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APBRmetrics
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jeahwe
Joined: 07 Oct 2009
Posts: 3
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 Posted: Thu Jan 06, 2011 2:49 pm Post subject: How adjusted plus minus is calculated? |
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| Could anyone explain how APM is calculated? I know all articles from 82games.com or countthebasket so I don't want another link. I would like to see some examaple, step by step, how APM is calculated for player X. |
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DLew
Joined: 13 Nov 2006
Posts: 224
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| Posted: Thu Jan 06, 2011 6:38 pm Post subject: |
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| Are you familiar the (basic) statistical technique of linear (OLS) regression? The most straight forward way of calculating adjusted plus-minus uses linear (OLS) regression, so if you are not familiar with that technique it will be difficult to explain. |
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jeahwe
Joined: 07 Oct 2009
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| Posted: Fri Jan 07, 2011 7:06 am Post subject: |
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| I'm rather not familiar with that technique. I mean, I know what linear regression is, but I'm not a statistician. That's why I asking for detailed step-by-step example with one player - because I think when I see that kind of example it would be easier to understand. |
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DSMok1
Joined: 05 Aug 2009
Posts: 608
Location: Where the wind comes sweeping down the plains
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| Posted: Fri Jan 07, 2011 7:18 am Post subject: |
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The basic theory is like this:
You have 10 players on the court at once, 5 from each team. During this matchup, one team scores X points and the other team scores Y points.
So, we pose an expression for what happened:
p1 + p2 + p3 + p4 + p5 - q1 - q2 - q3 - q4 - q5 = (X - Y)/possessions
Create a similar equation for every matchup that happened, weight by the number of possessions for each matchup, and solve for all of the p's and q's.
That's the basic concept; it gets tricky if p1 and p2 always play together (which one is contributing?) or if p1 and p6 always substitute for each other and never for anyone else on the team (they can vary inversely with the team and there is no way to know whether it's them or the team contributing).
Also, some players don't have enough possessions to get a decent read.
So the difficult part of the implementation is dealing with such issues. At it's core, APM is a very elegant method.
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EvanZ
Joined: 22 Nov 2010
Posts: 272
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| Posted: Fri Jan 07, 2011 8:41 am Post subject: |
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DS, this is probably going to show my ignorance, but I thought what you just described is unadjusted +/-, and that APM takes those numbers and adjusts for quality of lineups.
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DSMok1
Joined: 05 Aug 2009
Posts: 608
Location: Where the wind comes sweeping down the plains
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| Posted: Fri Jan 07, 2011 8:50 am Post subject: |
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| EvanZ wrote: | | DS, this is probably going to show my ignorance, but I thought what you just described is unadjusted +/-, and that APM takes those numbers and adjusts for quality of lineups. |
Unadjusted plus/minus simply looks at the player and says: what was the score when he was on the floor? So, if p1 was on the floor 30 minutes with 10 different combinations of players, and during that 30 minutes his team outscored the other 65 - 59, p1 will have an unadjusted plus/minus of +6.
Unadjusted plus/minus doesn't account for opponent or teammate at all. It's easy to track, though, which is why the NBA tracks it and puts it in the box score.
Adjusted takes each lineup combination of 10 player, uses it as an independent equation, and takes the whole league as a system of n equations with p unknowns, where n is each lineup-combination instance and p are the total number of players in the league.
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jeahwe
Joined: 07 Oct 2009
Posts: 3
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| Posted: Fri Jan 07, 2011 9:41 am Post subject: |
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| DSMok1 wrote: |
p1 + p2 + p3 + p4 + p5 - q1 - q2 - q3 - q4 - q5 = (X - Y)/possessions
Create a similar equation for every matchup that happened, weight by the number of possessions for each matchup, and solve for all of the p's and q's.
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But how?
We have:
1. team A (p1, p2, p3, p4, p5) vs team B (q1, q2, q3, q4, q5) = team A + 5 points during 20 possessions
2. team A (p1, p2, p3, p6, p7) vs team B (q1, q2, q3, q4, q5) = team A + 3 points during 15 possessions
3. team A (p2, p3, p4, p5, p6) vs team B (q1, q2, q3, q4, q5) = team A - 9 points during 20 possessions
and how to calculate APM for player p1? |
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DSMok1
Joined: 05 Aug 2009
Posts: 608
Location: Where the wind comes sweeping down the plains
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| Posted: Fri Jan 07, 2011 10:26 am Post subject: |
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| jeahwe wrote: | | DSMok1 wrote: |
p1 + p2 + p3 + p4 + p5 - q1 - q2 - q3 - q4 - q5 = (X - Y)/possessions
Create a similar equation for every matchup that happened, weight by the number of possessions for each matchup, and solve for all of the p's and q's.
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But how?
We have:
1. team A (p1, p2, p3, p4, p5) vs team B (q1, q2, q3, q4, q5) = team A + 5 points during 20 possessions
2. team A (p1, p2, p3, p6, p7) vs team B (q1, q2, q3, q4, q5) = team A + 3 points during 15 possessions
3. team A (p2, p3, p4, p5, p6) vs team B (q1, q2, q3, q4, q5) = team A - 9 points during 20 possessions
and how to calculate APM for player p1? |
Since the problem in actuality would be over-parametrized (one cannot solve directly because all of the equations are not consistent--play varies), one must set up a system to try to minimize the error. Your example there doesn't have very many equations, considering the 12 unknowns present.
In Excel, if there are fewer than 200 players being evaluated, one can do it directly with solver. Set up a cell for each player in the matchup and look up from a table of player values. Create a residual for each matchup, where the residual is equal to (predicted margin - actual margin). Then, set up solver to solve for the player values in such a way as to minimize the sum of the residuals squared.
Now, Excel can't handle more than 200 players. Some better statistical package is necessary. R comes to mind, and fortunately, Eli Witus wrote the comprehensive guide to creating your own Adjusted Plus/Minus at his Count the Basket blog. Read that! I should have referred you there in the first place, if you want to understand the nuts and bolts.
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EvanZ
Joined: 22 Nov 2010
Posts: 272
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| Posted: Fri Jan 07, 2011 5:03 pm Post subject: |
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| DSMok1 wrote: | | EvanZ wrote: | | DS, this is probably going to show my ignorance, but I thought what you just described is unadjusted +/-, and that APM takes those numbers and adjusts for quality of lineups. |
Unadjusted plus/minus simply looks at the player and says: what was the score when he was on the floor? So, if p1 was on the floor 30 minutes with 10 different combinations of players, and during that 30 minutes his team outscored the other 65 - 59, p1 will have an unadjusted plus/minus of +6.
Unadjusted plus/minus doesn't account for opponent or teammate at all. It's easy to track, though, which is why the NBA tracks it and puts it in the box score.
Adjusted takes each lineup combination of 10 player, uses it as an independent equation, and takes the whole league as a system of n equations with p unknowns, where n is each lineup-combination instance and p are the total number of players in the league. |
Ah, I didn't realize that. Thanks!
(I thought they should call that "Team +/-" versus "Individual +/-")
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EvanZ
Joined: 22 Nov 2010
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DSMok1
Joined: 05 Aug 2009
Posts: 608
Location: Where the wind comes sweeping down the plains
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| Posted: Fri Jan 07, 2011 5:17 pm Post subject: |
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| EvanZ wrote: | | Is Adj.+/- broken down into offense vs. defense somewhere? |
Not publicly; not up to date. Ilardi posted some multi-year numbers that were split out. Eli Witus showed how to do it in his blog, which I linked to above.
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