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Re: The debut and popularization of BPM
Posted: Mon Dec 22, 2014 1:14 pm
by Mike G
colts18 wrote: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.
Re: The debut and popularization of BPM
Posted: Mon Dec 22, 2014 9:46 pm
by Statman
colts18 wrote: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.
Re: The debut and popularization of BPM
Posted: Mon Dec 22, 2014 9:57 pm
by Statman
Mike G wrote:colts18 wrote: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.
Re: The debut and popularization of BPM
Posted: Tue Dec 23, 2014 12:49 am
by permaximum
Statman wrote:
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.
Re: The debut and popularization of BPM
Posted: Mon Jan 05, 2015 11:14 am
by 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.
Re: The debut and popularization of BPM
Posted: Wed Jan 07, 2015 12:57 pm
by 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.
Re: The debut and popularization of BPM
Posted: Wed Jan 07, 2015 5:40 pm
by 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.
Re: The debut and popularization of BPM
Posted: Wed Jan 07, 2015 10:17 pm
by 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.
Re: The debut and popularization of BPM
Posted: Wed Jan 07, 2015 10:47 pm
by 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?
Re: The debut and popularization of BPM
Posted: Wed Jan 07, 2015 10:51 pm
by 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.
Re: The debut and popularization of BPM
Posted: Thu Jan 08, 2015 1:35 pm
by DSMok1
Mike G wrote: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).
Re: The debut and popularization of BPM
Posted: Thu Jan 08, 2015 2:34 pm
by Mike G
From a concurrent thread:
DSMok1 wrote:Mike G wrote:... 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:
Mike G wrote:..., 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.
Re: The debut and popularization of BPM
Posted: Thu Jan 08, 2015 2:55 pm
by DSMok1
Mike G wrote:From a concurrent thread:
DSMok1 wrote:Mike G wrote:... 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:
Mike G wrote:..., 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.
Re: The debut and popularization of BPM
Posted: Thu Jan 08, 2015 3:14 pm
by 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.
Re: The debut and popularization of BPM
Posted: Thu Jan 08, 2015 3:34 pm
by 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.