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John Stockton and BPM
Posted: Tue Aug 21, 2018 2:05 pm
by Jinxed
Hey I have some questions regarding how BPM is calculated, using John Stockton as an example.
1. Looking at basketballreference's explanation of BPM, the coefficient value for assist % is negative. Does this mean Stockton gets docked for having a high assist percentage? Or am I reading that wrong? And if so, how did Russell Westbrook basically break the stat these last two years with his high assist percentage?
2. Why is Stockton's DBPM so poor? We know he was a great defensive player, and his defensive RAPM even as a geriatric, supports this. I understand that DBPM is BPM  Offensive BPM, so for Stockton, is his true offensive value supposed to be lower, and his defensive value higher to equal his actual BPM, or should his total BPM be much higher  keeping his same offensive BPM and adding his true defensive value  in other words..BPM is not capturing his true value.
Re: John Stockton and BPM
Posted: Tue Aug 21, 2018 3:58 pm
by eminence
Raw BPM = a*ReMPG + b*ORB% + c*DRB% + d*STL% + e*BLK% + f*AST%  g*USG%*TO% +
h*USG%*(1TO%)*[2*(TS%  TmTS%) + i*AST% + j*(3PAr  Lg3PAr)  k] + l*sqrt(AST%*TRB%)
I'm not seeing where you say AST% has a negative coefficient. It's that last term with AST%*TRB% where Westbrook's number kind of goes nuts.
Re: John Stockton and BPM
Posted: Tue Aug 21, 2018 7:28 pm
by Jinxed
Coeff. Term BPM Value
a Regr. MPG 0.123391
b ORB% 0.119597
c DRB% 0.151287
d STL% 1.255644
e BLK% 0.531838
f AST% 0.305868
Isn't this a negative coefficient?
Re: John Stockton and BPM
Posted: Tue Aug 21, 2018 8:38 pm
by shadow
From the About BPM page:
"Assist% is a linear term, but assists also figure in both of the interaction terms in the regression, so the specific coefficient for this linear term has no meaning by itself."
Re: John Stockton and BPM
Posted: Tue Aug 21, 2018 9:48 pm
by Jinxed
shadow wrote: ↑Tue Aug 21, 2018 8:38 pm
From the About BPM page:
"Assist% is a linear term, but assists also figure in both of the interaction terms in the regression, so the specific coefficient for this linear term has no meaning by itself."
Yea I guess I'm just not understanding how it has no meaning by itself if it is included as one of the coefficients.
Re: John Stockton and BPM
Posted: Tue Aug 21, 2018 10:42 pm
by Crow
ast% appears several places in formula. IF the sum of these terms Is always positive then the negative sign in front of one term isn't meaningful in itself.
the positive coefficient l is many times the size of f.
Re: John Stockton and BPM
Posted: Wed Aug 22, 2018 4:59 pm
by DSMok1
Jinxed wrote: ↑Tue Aug 21, 2018 2:05 pm
Hey I have some questions regarding how BPM is calculated, using John Stockton as an example.
1. Looking at basketballreference's explanation of BPM, the coefficient value for assist % is negative. Does this mean Stockton gets docked for having a high assist percentage? Or am I reading that wrong? And if so, how did Russell Westbrook basically break the stat these last two years with his high assist percentage?
2. Why is Stockton's DBPM so poor? We know he was a great defensive player, and his defensive RAPM even as a geriatric, supports this. I understand that DBPM is BPM  Offensive BPM, so for Stockton, is his true offensive value supposed to be lower, and his defensive value higher to equal his actual BPM, or should his total BPM be much higher  keeping his same offensive BPM and adding his true defensive value  in other words..BPM is not capturing his true value.
Hello!
1. Yes, you are reading that correctly. The linear AST% coefficient is negative. However, the h*USG%*(1TO%)*i*AST% part of the regression is positive, and the interaction term l*sqrt(AST%*TRB%) is also strongly positive.
Coeff. 
Term 
BPM Value 
Variable Format 
f 
AST% 
0.305868 
100.0 
h 
Scoring 
0.711217 


USG% 

100.0 

TO% 

0.000 
i 
AST Interaction 
0.017022 
100.0 
l 
sqrt(AST%*TRB%) 
0.72593 
100.0*100.0 
Notice that last item, the interaction with rebounding. This term has a very large coefficient.
Let's do some math.
Let's assume a TO% of 25%, a TRB% of 4%, and a USG% of 20%. In other words, John Stockton. His TRB% was quite low versus someone like Russell Westbrook, who has a TRB% up around 15%.
If I only allow AST% to vary, here's the curve the raw BPM will describe:
Hmm. Well, that's interesting. And it looks like a problematic quirk with the current BPM formulation.
The current setup doesn't really reward high AST% for players that don't get rebounds! That's not good. That is because the primary positive term is the l*sqrt(AST%*TRB%) interaction with TRB%. The USG*AST interaction term is really quite small in magnitude.
Sounds like something needs to be tweaked in the formula.
2. Stockton is rather odd, isn't he? BPM generates OBPM and DBPM by a setting coefficients to "split" the overall BPM result. Depending on how the OBPM/DBPM split coefficients fall, it sometimes is inaccurate as to where the player's value is coming from. In this case, I think the split coefficients see the ridiculous AST% and assume this is a really offensivelyminded player.
I know that's a a clumsy explanation, but in essence the quirks of the nonlinear terms of the regression come out with outlier players, players with highly unusual statistical profileslike Stockton and Westbrook. A linear metric would do better with these outliers than a nonlinear metric like BPM!
Re: John Stockton and BPM
Posted: Wed Aug 22, 2018 5:16 pm
by Jinxed
Great explanation DSMok. Thank you.
Re: John Stockton and BPM
Posted: Wed Aug 22, 2018 6:44 pm
by Mike G
Another thing that devalues Stockton relative to other point guards is that his assists at home were not inflated by much, relative to the league at the time.
Nash is an even more extreme example of his Ast% being too low: Phoenix scorekeepers gave their own guys fewer assists (per made FG) than they got on the road.
It's pretty simple to look up a team's home and away Ast/FG and devalue their home assists accordingly. Or, in rare cases, inflate them (as with Nash).
The team you are on may affect your Ast totals by 10% or more.
Re: John Stockton and BPM
Posted: Thu Aug 23, 2018 10:15 pm
by mtamada
DSMok1 wrote: ↑Wed Aug 22, 2018 4:59 pm
1. Yes, you are reading that correctly. The linear AST% coefficient is negative. However, the h*USG%*(1TO%)*i*AST% part of the regression is positive, and the interaction term l*sqrt(AST%*TRB%) is also strongly positive.
[...]
I know that's a a clumsy explanation, but in essence the quirks of the nonlinear terms of the regression come out with outlier players, players with highly unusual statistical profileslike Stockton and Westbrook. A linear metric would do better with these outliers than a nonlinear metric like BPM!
Yes, the interactive terms with AST% (i.e. the ones that include variables besides just AST% alone) create complexity. Is the relationship between BPM and AST% positive or negative? When there are interactive terms, we can't just look at the coefficient on AST%. In fact we can't just look at the coefficients period; we have to wade through the calculations as DSMok1 did to see if BPM is rising or falling. The nonlinearities mean that we have to pay attention to the values of the explanatory variables in addition to the values of the coefficients.
And as DSMok1 aptly observes, another disadvantage of interactive terms is that they make it more likely that extreme or outlier players will be poorly predicted; strictly linear models are more likely to stay within reasonable bounds.
But often the interactive terms are necessary to make the models more realistic and to make the predictions more accurate. So we have to live with the complexity.