The debut and popularization of BPM

[Mike G]

I think some of you are in danger of overrating MPG. Players with high MPG aren't always that good. You end up overrating players like Drew Gooden who played a lot of minutes but didn't add value to his teams.

Nobody has suggested supplementing known RAPM with MPG info; it's about using MPG to augment boxscore based ratings.
Drew Gooden has career PER of 16.6, and he's averaged 26.5 mpg
Of 76 players since 2000 with a PER in the 15.6 to 17.6 range, his mpg rank 50th. The median is 29.4 . So even playing for mostly bad teams, he's gotten fewer minutes than most in his productivity range. For whatever reason that is, accounting for it would seem to depress his ratings.

One way to account for 'minutes with mostly bad teams' is to factor in the % of career minutes which are in playoff games.
This may inadvertently include 'playoff performance', especially if the player is a star who carries (or fails to carry) his team.

Gooden has gotten 6.6% of his career minutes in playoffs. This isn't actually much below the norm of 8% for major players.
His po/rs is .88, well below the modern norm of .92 and in the bottom 1/3 of players active last season.

These numbers all suggest he's a bit overrated by PER; perhaps also by WS/48 (.107 career). BPM may be harsh, at -1.9; though his RAPM is considerably lower.

[Statman]

I think some of you are in danger of overrating MPG. Players with high MPG aren't always that good. You end up overrating players like Drew Gooden who played a lot of minutes but didn't add value to his teams.

As far as Bruce Bowen, here are his net on/off numbers with the Spurs:
+5.5
+7.6
+1.5
+0.4
+0.7
+10.4
-0.2
-6.1

+2.8 average during his Spurs tenure

Overall he seems more positive than the backup Spurs option until 2008. So BPM should have him positive but not more than +1.

I agree, high MPG don't mean a player should get a boost in rating. It's all relative.

I do playing time adjustments - but the way I do them, guys like Gooden (or Boozer, or Chris Gatling, etc) will pretty much always rank worse by my WAR/48 than they would PER or WS/48. Guys like Bowen, Battier, Tony Allen, Michael Cooper, etc will always rank better. It's trying to find the best that relationship between playing time (relative to quality of team) & production, & how that tells us how much to boost or regress their "production only" rating.

[Statman]

I think some of you are in danger of overrating MPG. Players with high MPG aren't always that good. You end up overrating players like Drew Gooden who played a lot of minutes but didn't add value to his teams.

Nobody has suggested supplementing known RAPM with MPG info; it's about using MPG to augment boxscore based ratings.
Drew Gooden has career PER of 16.6, and he's averaged 26.5 mpg
Of 76 players since 2000 with a PER in the 15.6 to 17.6 range, his mpg rank 50th. The median is 29.4 . So even playing for mostly bad teams, he's gotten fewer minutes than most in his productivity range. For whatever reason that is, accounting for it would seem to depress his ratings.

Yep, that's exactly how my model "sees" a guy like Drew Gooden, playing less that what his per minute (mainly offensive) production would suggest relative to his teammates every year - so his rating gets depressed a bit.

In my metrics, all players get's regressed to the mean (I use team mean production w/o the player's contribution - quality of team & teammates matters), many very little - while the more extreme outliers might be quite a bit. Every player is different.

[permaximum]

I agree, high MPG don't mean a player should get a boost in rating. It's all relative.

MPG couldn't be a factor if we somehow captured everything box-score misses. We can't do that, so MPG is an important factor. In fact, MPG beats PER and WP in prediction which means ranking players according to MPG is better than ranking them according to PER and WP.

Coaches are not that bad at distributing minutes.

[Mike G]

xyz = sqrt(PER*ws/48*BPM)
Since 1974:

Code: Select all

xyz       1-10            yr    Tm    PER   WS/48   BPM
11.09  LeBron James      2009   CLE   31.7   .318  12.2
10.48  LeBron James      2013   MIA   31.6   .322  10.8
10.48  LeBron James      2010   CLE   31.1   .299  11.8
10.36  Michael Jordan    1988   CHI   31.7   .308  11.0
10.26  Michael Jordan    1989   CHI   31.1   .292  11.6

10.02  Michael Jordan    1991   CHI   31.6   .321   9.9
9.66   LeBron James      2012   MIA   30.7   .298  10.2
9.50   Chris Paul        2009   NOH   30.0   .292  10.3
9.48   David Robinson    1994   SAS   30.7   .296   9.9
9.29   Michael Jordan    1990   CHI   31.2   .285   9.7

xyz       11-20           yr    Tm    PER   WS/48   BPM
8.73   Shaquille O'Neal  2000   LAL   30.6   .283   8.8
8.69 Kareem Abdul-Jabbar 1977   LAL   27.8   .283   9.6
8.63   Michael Jordan    1996   CHI   29.4   .317   8.0
8.58   Kevin Garnett     2004   MIN   29.4   .272   9.2
8.56   LeBron James      2008   CLE   29.1   .242  10.4

8.49   Kevin Durant      2014   OKC   29.8   .295   8.2
8.41   David Robinson    1996   SAS   29.4   .290   8.3
8.41   Tracy McGrady     2003   ORL   30.3   .262   8.9
8.40   Michael Jordan    1993   CHI   29.7   .270   8.8
8.36   Dwyane Wade       2009   MIA   30.4   .232   9.9

xyz       21-30           yr    Tm    PER   WS/48   BPM
8.33   Charles Barkley   1991   PHI   28.9   .258   9.3
8.31   Chris Paul        2008   NOH   28.3   .284   8.6
8.19   Charles Barkley   1990   PHI   27.1   .269   9.2
8.19   Stephen Curry     2015   GSW   26.8   .278   9.0
8.08   Magic Johnson     1990   LAL   26.6   .270   9.1

8.06   LeBron James      2014   MIA   29.3   .264   8.4
7.98   David Robinson    1992   SAS   27.5   .260   8.9
7.92   Charles Barkley   1989   PHI   27.0   .250   9.3
7.90   Magic Johnson     1989   LAL   26.9   .267   8.7
7.89   Kevin Garnett     2005   MIN   28.2   .248   8.9

xyz       31-40           yr    Tm    PER   WS/48   BPM
7.86   James Harden    * 2015   HOU   26.5   .271   8.6
7.84 Kareem Abdul-Jabbar 1978   LAL   29.2   .257   8.2
7.82   Karl Malone       1997   UTA   28.9   .268   7.9
7.79   Michael Jordan    1992   CHI   27.7   .274   8.0
7.74 Kareem Abdul-Jabbar 1976   LAL   27.2   .242   9.1

7.72   David Robinson    1995   SAS   29.1   .273   7.5
7.61   Charles Barkley   1988   PHI   27.6   .253   8.3
7.59   Kevin Durant      2013   OKC   28.3   .291   7.0
7.58   Michael Jordan    1987   CHI   29.8   .247   7.8
7.49   LeBron James      2006   CLE   28.1   .232   8.6

xyz       41-50           yr    Tm    PER   WS/48   BPM
7.47   Larry Bird        1987   BOS   26.4   .243   8.7
7.44   Larry Bird        1988   BOS   27.8   .243   8.2
7.43   Dwyane Wade       2010   MIA   28.0   .224   8.8
7.42   Anthony Davis   * 2015   NOP   31.4   .283   6.2
7.41   David Robinson    1991   SAS   27.4   .264   7.6

7.41   Larry Bird        1986   BOS   25.6   .244   8.8
7.39   Magic Johnson     1987   LAL   27.0   .263   7.7
7.39   LeBron James      2011   MIA   27.3   .244   8.2
7.35   Chris Paul        2012   LAC   27.0   .278   7.2
7.29   David Robinson    1998   SAS   27.8   .269   7.1

xyz       51-60           yr    Tm    PER   WS/48   BPM
7.23   Chris Paul        2013   LAC   26.4   .287   6.9
7.22   Kevin Love        2014   MIN   26.9   .245   7.9
7.09   Magic Johnson     1981   LAL   25.7   .225   8.7
7.06   Larry Bird        1985   BOS   26.5   .238   7.9
7.06   Shaquille O'Neal  2002   LAL   29.7   .262   6.4

7.05   Magic Johnson     1991   LAL   25.1   .251   7.9
7.04   Charles Barkley   1993   PHO   25.9   .242   7.9
7.03   Dwyane Wade       2007   MIA   28.9   .219   7.8
6.99   Shaquille O'Neal  2001   LAL   30.2   .245   6.6
6.97   Tim Duncan        2002   SAS   27.0   .257   7.0

xyz       61-70           yr    Tm    PER   WS/48   BPM
6.97   Hakeem Olajuwon   1993   HOU   27.3   .234   7.6
6.95   Chris Paul        2014   LAC   25.9   .270   6.9
6.94   Kevin Garnett     2003   MIN   26.4   .225   8.1
6.93   Michael Jordan    1997   CHI   27.8   .283   6.1
6.91   Karl Malone       1998   UTA   27.9   .259   6.6

6.90 Kareem Abdul-Jabbar 1974   MIL   24.4   .250   7.8
6.80   Dwyane Wade       2006   MIA   27.6   .239   7.0
6.79   Dirk Nowitzki     2007   DAL   27.6   .278   6.0
6.74   Kevin Garnett     2006   MIN   26.8   .242   7.0
6.74   Tim Duncan        2003   SAS   26.9   .248   6.8

xyz       71-80           yr    Tm    PER   WS/48   BPM
6.70   Kevin Garnett     2008   BOS   25.3   .265   6.7
6.70   David Robinson    1999   SAS   24.9   .261   6.9
6.67   Tim Duncan        2004   SAS   27.1   .249   6.6
6.67   Shaquille O'Neal  1999   LAL   30.6   .255   5.7
6.64   Julius Erving     1981   PHI   25.1   .231   7.6

6.59   Manu Ginobili     2008   SAS   24.3   .232   7.7
6.58   Julius Erving     1982   PHI   25.9   .229   7.3
6.56   Karl Malone       1993   UTA   26.2   .238   6.9
6.53   Grant Hill        1997   DET   25.5   .223   7.5
6.52   Karl Malone       2000   UTA   27.1   .249   6.3

xyz       81-90           yr    Tm    PER   WS/48   BPM
6.51   Shaquille O'Neal  1994   ORL   28.5   .252   5.9
6.49 Kareem Abdul-Jabbar 1975   MIL   26.4   .225   7.1
6.43   Karl Malone       1999   UTA   25.6   .252   6.4
6.42   Karl Malone       1996   UTA   26.0   .233   6.8
6.38   Karl Malone       1990   UTA   27.2   .245   6.1

6.37   Shaquille O'Neal  2003   LAL   29.5   .250   5.5
6.30 Kareem Abdul-Jabbar 1979   LAL   25.5   .219   7.1
6.29   Tim Duncan        2007   SAS   26.1   .230   6.6
6.19   Tim Duncan        2005   SAS   27.0   .245   5.8
6.19   Chris Paul      * 2015   LAC   24.5   .244   6.4

xyz       91-100          yr    Tm    PER   WS/48   BPM
6.16   Kyle Lowry      * 2015   TOR   24.4   .229   6.8
6.16   Larry Bird        1984   BOS   24.2   .215   7.3
6.06   David Robinson    1990   SAS   26.3   .241   5.8
5.88   Dwyane Wade       2012   MIA   26.3   .227   5.8
5.87 Kareem Abdul-Jabbar 1980   LAL   25.3   .227   6.0

5.86   Anfernee Hardaway 1996   ORL   24.6   .229   6.1
5.78   Elton Brand       2006   LAC   26.5   .229   5.5
5.74   Karl Malone       1989   UTA   24.4   .233   5.8
5.60   Tim Duncan        2000   SAS   24.8   .218   5.8
5.59   Dwyane Wade       2011   MIA   25.6   .218   5.6

These aren't necessarily the top100 xyz seasons since 1974. They all rank in the top 200 in all 3 stats.
Kind of fun to see them in chronological order:
http://bkref.com/tiny/VWHdC

Jordan appears 9 times in the list; Robinson, Malone, LeBron 8 apiece; Kareem 7 (since 1974); Duncan, Shaq, Paul*, and Wade (6); Barkley, Bird, Garnett, Magic (5).
Then a precipitous drop to 2 for Durant and Erving; a single appearance by Brand, Curry*, ADavis*, JDrew, Ginobili, Penny, Harden*, Hill, Love, McGrady, Dirk, Hakeem.
* -- this year, at ~40% of the season.
No one makes the list for 1983; Moses doesn't make the list at all.

[Mike G]

While I mentioned Moses above (as he was discussed earlier in the thread), others had seasons with better PER and WS/48, but failed to make the top 200 BPM player-seasons -- Nowitzki 3 times.
http://bkref.com/tiny/ZcJmk
So here are the 33 seasons with top 200 PER and WS/48, but BPM <5.5 :

Code: Select all

xyz     Player           yr    Tm    PER   WS/48   BPM
6.28   Dirk Nowitzki    2006   DAL   28.1   .275   5.1
5.82   Kobe Bryant      2006   LAL   28.0   .224   5.4
5.76   Dirk Nowitzki    2003   DAL   25.6   .249   5.2
5.75   Dirk Nowitzki    2005   DAL   26.1   .248   5.1
5.68   Terrell Brandon  1996   CLE   25.2   .237   5.4

5.62   Shaquille O'Neal 1995   ORL   28.6   .230   4.8
5.49   Karl Malone      1991   UTA   24.8   .225   5.4
5.43   Karl Malone      1992   UTA   25.4   .237   4.9
5.38   Karl Malone      2001   UTA   24.7   .217   5.4
5.38   Kevin Durant     2012   OKC   26.2   .230   4.8

xyz     Player           yr    Tm    PER   WS/48   BPM
5.36   David Robinson   2000   SAS   24.6   .238   4.9
5.36   Kevin Durant     2010   OKC   26.2   .238   4.6
5.31   Arvydas Sabonis  1996   POR   24.7   .233   4.9
5.20   Tim Duncan       2010   SAS   24.7   .215   5.1
5.19 Kareem AbdulJabbar 1981   LAL   25.5   .230   4.6

5.14   Shaquille O'Neal 1998   LAL   28.8   .224   4.1
5.08   Robert Parish    1981   BOS   25.2   .228   4.5
5.08   Dirk Nowitzki    2008   DAL   24.6   .223   4.7
5.08   Dwight Howard    2011   ORL   26.1   .235   4.2
5.06   Bob McAdoo       1975   BUF   25.8   .242   4.1

xyz     Player           yr    Tm    PER   WS/48   BPM
5.02   Michael Jordan   1998   CHI   25.2   .238   4.2
4.91   Adrian Dantley   1986   UTA   24.6   .223   4.4
4.90   Bob McAdoo       1974   BUF   24.7   .231   4.2
4.89   Moses Malone     1982   HOU   26.8   .218   4.1
4.88   Dwight Howard    2009   ORL   25.4   .234   4.0

4.82   Kevin Love       2012   MIN   25.4   .223   4.1
4.81  Amar'e Stoudemire 2008   PHO   27.6   .262   3.2
4.81   Adrian Dantley   1984   UTA   24.6   .235   4.0
4.78   Alonzo Mourning  1999   MIA   24.6   .216   4.3
4.77   Alonzo Mourning  2000   MIA   25.8   .226   3.9

xyz     Player           yr    Tm    PER   WS/48   BPM
4.60   Moses Malone     1983   PHI   25.1   .248   3.4
4.33  Amar'e Stoudemire 2005   PHO   26.6   .243   2.9
3.24   Yao Ming         2007   HOU   26.5   .220   1.8

Only the top 3 here would penetrate the top 100 list above it.

[Crow]

I would weight the blend much differently so PER didn't dominate but I like the use of a blend. The weighting might not change the general story much, but might be interesting to check a blend where the 3 metrics were equal in impact or much closer.

[Mike G]

Why do you say PER dominates? It actually has the lowest correlation to xyz as defined:
BPM-- .697
WS/48 .552
PER-- .468

A better ranking might be made by adjusting to replacement value.
xyz = sqrt((PER-10)*(WS/48-.05)*(BPM+2))

This list of 33 isn't typical of anything, as it's a list of those with unusually low BPM, relative to others with similar PER and WS/48.

[Crow]

"Why do you say PER dominates?"

Because it is roughly 5-6 times the size of the BPM input and 100 times the WS input?

[Mike G]

It's the same scale for every player-season listed, so everyone's rank is the same if you divide all PER by 1000 or whatever.

[DSMok1]

It's the same scale for every player-season listed, so everyone's rank is the same if you divide all PER by 1000 or whatever.

I think he was commenting that in order to do a metric blend, the data should be standardized (same mean and standard deviation).

[Mike G]

From a concurrent thread:

... BPM has a "raw" form (ASPM) which is then adjusted -- sometimes radically -- for players on a team, so that the team then has aggregate BPM equivalent to their point differential. ..

BPM should not be thought of as a raw form that is then adjusted--the adjustment was an inherent part of the derivation regression itself.

My impression of the team adjustment was based on your spreadsheet. Earlier in this thread, the interpretation was unchallenged:

..., check out the 1983 Philly/Moses 4-5-4 champs:

Code: Select all

'83 Sixers       %Min  rawSPM  rContr  TmAdj   BPM   Contrib    bpm2  Contr2
Moses Malone     .74    1.73    1.28   1.66    3.39   2.50      6.18   4.55
Andrew Toney     .62    -.94    -.59   1.66     .72    .45      1.40    .88
Maurice Cheeks   .62    1.66    1.03   1.66    3.32   2.07      3.97   2.47
Julius Erving    .61    4.24    2.59   1.66    5.90   3.60      6.40   3.90
Bobby Jones      .44    2.41    1.06   1.66    4.07   1.79      3.02   1.33

Clint Richardson .44   -1.15    -.51   1.66     .51    .23      -.52   -.23
Marc Iavaroni    .41   -2.55   -1.04   1.66    -.89   -.36     -2.10   -.85
Franklin Edwards .32   -3.03    -.97   1.66   -1.37   -.44     -2.85   -.91
Earl Cureton     .25   -3.59    -.89   1.66   -1.92   -.48     -3.52   -.88
Russ Schoene     .18   -3.04    -.54   1.66   -1.38   -.24     -3.03   -.54

Clemon Johnson   .18   -1.07    -.19   1.66     .59    .10     -1.05   -.19
Reggie Johnson   .14   -3.83    -.53   1.66   -2.17   -.30     -3.82   -.53
Mark McNamara    .05   -8.17    -.38   1.66   -6.51   -.30     -8.17   -.38
J.J. Anderson    .01  -11.79    -.14   1.66  -10.13   -.12    -11.79   -.14

. totals        5.00             .20                  8.50             8.50

rContr = raw contributions = %Min*rawSPM
Contrib = %Min*BPM
Raw contributions total +0.20 points per game. This means all the calculations based on regressions and fits with RAPM rate this super- team at barely NBA average.
The team correction of 1.66 is then applied to all players' raw SPM, and contributions from BPM total 8.5 per game. Of course all 5 players getting 1.66 better will do that. But that means the raw SPM was in error by some (1.66*5= ) 8.30 pts/G ...

The bpm2 column uses an alternative 'team' adjustment using %Min as the basis for reward.

How do you 'pre-adjust' your BPM according to the team's ultimate sum of rawSPM*%Min ?
Unless you are referring to the fact that 'advanced' stats incorporate team and opponent rates? And then you apply an additional team adjustment to square up team SRS and summary BPM.

[DSMok1]

From a concurrent thread:

... BPM has a "raw" form (ASPM) which is then adjusted -- sometimes radically -- for players on a team, so that the team then has aggregate BPM equivalent to their point differential. ..

BPM should not be thought of as a raw form that is then adjusted--the adjustment was an inherent part of the derivation regression itself.

My impression of the team adjustment was based on your spreadsheet. Earlier in this thread, the interpretation was unchallenged:

..., check out the 1983 Philly/Moses 4-5-4 champs:

Code: Select all

'83 Sixers       %Min  rawSPM  rContr  TmAdj   BPM   Contrib    bpm2  Contr2
Moses Malone     .74    1.73    1.28   1.66    3.39   2.50      6.18   4.55
Andrew Toney     .62    -.94    -.59   1.66     .72    .45      1.40    .88
Maurice Cheeks   .62    1.66    1.03   1.66    3.32   2.07      3.97   2.47
Julius Erving    .61    4.24    2.59   1.66    5.90   3.60      6.40   3.90
Bobby Jones      .44    2.41    1.06   1.66    4.07   1.79      3.02   1.33

Clint Richardson .44   -1.15    -.51   1.66     .51    .23      -.52   -.23
Marc Iavaroni    .41   -2.55   -1.04   1.66    -.89   -.36     -2.10   -.85
Franklin Edwards .32   -3.03    -.97   1.66   -1.37   -.44     -2.85   -.91
Earl Cureton     .25   -3.59    -.89   1.66   -1.92   -.48     -3.52   -.88
Russ Schoene     .18   -3.04    -.54   1.66   -1.38   -.24     -3.03   -.54

Clemon Johnson   .18   -1.07    -.19   1.66     .59    .10     -1.05   -.19
Reggie Johnson   .14   -3.83    -.53   1.66   -2.17   -.30     -3.82   -.53
Mark McNamara    .05   -8.17    -.38   1.66   -6.51   -.30     -8.17   -.38
J.J. Anderson    .01  -11.79    -.14   1.66  -10.13   -.12    -11.79   -.14

. totals        5.00             .20                  8.50             8.50

rContr = raw contributions = %Min*rawSPM
Contrib = %Min*BPM
Raw contributions total +0.20 points per game. This means all the calculations based on regressions and fits with RAPM rate this super- team at barely NBA average.
The team correction of 1.66 is then applied to all players' raw SPM, and contributions from BPM total 8.5 per game. Of course all 5 players getting 1.66 better will do that. But that means the raw SPM was in error by some (1.66*5= ) 8.30 pts/G ...

The bpm2 column uses an alternative 'team' adjustment using %Min as the basis for reward.

How do you 'pre-adjust' your BPM according to the team's ultimate sum of rawSPM*%Min ?
Unless you are referring to the fact that 'advanced' stats incorporate team and opponent rates? And then you apply an additional team adjustment to square up team SRS and summary BPM.

When I developed the regression, the team adjustment was part of the regression itself--the coefficients of BPM were developed while accounting for the team adjustment. Mathematically, it is compiled as raw and then adjusted, but that whole adjustment process was PART of the actual coefficient development, not applied after the fact.

I don't say, though, that there may not be a better methodology to do the team adjustment mathematically, but then the actual coefficients should be adjusted to account for that new method.

[Mike G]

So, correct me if I'm wrong, but the regressions minimize the team adjustments? And then you still have to adjust rawSPM to get your final BPM's?

Can you still say "that whole adjustment process was PART of the actual coefficient development, not applied after the fact." -- when in fact you have a 'team adjustment' of 1.66 per player, summing to 8.3 PPG for the team?

The team adjustments are team-specific, and in some cases they 'adjust' the team by more than 10 PPG.

I don't say, though, that there may not be a better methodology to do the team adjustment mathematically, but then the actual coefficients should be adjusted to account for that new method.

If Moses Malone's BPM are too low by 2 or 3 in many years, his career BPM are too low.
Since there are head scratcher anomalies among players, and the team adjustments can be pretty huge, maybe coefficient changes would make sense.

[DSMok1]

Sorry, you're wrong... I'll correct:

The process, as laid out in the About BPM article, is as follows:

Mathematically: Coefficients -> Raw SPM -> Team Adjustment -> Final BPM.

Derivation: coefficients were found by minimizing FINAL BPM error. So the coefficients were varied to minimize error of Final BPM onto RAPM.

This wasn't a normal SPM linear regression where Raw SPM was found to minimize error on RAPM, and then an ad-hoc team adjustment was added after the fact. The coefficients were found with the team adjustment already in place, dynamically.