Reconstructing Box Plus/Minus

[Crow]

"Add a constant (the “team adjustment”) to the raw BPM of all of the players on the team so that the team total sums to 1.2 times the team adjusted efficiency."

I still don't get this 1.2. Why is it 1.2 instead of 1 for every team? Does this have to do with playing ahead? I don't think so but I do not know what it is.

At one point you say: "The team adjustment is fairly simple. If a team is a +0.0 efficiency (in points per 100 possessions) team, then the adjusted GmBPM values, when weighted by % of possessions played, must sum to +0.0." Then above you say 1.2... Are both of these true? I don't get it. Are you raising the team sum by the 1.2 x, then lowering it later in different steps?



Did you consider assigning position for offense and defense separately instead of all together? I see that you the position assignment differently for offense and defense but should the assignment by for offense and defense? How much have you compared your position assignments to official positions, other databases (like PIPM and Raptor), knarsu3's defensive assignments, etc.? What are the correlations, standard deviations, max deviations? If position is so vital to the calculations and the league has some hybrids (I don't know how common), should you go all in for positions at both ends of the court?

Overall BPM2.0 is calculated then OBPM2 and DBPM2 are calculated separately. Does overall BPM2.0 equal the sum of OBPM2 and DBPM2? I get impression they might not at player level but might at team and / or league level?? What is true? If not, that needs more highlighting and more explaining imo.

[DSMok1]

"Add a constant (the “team adjustment”) to the raw BPM of all of the players on the team so that the team total sums to 1.2 times the team adjusted efficiency."

I still don't get this 1.2. Why is it 1.2 instead of 1 for every team? Does this have to do with playing ahead? I don't think so but I do not know what it is.

At one point you say: "The team adjustment is fairly simple. If a team is a +0.0 efficiency (in points per 100 possessions) team, then the adjusted GmBPM values, when weighted by % of possessions played, must sum to +0.0." Then above you say 1.2... Are both of these true? I don't get it. Are you raising the team sum by the 1.2 x, then lowering it later in different steps?

I actually missed removing this statement when I corrected my approach. The more detailed, corrected writeup is lower in the document:

Now, we do not actually sum to the team’s efficiency. Jeremias Englemann demonstrated that players play worse with the lead and better if behind. The effect is linear and has been consistently replicated. The team in the lead plays about 0.35 pts/100 possessions worse for every point of lead. To adjust for this, we must estimate what the team’s average lead was, and then add or subtract one half of the effect (the other half is assumed to belong to the opponents). There are a number of ways to estimate the lead (or actually calculate it). A quick estimate puts 2017 Cleveland at an average lead of around 1.4 points. The effect of playing with that lead is -0.35/2*1.4 = -0.24, which shifts the Team’s Adjusted Rating from +3.0 to +3.24.

Did you consider assigning position for offense and defense separately instead of all together? I see that you the position assignment differently for offense and defense but should the assignment by for offense and defense? How much have you compared your position assignments to official positions, other databases (like PIPM and Raptor), knarsu3's defensive assignments, etc.? What are the correlations, standard deviations, max deviations? If position is so vital to the calculations and the league has some hybrids (I don't know how common), should you go all in for positions at both ends of the court?

The position assignment I used was purely based on regressing box score statistics to best predict a player's 1 to 5 position assignment, as shown on Basketball Reference. Since the BPM regression is based on this position assignment value, it's coefficients are tuned to best take advantage of this particular method of position assignment. If a player's assignment is off by 0.5 one way or the other, it doesn't actually make much difference.

Overall BPM2.0 is calculated then OBPM2 and DBPM2 are calculated separately. Does overall BPM2.0 equal the sum of OBPM2 and DBPM2? I get impression they might not at player level but might at team and / or league level?? What is true? If not, that needs more highlighting and more explaining imo.

Since this is all linear, you can look at it either way. I describe it as BPM, and then calculate OBPM, and DBPM is simply BPM minus OBPM. Since it is linear, though, you could simply subtract out the coefficients and calculate DBPM directly. Either way works. It all sums up nicely.

[Crow]

Are recent feedback from teams that you are willing to share? In general and about position-tuning of the metric?

[DSMok1]

Box Plus/Minus 2.0 was released yesterday!

My explainer is located at https://www.basketball-reference.com/about/bpm2.html.

Hopefully it resolves most, if not all, of the issues present with BPM 1.0.

[Crow]

So all the "BPM" at BRef is now BPM2.0, though simply labeled as BPM.

More info:

https://www.sports-reference.com/blog/2 ... g-bpm-2-0/

[DSMok1]

Yes, it is a full replacement for BPM 1.0. In general it keeps the same philosophical approach but revises and corrects things.

[Mike G]

Cool!
I see Moses Malone is still only #4 on the 1983 Sixers in BPM, after Doc, Cheeks, and B Jones. He led the league in WS/48 and PER.
Steve Francis once led the league in VORP (also BPM?), but in BPM2 he gets only as high as 10th (13th).

[DSMok1]

Here's a visualization for looking at careers through BPM 2.0:

https://public.tableau.com/profile/dsmo ... ublish=yes

[Crow]

30 guys over 1000 minutes this season at plus 3 or better.

http://bkref.com/tiny/jqiSp

Bucks and Thunder with 3. A handful with 2. 11 with none.

[Dr Positivity]

Looks good

Interesting that Iverson and Rose’s MVP season numbers (6.1 for Iverson, 6.8 for Rose) appears to have gotten better despite the change hurting Westbrook.

[DSMok1]

Looks good

Interesting that Iverson and Rose’s MVP season numbers (6.1 for Iverson, 6.8 for Rose) appears to have gotten better despite the change hurting Westbrook.

Yes, Iverson's numbers went up. His offensive BPM stayed exactly the same (+5.0) but his defensive numbers went from -0.1 to +1.1.

Rose went from +5.8 offense and +0.1 defense to +6.3 offense and +0.5 defense.

Most point guards were actually helped by the shift from 1.0 to BPM 2.0. Offensive engines (that weren't big rebounders also) were the biggest beneficiaries. Rebounding defensive bigs with poor offensive games were the biggest losers.

[Dr Positivity]

I've had the belief for many years that individual rebounds per game is overrated. Rebounding is valuable but rebounds per game as limited at telling you who's helping his team rebound the most as boxing out the opponent's best offensive rebounder can be more valuable than the guy who ends up with the board on the statsheet. Assists have turnovers, points have FG% or TS%, but rebounds per game is missing the extra contextual stat. In the future a stat showing how strong a player's box out ability is would solve this problem. Then again I understand how in the context of BPM the value of rebounding is as much predicting offensive or defensive skills as it is the rebounding itself

[DSMok1]

One of the big advantages for reconstructing Box Plus/Minus in a linear manner is now available: single-game BPM values, in the Play Index at Basketball Reference.

Here are the best BPMs of all time, minimum 24 minutes played: https://www.basketball-reference.com/pl ... der_by=bpm

Notice: when a player had a particularly dominant game, they often ended up sitting much of the second half. Victor Oladipo, for instance: https://www.basketball-reference.com/bo ... 60IND.html

In that game, Indiana was up 27 by halftime. Oladipo had 23 points on 11 FGA, 9 assists, 6 rebounds, and 5 steals in 23:36 of game time. His per-minute production was ridiculous, and that is what BPM picks up on.

It is interesting the unusual names that may have had an absurdly dominant game.

If accounting for playing time in the game, the top VORP game is Jordan's 69 point game on 3/28/1990 vs. Cleveland.

[Mike G]

... If accounting for playing time in the game, the top VORP game is Jordan's 69 point game on 3/28/1990 vs. Cleveland.

And that is only his 8th highest one-game BPM.
What's the formula to convert BPM to VORP?

Also: Any chance b-r.com would add a decimal place to VORP? Esp. in playoffs, when lots of guys total 0.0 or 0.1.

[Mike G]

Most playoff games with BPM>15, 20, 25, and 30 (since 1985, 24+ mpg)
T (total) just adds the 4. In other words, 20's are counted twice, 25's 3 times.

Code: Select all

T      BPM:    15+  20+  25+  30
81    LeBron   54   20    6    1
68    Jordan   49   14    5    
36    Kawhi    24   10    2    
29    Ginobili 16    7    5    1
27    Harden   21    5    1    
27    Wade     21    6    0    
25    Paul     15    6    3    1
23    Curry    18    3    1    1
22    Kobe     17    4    1    
22    Reggie   14    8    0    
21    Barkley  14    4    2    1
18    Magic    14    3    1    
18    Pippen   16    2    0    
17    Dirk     14    3    0    
17    Duncan   16    1    0    
17    Shaq     12    3    2    
16    Durant   13    3    0    
14    Allen    10    4    0    
14    Billups  11    2    1    
14    Kidd      8    4    2    
14    Stockton 12    2    0    
13    Isiah    12    1    0    
12    Drexler   9    3    0    
12    Hakeem   12    0    0    
12    Pierce    9    3    0    
12    Robinson 12    0    0    
11    Carter    5    3    2    1
11    Da Green  6    4    1    
11    Draymond  9    2    0    
10    Kukoc     9    1    0    
10    Malone    8    2    0    
10   Westbrook  9    1    0    
9    Bird       9    0    0    
9    Garnett    8    1    0    
9    George     6    3    0    
8    Porter     3    2    2    1
7    Gibson     2    2    2    1
7    Iverson    4    3    0    

It looks to me that Shaq, Duncan, Olajuwon, and other great rebounders are severely under-represented here.
Break it down by Game Score, and the bigs get their share; Bird is almost = Magic, Malone >> Stockton, etc.

Daniel "Boobie" Gibson had a couple of great playoff games!