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The Wins Produced Theoretical Model
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Dan Rosenbaum



Joined: 03 Jan 2005
Posts: 541
Location: Greensboro, North Carolina

PostPosted: Fri Dec 14, 2007 10:30 pm    Post subject: The Wins Produced Theoretical Model Reply with quote

dberri wrote:
All of Wins Produced [my italics] comes from a regression. You can debate the formulation and results of that regression if you like. But all of it comes from a regression.

http://dberri.wordpress.com/2007/12/14/reviewing-the-central-division/#comment-50743

This is just not true.

The coefficient for points, possessions, assists, fouls, and blocks come from regression (or at least something empirical). But that is not "all of Wins Produced."

The relative possession value of offensive rebounds, defensive rebounds, made shots, missed shots, and turnovers are all determined not by regression, but by theory.

The only way Berri can come close to saying these values all come from a regression is to claim they come from a constrained regression where all of the relative possession values are set by theory. Here are some questions to ask Berri?

How is the ratio of the weights for offensive rebounds relative to defensive rebounds determined? Answer: 100% by theory
How is the ratio of the weights for turnovers relative to missed shots determined? Answer: 100% by theory
How is the ratio of the weights for made shots relative to missed shots determined? Answer: 100% by theory (although, as mentioned above, the relative weight of the points generated from the made shots are determined by regression)

In my peer-reviewed paper with Justin Kubatko, Kevin Pelton, and Dean Oliver, we show that there are an infinite number of possibilities for the ratios of these relative weights. There is nothing wrong with using theory to determine these relative weights, but it is worrisome that Berri does not seem to understand that he is using theory here, despite the fact that this point has been made in a peer-reviewed journal.

So how does Berri theoretically justify his assumptions about these relative ratios? Before getting to that, let me take a step back and discuss how possessions are produced. Well technically, it isn't possessions that are produced. It is points that are produced and possessions are the resource used to produce those points. Possessions are used by all ten players on the floor at any given time and should follow three conditions (to simplify the exposition I will ignore free throws), as laid out in the my peer-reviewed paper with Kubatko, Pelton, and Oliver.

(i) Each turnover and made field goal constitutes a full possession, i.e. has a possession value of one.
(ii) Missed field goal attempts share credit for the possession with defensive rebounds. Missed field goal attempts get an alpha share of the possession, while the defensive rebound gets a 1 – alpha share.
(iii) Offensive rebounds undo missed field goal attempts, so their possession value is -alpha.

There is a fourth condition that should be added to this list.

(iv) How possessions are produced is symmetrical, i.e. it is the same regardless of whether the own team or opponents have the ball. (This is implies that alpha is the same, regardless of which team has the ball.)

The theory behind Wins Produced follows conditions (i)-(iii), but violates (iv). When the own team has possession, Berri assumes alpha equals 0, but he assumes alpha equals 1 when the opponents have possession. That doesn't make any sense. Possessions are allocated in exactly the same way on both sides of the court.

And even if Berri wants to argue that point, the peer-reviewed paper with Kubatko, Pelton, and Oliver shows that there are an infinite number of values for alpha that could be used and they all would have different implications for how much rebounds are valued and how much scorers are valued. For example, assuming alpha equals 0.7 on both sides of the court drops the break-even true shooting percentage from 51.5% to 36.1%. Is 0.7 right? No, but there are an infinite number of values that can be used for alpha and Berri needs to explain why his theoretical assumptions are preferred over this infinite number of other options. And not pretend that his model allows this to be determined by regression. That is simply untrue and it is worrisome that Berri does not get that.

Oh, and by the way, if Berri didn't get this already, the paper with Kubatko, Pelton, and Oliver is peer-reviewed and Berri has never responded to these points. Given that, I just don't find it credible that he will ever substantively respond to legitimate critiques of his model. It is easier (and more effective) to just ignore the criticism.
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John Hollinger



Joined: 14 Feb 2005
Posts: 175

PostPosted: Mon Dec 17, 2007 10:05 am    Post subject: Reply with quote

Not sure if everyone's seen this yet, but this is genius:

http://ballhype.com/story/the_foibles_of_formulas_a_quiz
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KD



Joined: 30 Jan 2005
Posts: 163

PostPosted: Mon Dec 17, 2007 12:10 pm    Post subject: Reply with quote

John Hollinger wrote:
Not sure if everyone's seen this yet, but this is genius:

http://ballhype.com/story/the_foibles_of_formulas_a_quiz


Despite the obvious, "choose the crappier player" pattern, save for Calderon, it pretty much boils down to, "pick the better rebounder."

EDIT: Actually, that's not even true. Who are the trusted?!?
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NickS



Joined: 30 Dec 2004
Posts: 384

PostPosted: Mon Dec 17, 2007 1:21 pm    Post subject: Reply with quote

Everything Dan says is correct, but I want to highlight one portion for further comment

Quote:
The theory behind Wins Produced follows conditions (i)-(iii), but violates (iv). When the own team has possession, Berri assumes alpha equals 0, but he assumes alpha equals 1 when the opponents have possession. That doesn't make any sense. Possessions are allocated in exactly the same way on both sides of the court.


The more I've looked at Wins Produced the more convinced I am that it makes sense to view it as using a consistent alpha of .5 throughout.

You will be confused by this if you only look at the credits assigned to individual players, but looking at the team level, it is effectively an alpha of .5.

I've gone on at length about this point, but suffice it to say that if Berri is using an alpha of .5 you would expect an OR, DR, or FGX to have half the weight of a FGM, or TO, and this is what you see at the team level. A team that forces a TO is ranked as 2 points better than the opponent, the same as the sequence of FGX --> DR, and twice the value of either FGX or DR individually.

Furthermore, I find this a more useful way to describe Wins Produced (and the problem it creates) than Dan's description of a shifting alpha, because it makes sense when looking at the sequence of FGX --> OR/DR.

Part of the problem in talking about the weights of rebounds in Wins Produced is that rebounds never occur in isolation, they always occur in the sequence FGX --> OR or FGX --> DR and, at the team level, Wins Produced scores both of these sequences correctly. So a Wages of Wins defender can always say that an OR does cancel out a FGX, and that a FGX --> DR adds up to the same as a TO --> Stl (as it should).
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mtamada



Joined: 28 Jan 2005
Posts: 377

PostPosted: Mon Dec 17, 2007 5:57 pm    Post subject: Reply with quote

John Hollinger wrote:
Not sure if everyone's seen this yet, but this is genius:

http://ballhype.com/story/the_foibles_of_formulas_a_quiz


Thanks for pointing out that link! I think I can claim to be the first person, in 2002, to apply the phrase "laugh test" to Berri's initial results showing that Dennis Rodman contributed the most wins of any NBA player.
http://sports.groups.yahoo.com/group/APBR/message/6877

The "laugh test" was meant to be metaphorical. But BallHype has created a literal Laugh Test! One that is both funny and pointed.
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gabefarkas



Joined: 31 Dec 2004
Posts: 1313
Location: Durham, NC

PostPosted: Mon Dec 17, 2007 6:23 pm    Post subject: Re: The Wins Produced Theoretical Model Reply with quote

Dan Rosenbaum wrote:
dberri wrote:
All of Wins Produced [my italics] comes from a regression. You can debate the formulation and results of that regression if you like. But all of it comes from a regression.

http://dberri.wordpress.com/2007/12/14/reviewing-the-central-division/#comment-50743

This is just not true.

The coefficient for points, possessions, assists, fouls, and blocks come from regression (or at least something empirical). But that is not "all of Wins Produced."

The relative possession value of offensive rebounds, defensive rebounds, made shots, missed shots, and turnovers are all determined not by regression, but by theory.

The only way Berri can come close to saying these values all come from a regression is to claim they come from a constrained regression where all of the relative possession values are set by theory. Here are some questions to ask Berri?

How is the ratio of the weights for offensive rebounds relative to defensive rebounds determined? Answer: 100% by theory
How is the ratio of the weights for turnovers relative to missed shots determined? Answer: 100% by theory
How is the ratio of the weights for made shots relative to missed shots determined? Answer: 100% by theory (although, as mentioned above, the relative weight of the points generated from the made shots are determined by regression)
Dan - I ask the following completely out of curiousity and only because I'm not entirely familiar with the Rosenbaum-Berri conflict. I know only what I've read on this board (and I can't say that I remember 100% of it).

What, if any, criticism has Berri made to adjusted +/- or any of your other methods? Do you feel the criticism he made (if any) was valid and relevant? Also, has Berri made any claims that his methods are better than other specific methods, or just that WoW is very good?

Dan Rosenbaum wrote:
In my peer-reviewed paper with Justin Kubatko, Kevin Pelton, and Dean Oliver, we show that there are an infinite number of possibilities for the ratios of these relative weights. There is nothing wrong with using theory to determine these relative weights, but it is worrisome that Berri does not seem to understand that he is using theory here, despite the fact that this point has been made in a peer-reviewed journal.

So how does Berri theoretically justify his assumptions about these relative ratios? Before getting to that, let me take a step back and discuss how possessions are produced. Well technically, it isn't possessions that are produced. It is points that are produced and possessions are the resource used to produce those points. Possessions are used by all ten players on the floor at any given time and should follow three conditions (to simplify the exposition I will ignore free throws), as laid out in the my peer-reviewed paper with Kubatko, Pelton, and Oliver.

(i) Each turnover and made field goal constitutes a full possession, i.e. has a possession value of one.
(ii) Missed field goal attempts share credit for the possession with defensive rebounds. Missed field goal attempts get an alpha share of the possession, while the defensive rebound gets a 1 – alpha share.
(iii) Offensive rebounds undo missed field goal attempts, so their possession value is -alpha.

There is a fourth condition that should be added to this list.

(iv) How possessions are produced is symmetrical, i.e. it is the same regardless of whether the own team or opponents have the ball. (This is implies that alpha is the same, regardless of which team has the ball.)


The theory behind Wins Produced follows conditions (i)-(iii), but violates (iv). When the own team has possession, Berri assumes alpha equals 0, but he assumes alpha equals 1 when the opponents have possession. That doesn't make any sense. Possessions are allocated in exactly the same way on both sides of the court.
Okay, I think I understand what you're saying here. However, I would think that for Team A and Team B, alpha-A and alpha-B are different, depending on the relative skill sets, availability of missed shots, and performance of opponent. Furthermore, along these lines I would think it's different for every different 5-man lineup. I mean, if Team A is very skilled at defensive rebounding, this would imply to me that alpha-A is relatively small, no? Am I misreading (i) through (iii)?
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Harold Almonte



Joined: 04 Aug 2006
Posts: 616

PostPosted: Mon Dec 17, 2007 6:25 pm    Post subject: Reply with quote

Rebounding (DR/OR), like scoring (FGA=FGM/FGMissed) is treated as binary. That's what this possession logic says, and is true. But when you weight those stats, scoring has punishment between the stats, but rebounding not. In one "binary" mode, you are 1 or 0, in another you are +1 and -1, strange no?. But the most strange is that scoring can be -1 and -1, and the punishment must be done between FGMissed and DR.

But, the real problem is that the possibility of happening is not included. I don't know if this is a thing to be obviated when you weight. We are trying to include it at rebounding where as Dan said, there are almost infinite possibilities (but, the ranges of average are very narrow: near 70% after a FGMissed, lower than 60% after a block, and near 90% after a FTMissed), but I've never heard about using possibilities of happening at scoring. I would dare to bet this just would become scoring break even in the league average break even.
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gabefarkas



Joined: 31 Dec 2004
Posts: 1313
Location: Durham, NC

PostPosted: Mon Dec 17, 2007 7:04 pm    Post subject: Reply with quote

John Hollinger wrote:
Not sure if everyone's seen this yet, but this is genius:

http://ballhype.com/story/the_foibles_of_formulas_a_quiz


I love that Jeff Foster looks like he's crying, Sheldon Williams is in a warm-up suit, and Jared Jeffries is in street clothes
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Dan Rosenbaum



Joined: 03 Jan 2005
Posts: 541
Location: Greensboro, North Carolina

PostPosted: Tue Dec 18, 2007 12:17 am    Post subject: Reply with quote

GF:

Berri has complained that adjusted plus/minus is noisy, but that is a criticism I also have made. To be honest, I wish that Berri had criticized adjusted plus/minus more. My frustration is more due to his evasiveness and lack of substance in his responses to legitimate critiques of his model.

Yes, alpha could vary from team to team (just like our 0.44 free throws multiplier could vary from team to team), but Berri is assuming something very different. He is assuming that for every team it is zero on one side of the court and one on the other. That is a bizarre assumption.
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Dan Rosenbaum



Joined: 03 Jan 2005
Posts: 541
Location: Greensboro, North Carolina

PostPosted: Tue Dec 18, 2007 12:25 am    Post subject: Reply with quote

NickS:

Wins Produced is not assuming an alpha=0.5. Otherwise, the absolute value of the weights for rebounds and missed shots would be half that of the absolute value of the weights for turnovers and made shots.
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NickS



Joined: 30 Dec 2004
Posts: 384

PostPosted: Tue Dec 18, 2007 10:01 am    Post subject: Reply with quote

Dan Rosenbaum wrote:
NickS:

Wins Produced is not assuming an alpha=0.5. Otherwise, the absolute value of the weights for rebounds and missed shots would be half that of the absolute value of the weights for turnovers and made shots.


That is precisely my point. It is true that, "Otherwise, the absolute value of the weights for rebounds and missed shots would be half that of the absolute value of the weights for turnovers and made shots" at the team level.

That's why I'm emphasizing that there's a dichotomy between the value for stats assigned to individual players and to the team.

If you look at the page (121?) in WoW that gives the values for each event you will see, for example, that a made FG gives +1 to the team that made the FG and -1 to the opposing team, for a net value of +2. A missed FG followed by a DR gives (as a sequence) -1 to the missing team and +1 to the rebounding team.

So the sequence FGX --> DR is equal in value and opposite in sign to FGM. Which is to say that, as you suggest in the quoted passage, that each of FGX and DR have half the value of FGM.

(similarly a TO is -1 to the team turning the ball over, and +1 to the defending team. So, again, the sequence FGX --> DR has exactly the same value as a TO at the level of the team.)

The confusion is created because the credit assigned to individual players from the sequece FGX --> DR has twice the magnitude of the value of FGM but, I argue, that's caused by the fact that Berri is inconsistent in what credits he gives to individual players, and what he gives to the team.

Does that make sense? I know, for me, the oddities of Wins Produced made much more sense when I figured out this point.
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gabefarkas



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PostPosted: Tue Dec 18, 2007 11:05 am    Post subject: Reply with quote

Dan Rosenbaum wrote:
Yes, alpha could vary from team to team (just like our 0.44 free throws multiplier could vary from team to team), but Berri is assuming something very different. He is assuming that for every team it is zero on one side of the court and one on the other. That is a bizarre assumption.
I agree that his way (from your description of it) makes no sense. However, I'm not sure that what you're saying makes sense either:

Quote:
(iv) How possessions are produced is symmetrical, i.e. it is the same regardless of whether the own team or opponents have the ball. (This is implies that alpha is the same, regardless of which team has the ball.)
Your way also implies a relationship between alphaA and alphaB. The difference is that while Berri says alphaA=1-alphaB, you say alphaA=alphaB. I think the two are unrelated.
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NickS



Joined: 30 Dec 2004
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PostPosted: Tue Dec 18, 2007 11:22 am    Post subject: Reply with quote

To follow up, looking at this post the chart on page 103 of Wages of Wins (hardback) has the information I'm talking about.

You can find it by doing a "search inside this book" on amazon and searching for "opponent field goal".

All I'm saying is that there are entries on that chart that reflect value distributed at the team level, rather than credited to individual players, and that it helped me understand Wins Produced to think about how those fit into the model.

Think about the entries for "opponent's field goals made", "opponent's free throws made", and "opponent's turnovers" and what work they're doing. Think about why there's no line-item for "opponent's field goals missed".

I can just say that I came to this from trying to construct a scenario in which a losing team would have more Wins Produced than a winning team, and I found that those entries for "opponent's field goals made" etc were required to balance the values so that the team Wins Produced corresonded to the margin of victory.

Which then lead me to thinking about why, as I've said, a Field Goal Made is worth twice as much at the team level as a Defensive Rebound, but has the same credit given to the individual player. Phrasing it that way may be a tangent, but my point is that it also answers Dan's question about alpha.
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Flint



Joined: 25 Mar 2007
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PostPosted: Tue Dec 18, 2007 12:12 pm    Post subject: Reply with quote

Berri responded to the Ballyhype column discussed above last night.

http://dberri.wordpress.com/2007/12/18/different-answers-same-conclusions/#more-674
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NickS



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PostPosted: Tue Dec 18, 2007 12:43 pm    Post subject: Reply with quote

That's a great post by Berri, I agree with almost everything he says.

It also gets at my frustration with Berri, which is that he seems disinclined to talk about the choices that he's made with Wins Produced, it's strengths and weaknesses. He does talk about Wins Produced vs NBA efficiency and PER occasionally, but mostly as a way to talk about scoring efficiency, rather than engaging the model behind them (well, the model behind PER, I'm not sure there is a model behind NBA efficiency).

What's implied, in that post, is that Berri does understand the various other advanced statistics out there, it's just that, as a casual reader, he so rarely engages with them. Even more frustrating (from the point of view of this APBRMetrician, who likes to take models apart to see how they tick) Berri frequently describing the model behind Wins Produced as compelled by the regressions, rather than based on a combination of regressions and choices of model, as Dan points out in the opening post in this thread.

If Berri had more posts like that one, and engaged questions about the differencences in what is being measured by PER, PW%, Wins Produced, and adjusted +/- I would have far less complaints.
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