ratings."

    "Because both offensive and defensive rating get shifted to be more positive and because we subtract expected defensive efficiency from expected offensive efficiency the point differential forecast for each 5 against 5 lineup stays the same with the shift. But the penalizing term somehow seems to get better (lower) through the shift. How much shift there is is dependent on rating distribution of the players. As mentioned earlier the system should benefit by moving everyone closer to '0' or by centering ratings around '0' and that's exactly what it does here. The problem is that the players with more positive ratings get more minutes and so the final team ratings are a bit skewed. They do work just as well when we want to forecast expected point differential between two teams but if we don't subtract one team's rating by the other one's things get a bit weird. I think it's the nature of ridge regression and everybody that wants to plug resulting team numbers into a formula where the expected team differentials are not subtracted from one another needs to keep that in mind."

  • To make the ratings look more like, say, the BBR Rankings, Jeremias suggested a hack whereby you subtract 0.5 (per 100) from both offensive and defensive RAPM for each player. Here are the rankings if you do that:
    Team MP Offense Defense Overall
    MIA 479 8.5 3.7 12.2
    LAL 482 4.4 4.4 8.9
    BOS 479 1.6 6.5 8.1
    ORL 482 5.2 2.8 8.0
    POR 479 3.8 4.1 7.9
    DAL 480 4.2 3.4 7.6
    SAS 480 3.8 3.4 7.2
    DEN 480 3.3 2.4 5.7
    CHI 478 1.3 4.0 5.3
    OKC 481 1.5 2.9 4.4
    MEM 480 0.5 2.9 3.4
    NYK 482 4.8 -3.5 1.3
    PHI 479 -0.4 1.0 0.6
    ATL 481 -0.4 0.8 0.5
    NOH 480 0.2 0.2 0.3
    IND 479 -0.8 0.4 -0.4
  • Either way, Miami's rating is going to be artificially inflated for the same reason +/- systems predicted 68 wins for them before the season -- it doesn't take into account a diminishing-returns effect when multiple high-plus/minus players are on the floor at once. As mentioned above, adjusted plus/minus-style systems are additive, meaning a team's efficiency is the sum of the individual ratings of the players in a 5-man unit. This is a good model in the majority of situations, but an extreme outlier like Miami causes its efficiency prediction to be overestimated. This also affects other teams with "Big Threes" (like Boston), but for no team is the effect as pronounced as with the Heat.

Anyway, even with its flaws I thought it would be interesting to look at a set of "playoff power rankings" generated from individual RAPM scores. Many thanks to Jeremias, proprietor of this great resource, for walking me through some of RAPM's unique properties.

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19 Responses to “Playoff RAPM Power Rankings”

  1. DSMok1 Says:

    I don't know that the very high numbers at first are wrong at all, other than the diminishing-returns lack. There is a significant effect in shortening the rotations down (1 pt or more). There is also a significant effect of having everyone healthy (most teams are healthy right now). That could easily add up to several points. Maybe not 5, but certainly several.

  2. Matt, Colombia Says:

    Overrated by this model: Heat, Magic, Celtics and Lakers (They are still near the top, just not what they were, Kobe is starting to show his age)

    Underrated: OKC

  3. Jerry Says:

    DSMok1, the numbers really are too high. Let's ignore defense for a minute. If we just wanted to to know how many points each 5 man unit was "supposed to score" according to 4 year offensive RAPM and computed the average of "expected points per possession" for all units and possessions, then we end up at a higher "points per possession" than what was actually league average over that timespan. Only when we start subtracting defense from offense the "expected points score per possession" goes down to league average again.

  4. DSMok1 Says:

    You're right, Jerry. My bad.

    On another note: I just calculated the RAPM power ratings for the playoff distributions, except using the SAS with Manu back from the last game. In addition, I used the 1 year RAPM rather than 4-year, which perhaps would be more valid for this situation. Here are the team ratings:

    Team Offense Defense Overall
    MIA 6.54 4.22 10.84
    SAS 5.27 4.31 9.67
    BOS 2.15 7.08 9.06
    LAL 4.56 4.38 9.03
    ORL 4.52 3.94 8.56
    DAL 4.31 3.68 7.95
    DEN 4.63 3.06 7.85
    POR 4.73 3.11 7.81
    OKC 4.97 2.81 7.81
    CHI 2.24 5.30 7.56
    MEM 2.80 3.47 6.21
    PHI 0.70 3.56 4.34
    NYK 4.67 -1.07 3.41
    NOH 1.29 1.02 2.38
    ATL 0.04 2.08 2.19
    IND -0.35 0.87 0.59

  5. Neil Paine Says:

    That looks a lot better (although 2011 alone doesn't predict future outcomes as well as 2008-2011).

    FWIW, this is what you get if you plug SPM in instead of RAPM:

    Team Overall
    ORL 12.86
    MIA 11.03
    CHI 10.39
    BOS 9.37
    LAL 9.13
    SAS 7.82
    POR 6.28
    DEN 6.17
    DAL 6.12
    MEM 5.58
    OKC 4.78
    PHI 3.73
    NOH 1.47
    NYK -0.24
    IND -0.32
    ATL -0.40

    The Magic got to #1 thanks to this minute distribution:

    Player Team G MP SPM
    Dwight Howard ORL 2 94 7.24
    Hedo Turkoglu ORL 2 78 2.09
    Jameer Nelson ORL 2 74 2.20
    Jason Richardson ORL 2 70 2.30
    Ryan Anderson ORL 2 52 4.24
    Brandon Bass ORL 2 38 -1.22
    J.J. Redick ORL 2 38 -0.62
    Quentin Richardson ORL 2 20 -2.96
    Gilbert Arenas ORL 2 18 -1.06
  6. DSMok1 Says:

    "That looks a lot better (although 2011 alone doesn't predict future outcomes as well as 2008-2011)."

    For individual players, no. Perhaps for teams, though, since they're still playing the same players for the most part, 2011 may be best? Maybe a smaller lambda, even?

  7. Scott Says:

    The main benefit to regular APM is that it fits the model well on a whole as long as lineup combinations are expected to be similar. Multicolinearilty isn't an issue on the team level. RAPM is better on the individual level, but the bias towards 0 (for the 1 year model) and prior years hurt the overall fit.

    The only benefit I can think of for fitting RAPM to team ratings deals with overfitting. Perhaps the Knicks would be better predicted by RAPM since the playoff lineup might be significantly different than the regular season lineup.

  8. DSMok1 Says:

    I agree, Scott. Thus my thought that for best predicting out-of-sample TEAM performance, perhaps the Lambda ought to be lower. Perhaps, also, a Bayesian weighting system deprecating older play would be useful if we're trying to predict.

  9. DSMok1 Says:

    Of course, small sample size is still an issue in favor of some regression to the mean for each player and even for team ratings.

  10. Nathan Walker Says:

    One of the limitations of RAPM is its obvious lack of describing diminishing returns (or accurately measuring how a player performs when traded, etc).

    The Miami Heat's 4-year predicted efficiency differential is extremely biased, because it assumes Lebron/Bosh/Wade's usages on their prior teams. The big three's usage% has decreased significantly (as everyone projected)- and I bet if someone measured defensive usage, it would be the same.

    Basically, if we were playing "make it, take it" rather than actual basketball, the Heat's numbers would stand up :)

  11. Nathan Walker Says:

    Nevermind, I see that Neil addressed this in the post.

  12. EvanZ Says:

    BTW, Jeremias Engelmann communicated to me recently that he calculated y-t-y correlation for 1-yr RAPM. You can see the exchange here on one of my recent posts:

    http://thecity2.com/2011/04/15/the-city-2011-mip/#comment-1028

    It looks like R^2 for 1-yr RAPM is roughly 0.25.

    I'll also post the retrodiction results for ezpm once each series is finished. See how it stacks up against these other metrics.

  13. EvanZ Says:

    Oh, now I realized he posted here too. Anyway...

  14. Nathan Walker Says:

    I used Daniel (Dsmok1's) numbers here to simulate the playoffs:

    rating quarters semis finals champ champ rank
    1W SAN 9.67 0.655587031 0.4363 0.2696 0.1581 2
    8W MEM 6.21 0.344412969 0.1468 0.0581 0.0202 9
    4W OKC 7.81 0.788457489 0.3301 0.1723 0.0828 6
    5W DEN 7.85 0.211542511 0.0868 0.0444 0.0201 10
    3W DAL 7.95 0.796053256 0.4237 0.1902 0.0816 7
    6W POR 7.81 0.203946744 0.1085 0.0451 0.0186 11
    2W LAL 9.03 0.808013755 0.4378 0.2158 0.11 3
    7W NOR 2.38 0.191986245 0.03 0.0045 0.0009 12
    1E CHI 7.56 0.966930273 0.5222 0.1938 0.0782 8
    8E IND 0.59 0.033069727 0.0057 0.0004 0 16
    4E ORL 8.56 0.79666838 0.4381 0.1915 0.0842 5
    5E ATL 2.19 0.20333162 0.034 0.0052 0.0005 14
    3E bos 9.06 0.949857377 0.4069 0.2155 0.1056 4
    6E NYK 3.41 0.050142623 0.0066 0.0019 0.0003 15
    2E MIA 10.84 0.961516536 0.5782 0.39 0.2381 1
    7E PHI 4.34 0.038483464 0.0083 0.0017 0.0008 13

  15. Nathan Walker Says:

    Ehhh that's ugly. Why can't I delete my comments?

    rating quarters semis finals champ champ rank if quarters? if semis if finals
    1W SAN 9.67 0.655587031 0.4363 0.2696 0.1581 2 0.241157913 0.362365345 0.586424332
    8W MEM 6.21 0.344412969 0.1468 0.0581 0.0202 9 0.058650521 0.13760218 0.34767642
    4W OKC 7.81 0.788457489 0.3301 0.1723 0.0828 6 0.105015174 0.250833081 0.480557168
    5W DEN 7.85 0.211542511 0.0868 0.0444 0.0201 10 0.095016363 0.23156682 0.452702703
    3W DAL 7.95 0.796053256 0.4237 0.1902 0.0816 7 0.102505705 0.192589096 0.429022082
    6W POR 7.81 0.203946744 0.1085 0.0451 0.0186 11 0.091200279 0.171428571 0.412416851
    2W LAL 9.03 0.808013755 0.4378 0.2158 0.11 3 0.136136296 0.251256281 0.509731233
    7W NOR 2.38 0.191986245 0.03 0.0045 0.0009 12 0.004687836 0.03 0.2
    1E CHI 7.56 0.966930273 0.5222 0.1938 0.0782 8 0.080874498 0.149751053 0.403508772
    8E IND 0.59 0.033069727 0.0057 0.0004 0 16 0 0 0
    4E ORL 8.56 0.79666838 0.4381 0.1915 0.0842 5 0.105690149 0.192193563 0.439686684
    5E ATL 2.19 0.20333162 0.034 0.0052 0.0005 14 0.002459037 0.014705882 0.096153846
    3E bos 9.06 0.949857377 0.4069 0.2155 0.1056 4 0.111174585 0.259523224 0.490023202
    6E NYK 3.41 0.050142623 0.0066 0.0019 0.0003 15 0.005982934 0.045454545 0.157894737
    2E MIA 10.84 0.961516536 0.5782 0.39 0.2381 1 0.247629647 0.411795227 0.610512821
    7E PHI 4.34 0.038483464 0.0083 0.0017 0.0008 13 0.020788149 0.096385542 0.470588235

  16. Nathan Walker Says:

    Or preview what my code looks like...yuck. My bad.

    Useful data above:
    The only team with >50% of going to the Semis is Miami.

  17. Crow Says:

    And, by your numbers, Chicago.

  18. Mike Says:

    How does RAPM work? I'm curious about it; if it works how it was meant to work that would make it the go-to stat for measuring player value.

  19. Jerry Says:

    Mike:
    http://www.sloansportsconference.com/research-papers/2010-2/past-years/improved-nba-adjusted-using-regularization-and-out-of-sample-testing/