APBRmetrics

The discussion of the analysis of basketball through objective evidence, especially basketball statistics.
It is currently Mon Sep 22, 2014 8:11 am

All times are UTC




Post new topic Reply to topic  [ 1 post ] 
Author Message
PostPosted: Fri Apr 15, 2011 1:54 am 
Offline

Joined: Thu Apr 14, 2011 11:10 pm
Posts: 2353
page 1 of 3

Author Message
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/ ... ment-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.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
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_o ... las_a_quiz
Back to top
View user's profile Send private message AIM Address
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_o ... las_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?!?
Back to top
View user's profile Send private message
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).
Back to top
View user's profile Send private message
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_o ... las_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.
Back to top
View user's profile Send private message
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/ ... ment-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)?
Back to top
View user's profile Send private message Send e-mail AIM Address
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.
Back to top
View user's profile Send private message
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_o ... las_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
Back to top
View user's profile Send private message Send e-mail AIM Address
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.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
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.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
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.
Back to top
View user's profile Send private message
gabefarkas



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

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.
Back to top
View user's profile Send private message Send e-mail AIM Address
NickS



Joined: 30 Dec 2004
Posts: 384


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.
Back to top
View user's profile Send private message
Flint



Joined: 25 Mar 2007
Posts: 112


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/ ... /#more-674
Back to top
View user's profile Send private message
NickS



Joined: 30 Dec 2004
Posts: 384


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.

page 2 of 3

Author Message
Dan Rosenbaum



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

PostPosted: Wed Dec 19, 2007 12:09 am Post subject: Reply with quote
gabefarkas wrote:
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.

In these linear weight measures any coefficient in front of a statistic probably should vary a little from team to team, but we typically choose a single coefficient value and work with that. That is all that I am suggesting here.

Notice also what happens when the Bulls play the Pistions and the Bulls have the ball. When the Bulls are the "own team" offensive rebounds (for the Bulls) have a possession value of one and defensive rebounds (for the Pistons) have a possession value of zero. But when Berri flips around and looks at it from the Pistons perspective, "opponent" offensive rebounds (still for the Bulls) have zero possession value and defensive rebounds (still for the Pistons) have a possession value of one. So the exact same action has a different possession value depending on whether we are viewing it as an "own team" or "opponent" possession. I just am not sure how that can be justified.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
NickS



Joined: 30 Dec 2004
Posts: 384


PostPosted: Wed Dec 19, 2007 5:39 pm Post subject: Reply with quote
I hope I'm not being a bore here, but one more comment.

Dan -- I would be very interested if my last attempt to explain what I meant about an alpha of .5 made sense. From my point of view the idea is simple but subtle, and I'm trying to explain it as straightforwardly as I can.

I basically agree with everything Dan has written in this thread, I'm just trying to push for a slightly different explanation of this one point.

Dan Rosenbaum wrote:
Notice also what happens when the Bulls play the Pistions and the Bulls have the ball. When the Bulls are the "own team" offensive rebounds (for the Bulls) have a possession value of one and defensive rebounds (for the Pistons) have a possession value of zero. But when Berri flips around and looks at it from the Pistons perspective, "opponent" offensive rebounds (still for the Bulls) have zero possession value and defensive rebounds (still for the Pistons) have a possession value of one. So the exact same action has a different possession value depending on whether we are viewing it as an "own team" or "opponent" possession. I just am not sure how that can be justified.


I'm still not sure how far this way of looking at the problem takes you. It's correct as far as it goes, but I repeat my comment about OR and DR not occurring in isolation and always being part of the sequence FGX --> [OR,DR].

Those two sequences (FGX --> OR; FGX --> DR) do add up to either no change of possession in the first case, or a full change of possession from the perspective of both teams. It's just that, in the second case, the FGX counts as a full loss of possession for the offensive team (and nothing for the defensive team) which is symmetrical with the DR which counts as a full possession for the defensive team, and 0 for the offensive team.

This looks wrong, but works in accounting for team possessions as long as every FGX is followed by either a DR or an OR.
Back to top
View user's profile Send private message
Dan Rosenbaum



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

PostPosted: Wed Dec 19, 2007 6:50 pm Post subject: Reply with quote
NickS: I guess the point here is that the way I defined alpha at the beginning of this thread, Wins Produced uses a different alpha depending on whether it is an "own team" possession or an "opponents" possession. The average of the alphas that Wins Produced uses is 0.5, but it is never 0.5 for either the "own team" or "opponents" possession.

I think a lot of what you are saying is just that Wins Produced does satisfy conditions (i)-(iii). And I agree. In combination things add up, but I was trying to argue for a condition (iv) that would require alpha to not depend on whether a possession was an "own team" or "opponents" possession.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
NickS



Joined: 30 Dec 2004
Posts: 384


PostPosted: Wed Dec 19, 2007 7:46 pm Post subject: Reply with quote
Dan Rosenbaum wrote:
NickS: I guess the point here is that the way I defined alpha at the beginning of this thread, Wins Produced uses a different alpha depending on whether it is an "own team" possession or an "opponents" possession. The average of the alphas that Wins Produced uses is 0.5, but it is never 0.5 for either the "own team" or "opponents" possession.


I'm saying more than that.

I'm saying both, to quote myself,
Quote:
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.


and, implicitly, that Wins Produced tells two stories, a story of teams, and a story of individuals, and that Berri gets a lot of mileage out of referring to his story of teams, when he's defending his story of individuals. So, it's usefull to be able to spot the points at which those two stories diverge, and the problem areas of Wins Produced (Rebounding, and missed field goals) are, precisely, the points at which the two stories diverge.

As you say, Berri is good at hiting softballs, so you might as well make your criticisms of Wins Produced as specific and knowledgeable as possible.

I agree that everything you've said about Wins Produced is correct if you take Wins Produced to be defined by the weights it gives to individual players' box score statistics -- Win Score, essentially. I just know that I had the experience of arguing against Win Score, showing a limitation of Win Score and being told, correctly, that the problem I identified in Win Score didn't apply in Wins Produced, because of those lines for "opponent's field goal made" and "opponent's turnover."
Back to top
View user's profile Send private message
asimpkins



Joined: 30 Apr 2006
Posts: 245
Location: Pleasanton, CA

PostPosted: Wed Dec 19, 2007 8:45 pm Post subject: Re: The Wins Produced Theoretical Model Reply with quote
I've been following this discussion closely, and it's been very interesting. I had a quick question about the original post that's been bugging me.

Dan Rosenbaum wrote:
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,...


I was just curious how to correctly read that last part. Did you mean that 0.7 was definitely not right, that you suspected it wasn't right, or that it wasn't necessarily right?
Back to top
View user's profile Send private message
Dan Rosenbaum



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

PostPosted: Wed Dec 19, 2007 10:44 pm Post subject: Reply with quote
NickS wrote:
I agree that everything you've said about Wins Produced is correct if you take Wins Produced to be defined by the weights it gives to individual players' box score statistics -- Win Score, essentially. I just know that I had the experience of arguing against Win Score, showing a limitation of Win Score and being told, correctly, that the problem I identified in Win Score didn't apply in Wins Produced, because of those lines for "opponent's field goal made" and "opponent's turnover."

I am not talking about Win Score. Here is the own team possession equation, first assuming alpha=0.5 and then assuming alpha=1 as in Wins Produced. All of these statistics can be measured at the individual-level, except for DRB(O) which is measured at the team-level.

OWN TEAM POSSESSIONS
ALPHA=0.5 POSS(T) = FGM(T) + 0.5*FGX(T) - 0.5*ORB(T) + 0.5*DRB(O) + TO(T)
WP/ALPHA=1 POSS(T) = FGM(T) + FGX(T) - ORB(T) + TO(T)

Now for the the opponents possession equation, first assuming alpha=0.5 and then assumimg alpha=0 as in Wins Produced. Only DRB(T) and the steals part of TO(O) are measured at the individual-level; the rest are measured at the team-level.

OPPONENTS POSSESSIONS
ALPHA=0.5 POSS(O) = FGM(O) + 0.5*FGX(O) - 0.5*ORB(O) + 0.5*DRB(T) + TO(O)
WP/ALPHA=0 POSS(O) = FGM(O) + DRB(T) + TO(O)

My whole point is that the possession equations when alpha=0.5 are fine because they are symmetrical. The Wins Produced allocate possession differently depending on whether possessions are "own team" or "opponents" and that is weird. They still add up fine, but that is not the point.

I hope this makes it clear that I am definitely referring to Wins Produced and not Win Score.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
NickS



Joined: 30 Dec 2004
Posts: 384


PostPosted: Wed Dec 19, 2007 11:58 pm Post subject: Reply with quote
That helps, thanks.

Dan Rosenbaum wrote:
OWN TEAM POSSESSIONS
ALPHA=0.5 POSS(T) = FGM(T) + 0.5*FGX(T) - 0.5*ORB(T) + 0.5*DRB(O) + TO(T)
WP/ALPHA=1 POSS(T) = FGM(T) + FGX(T) - ORB(T) + TO(T)

Now for the the opponents possession equation, first assuming alpha=0.5 and then assumimg alpha=0 as in Wins Produced. Only DRB(T) and the steals part of TO(O) are measured at the individual-level; the rest are measured at the team-level.

OPPONENTS POSSESSIONS
ALPHA=0.5 POSS(O) = FGM(O) + 0.5*FGX(O) - 0.5*ORB(O) + 0.5*DRB(T) + TO(O)
WP/ALPHA=0 POSS(O) = FGM(O) + DRB(T) + TO(O)


Okay, I see what you're saying, I'm mixing the accounting for points, and the accounting of possessions, you're just talking about possessions. That makes a lot of sense.

So, finding myself in the odd position of defending wins produced, can you explain the reasoning for your proposed fourth requirement "How possessions are produced is symmetrical, i.e. it is the same regardless of whether the own team or opponents have the ball."

That idea made sense to me when you proposed it, but seeing the equations above it strikes me that

FGM(T) + FGX(T) - ORB(T) + TO(T)

will always equal

FGM(O) + DRB(T) + TO(O)

(ignoring team rebounds).

So if they're always equal why does it matter that the two calculations arrive at the number through different means?

I'm not trying to be dense, but having clarified the one misunderstanding I now realize I don't understand your original argument as well as I thought I did. You write above

Quote:
Notice also what happens when the Bulls play the Pistions and the Bulls have the ball. When the Bulls are the "own team" offensive rebounds (for the Bulls) have a possession value of one and defensive rebounds (for the Pistons) have a possession value of zero. ... So the exact same action has a different possession value depending on whether we are viewing it as an "own team" or "opponent" possession. I just am not sure how that can be justified.


Let me propose, playing Devil's Advocate, a way of making sense sense of Berri's weights. You're correct that if in the FGX --> OR sequence, if the FGX turns possession over to the Pistons, then the OR should be credited as taking away a possession. But imagine that possession has 3 states, rather than 2 -- Home team possession (HT), Away Team possession (AT), and Neither team (NT) has possession. A team counts as losing a possession if they go from having possession to either the other team having possession or neither team having possession. Similarly a team is credited with acquiring possession if they claim possession from either the other team or a situation in which neither team has possession.

If you view the situation when a FGX bounces off the rim as a moment when neither team has possession then a home team FGX --> OR looks like [HT --> NT --> HT], so the home team gived up possession and then regains it without the away team ever having possession.

Whereas a TO by the Home Team would look like [HT --> AT] and the HT would be credited with giving up possession and the AT would be credited with gaining possession.

Why isn't this an equally valid model of possessions?

Is your fourth postulate the equivilent of Euclid's fifth, and can we have non-Rosenbaumian arithmetic?

[Apologies for the silliness].

I'm just trying to understand a little better.
Back to top
View user's profile Send private message
Dan Rosenbaum



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

PostPosted: Thu Dec 20, 2007 2:53 am Post subject: Reply with quote
Because Wins Produced satisifies conditions (i)-(iii) it will always add up just fine. This isn't about how possessions add up. It is about how they are apportioned across box score stats. Maybe another example will help. Suppose Berri had assumed that alpha=0 for own team and alpha=1 for opponents possessions. Then these are the equations he would have ended up with.

OWN TEAM POSSESSIONS
POSS(T) = FGM(T) + DRB(O) + TO(T)

OPPONENTS POSSESSIONS
POSS(O) = FGM(O) + FGMX(O) - ORB(O) + TO(O)

Everything would still add up, but the only individual-level stats that would have possession value would be field goals made, turnovers, and steals. A metric produced from such a set-up would be just as valid as Wins Produced, but would give individuals no credit for rebounds and would not penalize individuals for missed shots. This metric would, in essence, be the anti-Wins Produced.

Having things add up, i.e. satisfying conditions (i)-(iii) is not enough here. The key is how the possession values are apportioned. And my condition (iv) just implies we give a missed shot, defensive rebound, or offensive rebound the same possession value, regardless of whether it is part of an own team possession or opponents possesion or whether it is measured at the individual-level or team-level.

(GF bring up the possibility of letting alpha vary by team or according to some other dimension, which is a possible extension of the model, but that is not what Berri is doing. He is letting it vary arbitrarily based upon how the possession is being counted.)

Berri chooses his two alphas in such a way that he maximizes the possession value that can be attributed to individuals. That is not crazy, but it leads to his overvaluation of rebounding and undervaluation of scoring. The anti-Wins Produced possessions values described above help demonstrate that point.

I think the whole problem is the concept of gaining or acquiring a possession. That terminology works OK when estimating the total number of possessions, but I think it is misleading when trying to apportion possessions to box score stats. A defensive rebound uses up a portion of the opponents possession; it does not acquire a possession. That may sound like semantics, but I think this is heart of why this can be confusing.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
Dan Rosenbaum



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

PostPosted: Thu Dec 20, 2007 3:01 am Post subject: Re: The Wins Produced Theoretical Model Reply with quote
asimpkins wrote:
I've been following this discussion closely, and it's been very interesting. I had a quick question about the original post that's been bugging me.

Dan Rosenbaum wrote:
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,...


I was just curious how to correctly read that last part. Did you mean that 0.7 was definitely not right, that you suspected it wasn't right, or that it wasn't necessarily right?

It is not necessirly right.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
Harold Almonte



Joined: 04 Aug 2006
Posts: 616


PostPosted: Thu Dec 20, 2007 9:11 am Post subject: Reply with quote
I think the main questions are: Can odds between teams, or between teammates, weight stats or the value of a possession at the individual level? yes or no? Must we accept that a teammate's OR can't cancel the shooter's individual lost credit (at least a portion) by a FGMissed in a single action? No player can be reduced in credit, individual or distributed, by an opponent to grabb an OR? Does really exist something like a "piece of possession", or is alpha just an odd?

Last edited by Harold Almonte on Thu Dec 20, 2007 12:11 pm; edited 1 time in total
Back to top
View user's profile Send private message
NickS



Joined: 30 Dec 2004
Posts: 384


PostPosted: Thu Dec 20, 2007 11:23 am Post subject: Reply with quote
Quote:
Everything would still add up, but the only individual-level stats that would have possession value would be field goals made, turnovers, and steals. A metric produced from such a set-up would be just as valid as Wins Produced, but would give individuals no credit for rebounds and would not penalize individuals for missed shots. This metric would, in essence, be the anti-Wins Produced.


Sure, and this gives me an excuse to quote the single most import thing, in my opinion, you've said in this thread:

Quote:
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.


I've joked before that given that the central regression in Wins Produced is to point differential you could produce an even more anti-win produced that just used points scores for each player and, with a team adjustment, it would work just as well. You wouldn't even need to count turnovers.

Perhaps that's all that needs to be said. Particularly since the second most important thing you've said, again in my opinion is,

Quote:
This isn't about how possessions add up. It is about how they are apportioned across box score stats.


I'm not sure that it's impossible to make a case for a system in which the value of an event depends on which team's perspective you take (within limits, of course), but I'll agree that the burden of proof is on anyone proposing that sort of scheme and that Berri has never even attempted to take on that burden of proof.

I'll also agree that his "All of Wins Produced comes from a regression." is a dodge since, in fact, the parts that people are arguing about are, as you put it, an arbitrary apportionment of the values derived from the regression.
Back to top
View user's profile Send private message
Dan Rosenbaum



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

PostPosted: Thu Dec 20, 2007 12:43 pm Post subject: Reply with quote
I am not sure that Berri is always dodging here. A lot of times when folks have a hard time viewing things from anything other than their own perspective, it is hard to understand critiques. It is something that we all struggle with to some degree. I have always told my students that one key to being a good student is understanding what you don't understand. But that maxim is true for all of us and maybe even more true for those of us with PhDs.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
Mike G



Joined: 14 Jan 2005
Posts: 3618
Location: Hendersonville, NC

PostPosted: Thu Dec 20, 2007 12:54 pm Post subject: Reply with quote
I used to tell friends who had gotten their PhD's, "So, now you're a Phuddy Duddy"...
_________________
`
36% of all statistics are wrong
Back to top
View user's profile Send private message Send e-mail
NickS



Joined: 30 Dec 2004
Posts: 384


PostPosted: Thu Dec 20, 2007 1:29 pm Post subject: Reply with quote
This conversation is a good example.

Ultimately we're saying the same thing -- that within the Wins Produced framework you would have a more theoretically sound metric if you have the defense some of the credit for a FGX, and if the offense was penalized slightly for giving up a DR, and we were still talking past each other about the ways in which each of us came to that conclusion.
Back to top
View user's profile Send private message
Guy



Joined: 02 May 2007
Posts: 128


PostPosted: Thu Dec 20, 2007 2:35 pm Post subject: Reply with quote
I'm not certain this is the same issue Dan is raising, but I think so: What's striking to me in the WP formula is the absence of opponent rebounds. Getting rebounds is presumed to be extremely valuable, but there is no accounting for the failure to get them. Presumably this is because there is no boxscore stat for REBMissed, and the WOW authors couldn't figure out how to deal with that. So while WP takes acount of both points and scoring opportunities consumed -- giving scoring a net value of zero -- it sees only the positive side of the rebounds ledger. That's too bad, because if they had wrestled with this they might have figured out that each rebound-above-average at the player level doesn't necessarily mean an extra rebound for the team.

The need for the position adjustment in WP is thus almost entirely a function of not incorporating opponent rebounds. Here is average Win Score and avg rebounds for each position (from Berri):
WS/REB
C 10.8 / 12.4
PF 10.3 / 11.4
SF 7.6 / 7.3
SG 5.6 / 6.1
PG 4.7 / 6.3
If you apportioned opponent rebounds to all players based on position and MP, you would get very close to a zero WS value for all positions. And Berri accomplishes basically the same thing with his position adjustment: by subtracting the average position WS -- which is almost 100% rebounds -- from each player's total, he's effectively bringing opposition rebounds in through the back door. At least, I think that's what's happening.

Last edited by Guy on Thu Dec 20, 2007 3:40 pm; edited 2 times in tota

page 3 of 3

Author Message
gabefarkas



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

PostPosted: Thu Dec 20, 2007 3:03 pm Post subject: Reply with quote
Dan Rosenbaum wrote:
Notice also what happens when the Bulls play the Pistions and the Bulls have the ball. When the Bulls are the "own team" offensive rebounds (for the Bulls) have a possession value of one and defensive rebounds (for the Pistons) have a possession value of zero. But when Berri flips around and looks at it from the Pistons perspective, "opponent" offensive rebounds (still for the Bulls) have zero possession value and defensive rebounds (still for the Pistons) have a possession value of one. So the exact same action has a different possession value depending on whether we are viewing it as an "own team" or "opponent" possession. I just am not sure how that can be justified.
I think that's the case because you're looking at it from two different perspectives. When the Bulls have the ball, ORs have a possession value of 1 because it allows them to obtain a possession in a situation (missed FGA) where the possession was up for grabs. At this same time, a Detroit DR has a possession value of 0 from the Bulls' perspective, since it does not gain them a possession.

As a caveat, I'm not advocating one position or another here, I'm just talking this through and saying what I think makes sense.
Back to top
View user's profile Send private message Send e-mail AIM Address
Harold Almonte



Joined: 04 Aug 2006
Posts: 616


PostPosted: Thu Dec 20, 2007 5:18 pm Post subject: Reply with quote
Guy:
Quote:
Presumably this is because there is no boxscore stat for REBMissed, and the WOW authors couldn't figure out how to deal with that.


But he figured out how to deal with oppFGMade, Points allowed, opp. not steal TOs, etc. He just was not interested in includding opp.FGMissed and opp.OR in the team defense adjust, or apply the odds or the alpha to these stats, because his logic about the OR is that it is a new possession for a different player, not a team continuation play that affects the stats of each individual involucrated in. He just won't give up about that, because that means to make a repair to the metric. He also could have copied or adapted the Dean's PGm distribution, that I'm sure he knew, and it's better than just distribute by minutes.

But thanks that players are not informed about this, because they just would avoid to take risky shots, and just would try to wait for an easy pass, and would be just interested in gambling an off. rebound being careless of the def. balance. The perimeter game would be eliminated. They wouldn't defend either, and will go quickly to try to grabb a deff. rebound, wich probably would be as valuable as the points allowed, specially for low minutes players and non-centers. That's what bad crediting and penalization, or the lack of one of both in this critical basketball play just does.
Back to top
View user's profile Send private message
Dan Rosenbaum



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

PostPosted: Fri Dec 21, 2007 7:49 am Post subject: Reply with quote
gabefarkas wrote:
Dan Rosenbaum wrote:
Notice also what happens when the Bulls play the Pistions and the Bulls have the ball. When the Bulls are the "own team" offensive rebounds (for the Bulls) have a possession value of one and defensive rebounds (for the Pistons) have a possession value of zero. But when Berri flips around and looks at it from the Pistons perspective, "opponent" offensive rebounds (still for the Bulls) have zero possession value and defensive rebounds (still for the Pistons) have a possession value of one. So the exact same action has a different possession value depending on whether we are viewing it as an "own team" or "opponent" possession. I just am not sure how that can be justified.
I think that's the case because you're looking at it from two different perspectives. When the Bulls have the ball, ORs have a possession value of 1 because it allows them to obtain a possession in a situation (missed FGA) where the possession was up for grabs. At this same time, a Detroit DR has a possession value of 0 from the Bulls' perspective, since it does not gain them a possession.

As a caveat, I'm not advocating one position or another here, I'm just talking this through and saying what I think makes sense.

I think it is the language of acquiring or gaining or obtaining possessions that causes the problems. This causes folks to give possession value only to the last action of the opponents. That doesn't make sense for own team possessions, so why does it make sense for opponents possessions? A missed shot uses part of a possession, regardless of whether it is the own team or opponents who missed the shot. Wins Produced assumes that if we had information on which player (or players) causes the opponents to miss a shot, we wouldn't use it, because missed shots by the opponents don't have any possession value. It also seems bizarre to me to assume that a defensive rebound by opponents does not have any possession value. If it is worth a full possession when the opponents have a possession, why is it worth nothing when own team has possession?
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
Guy



Joined: 02 May 2007
Posts: 128


PostPosted: Fri Dec 21, 2007 8:44 am Post subject: Reply with quote
Dan Rosenbaum wrote:
It also seems bizarre to me to assume that a defensive rebound by opponents does not have any possession value. If it is worth a full possession when the opponents have a possession, why is it worth nothing when own team has possession?


Dan: any thoughts on the connection between WP's treatment of rebounds and the position adjustment? (see my last post on previous page).
Back to top
View user's profile Send private message
Dan Rosenbaum



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

PostPosted: Fri Dec 21, 2007 12:56 pm Post subject: Reply with quote
Guy wrote:
Dan Rosenbaum wrote:
It also seems bizarre to me to assume that a defensive rebound by opponents does not have any possession value. If it is worth a full possession when the opponents have a possession, why is it worth nothing when own team has possession?


Dan: any thoughts on the connection between WP's treatment of rebounds and the position adjustment? (see my last post on previous page).

Actually, I think there is a parallel to the argument that I just made that Wins Produced would not use information on who caused missed shots (even if it was available), because opponents missed shots have no possession value. Similarly, Wins Produced would not use information on who allowed a defensive rebound or an opponents' offensive rebound, even if such information existed, again because those actions do not have any possession value.

In contrast, Alternate Win Score would use that information and in its absence just uses opponents defensive and offensive rebounds as placeholders. Perhaps a more reasonable way of thinking about this is to construct the possession values assuming we have perfect information and then work backwards with the information we do have.
Back to top
View user's profile Send private message Send e-mail Visit poster's website Yahoo Messenger
Harold Almonte



Joined: 04 Aug 2006
Posts: 616


PostPosted: Mon Dec 24, 2007 12:33 pm Post subject: Reply with quote
I've allways though that the regression method is bad method to use with that incomplete basketball boxscore, at least with stats where doesn't exist a counterpart stat (in punishing or rewarding) to regress. We know it does exist a zero sum between a FGMissed and the act of rebounding, and between the FGMade and the inbound. But each action theirselves are not zero sum (at the individual level), they are probabilistical, but not exactly the way like wether a ball in the air is like a coin in the air. In basketball the dices and the coins are fixed, and in the rebounding action the floor advantge just fixes the rebounding action, the same the way a shot is defended and the distance put some fix to scoring.

If you can't account the rebounds missed, nor the value of a closed defended shot, at the individual level, then the common sense just says that like we set an average W-L team, to rate the action of winning at the team level and set a break even, every player action will have a break even wich are with no doubt the actions's league average break even. Of course the problem with this is you would need to find break evens to every action in the game, besides scoring and rebounding.

The fact is that we need to cancel every action with an opponent action, and we just are obligued to apply the alpha (break even) to weight the stat wich account rebounds, because there is no way to account rebounds missed at the individual level, and that's the only way to adjust for that, but at the scoring level, we need some adjust in the FGMissed: in the zero sum against rebounding first (but knowing that players don't have possessions, teams have possessions), and in the opponent defensive weight later wich probably would approach us to scoring creation and other things.

Just another different attempt of explanation to the same problem. I just don't accept the economical point of view, obviating statistical rules.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 1 post ] 

All times are UTC


Who is online

Users browsing this forum: Yahoo [Bot] and 4 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
cron
Powered by phpBB® Forum Software © phpBB Group