The Wages of Wins Journal

44 responses so far ↓

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  Brad // March 2, 2008 at 6:01 pm

  I like how the blog posts now have graphics embedded in them. Very cool.

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  dberri // March 2, 2008 at 6:28 pm

  Brad,
  Not sure it will continue. I was just fooling around today (while I was grading - or not grading).

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  antonio // March 2, 2008 at 8:33 pm

  just curious- in your mind, would the mvp be the person with the highest wp /wp48 as long as they play enough minutes and games, or would it be person with the highest % of team wins. and right now is there a difference between the two?

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  dberri // March 2, 2008 at 9:31 pm

  Antonio,
  Not sure I have a good answer. Most Productive Player is the leader in Wins Produced. Is that the MVP? I think you could argue that it is, although MVP isn’t really defined. It could also be defined as the most efficient player, although you would have to figure out a minimum minute requirement.

  Percentage of wins on team would probably — although I haven’t looked — always go to a great player on a bad team. In other words, good teams have more than one good player. So the leader in wins percentage wouldn’t likely be on a good team.

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  Brad // March 3, 2008 at 3:00 am

  I keep waiting for someone to say in the comments thread that rebounds are overweighted in win score. (I thnk we’ve gone a full day without it for the first time ever!) I’m going to reply “Your idea is dumber than snake mittens.”

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  Costa // March 3, 2008 at 8:46 am

  Rebounds are overweighted in win score.

  Now if you’ll excuse me, I need to take my pet Slithery’s mittens out of the dryer.

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  Ryan Schwan // March 3, 2008 at 9:40 am

  Thanks for the mention, Dave. When I used your numbers and my own guesses at minutes, I actually predicted 50.

  http://thehornetsfan.blogspot.com/2007/10/in-which-i-crunch-numbers-and-predict.html

  I got scared of so lofty a number and went lower when I did my Season Preview. What can I say, I’m a cowardly blogger.

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  dberri // March 3, 2008 at 10:21 am

  About rebounds…
  I found this book that bolsters the whole diminishing returns argument. Turns out there are three economists who said rebounds have diminishing returns back in 2006. I forget the title… something like “Wages of Wins” (or something stupid like that). I will try and find the full citation sometime.

  Ryan,
  Sometimes it is hard to believe those damn numbers.

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  Eli W // March 3, 2008 at 12:38 pm

  Dave, do you have any plans to adjust the Wins Produced and Win Score calculations to account for the large effect of diminishing returns on defensive rebounding?

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  dberri // March 3, 2008 at 2:35 pm

  Eli,
  As I have said before… there are diminishing returns with respect to shot attempts and rebounds. So that impacts performance. But performance is also impacted by all the other things I have mentioned.

  My view is that we first measure performance — which Wins Produced does — then we look at how these other factors impact production. So it is a step-by-step approach.

  With respect to diminishing returns… the Wages of Wins clearly states that this effect exists. But the impact of diminishing returns depends upon your teammates. So it is not a constant number.

  Perhaps the other people leaving comments can help me out…. haven’t I already said all this before?

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  Eli W // March 3, 2008 at 3:23 pm

  I think the effect of diminishing returns for rebounding should be integrated directly into the Wins Produced calculation, and that could be done rather easily.

  Wins Produced is an attempt to measure how much a player contributes to his team winning. Through regression you calculated that each possession a team acquires contributes 0.033 wins. And since a team grabbing a defensive rebound is equivalent to acquiring a full possession (because if the team didn’t get it their opponent would 100% of the time), each defensive rebound a team grabs contributes 0.033 wins. Now there is the question of how to translate this to the player level. If every time a player got a defensive rebound, the offense would have got it if he had failed to grab it (no diminishing returns), then each player defensive rebound would contribute a full possession acquired and thus 0.033 wins. But research has shown that around 70% of the time, when a player gets a defensive rebound, one of his teammates would have got it anyway. So players aren’t really contributing a full acquired possession to their team, and each player defensive rebound actually contributes around 0.010 wins (30% of 0.033). If you don’t make this adjustment either initially or after the fact, then strong defensive rebounders will be overrated by Wins Produced and Win Score, and poor defensive rebounders will be underrated. A similar adjustment should also be made for offensive rebounds (though it would be much smaller - reduced by 20% rather than 70%, from 0.034 to 0.027).

  For Win Score, instead of “Points + Rebounds + Steals + 1/2 Assists + 1/2 Blocked Shots – Field Goal Attempts – Turnovers - 1/2 Free Throw Attempts - 1/2 Personal Fouls”, the formula would be “Points + 1/2 Rebounds + Steals + 1/2 Assists + 1/2 Blocked Shots – Field Goal Attempts – Turnovers - 1/2 Free Throw Attempts - 1/2 Personal Fouls”. (Really the value on rebounds would be closer to 0.45, since approximately 70% of rebounds are DRB and 30% are ORB, and 0.7*0.3 + 0.3*0.8 = 0.45.)

  You could also make these adjustments after the fact if you prefer to go step-by-step, but they have to be made at some point.

  If the objection is that the effect of diminishing returns is not identical for all players, that’s certainly true, and worthy of more study. But in the meantime, Wins Produced would be a more accurate rating of a player’s contribution to wins if it used player-to-team translations of 0.3 for DRB and 0.8 for ORB, rather than the current method of using 1.0 for both (which also fails to differentiate between players).

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  dberri // March 3, 2008 at 3:40 pm

  Eli,
  You said this before. I responded before. You responded with the same argument again. I responded again. At what point do we give up on this?

  You are perfectly free to create the Eli Model and have fun with that. Although, given your focus on diminishing returns, you are going to have to adjust for diminishing returns on shot attempts also.

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  Eli W // March 3, 2008 at 3:48 pm

  Dave, I’m just trying to understand your position. You said you liked the results of my most recent study, but I don’t understand why you’re not drawing the same conclusions from it as I am. If diminishing returns matter, they should be taken into account.

  Do you agree that the evidence suggests a large diminishing returns effect on defensive rebounding?

  Do you think that Wins Produced as currently calculated overrates the contribution to winning of players with high defensive rebounding percentages (and underrates those with low defensive rebounding percentages)?

  It seems to me that the second follows from the first.

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  Harold Almonte // March 3, 2008 at 4:35 pm

  Eli. Diminishing return does exist in every action where a decission making between two or more players is done, the player who executed the positive action and got to be rewarded, produced a diminishing return (in total reward) to the others, and that’s not only at rebounding. But when you measure efficiency R/Rattempts, or FGM/FGA(FG%), then you are using the same rule for every position, or for every usage.

  You could have an approximation of player rebounds margin (I’ll change the name of rebounds overrating in order to not be mittoned): R - RMissed(R allowed to the opponent)= 2*R - Rattempts.

  An approximation for DRattempts could be:
  (player pos. ave DR/five pos. ave DR)*on court (Tm FGMissed + 0.56Tm FTMissed).

  You can weight rebounds as you like, and the zero sum = rebounding margin = +/- poss. gained/lost by rebounding attempt, will cancel that:
  Lg.AVE (DR*0.3 - oppOR*0.7)=0

  But I don’t know if it’s also difficult for your basketball mindset to accept something like “Off. Rebounds Missed”, and penalize it.

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  Harold Almonte // March 3, 2008 at 4:41 pm

  The Tm stats are really oppTm.

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  Harold Almonte // March 3, 2008 at 5:53 pm

  If you don’t want to weight rebounds by performance difficulty (which I don’t like too much), then: Lg AVE (DR + OR - DRallowed - ORallowed)=0, and the break even would be 50% rebounds obtained for every attempt wich caroms at the player position at both side of the floor, to be above average.

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  Jason // March 3, 2008 at 7:51 pm

  Eli, I do not know what pays your rent/mortgage and puts food on your table, but I suspect that you are not an academic. You have every right to take a study or model like Dave’s, analyze it, look at its strengths and limitations, critique it, and try to design a better model. One thing that you should not expect though is that the author of the model will redesign it because of your critique *especially* when the critique does not address the actual performance of the model.

  It’s this last point that is important. What you have shown appears to be that adding a rebounder does not add their total of rebounds in a linear fashion. You drew from this that rebounds are overvalued in the model. If the model was the “count rebounds model” this would likely be true. But it isn’t and as such, there’s not immediate cause to chuck everything and go through the laborious process of a redesign.

  But this is not what the model says. The model says that a team’s success is the sum of the success of the players. It becomes a predictive model when the success of players remains relatively constant over time.

  It is possible that factoring in diminishing returns into rebounds (and/or other categories) might improve the predictive ability of the model. But if rebounds are adjusted and we do not see any resulting increase in explanatory power, then it doesn’t matter if you observed diminishing returns as *with respect to the model* rebounds were not overvalued. Please note the emphasis. It is important. It does seem like the critics want to split apart the model and examine the components but lose sight of what the model was designed to do.

  Now the observation of diminishing returns might be useful in constructing a better model. It might, it might not. I can think of a host of reasons either way, but the observation itself does not suggest that only one outcome is possible. It’s good to not lose sight of that. If another model captures current results as well *and* better predicts future performance, it is a better model. Please be aware that you have not addressed this latter part with respect to overall performance and efficiency. You believe that it follows that since diminishing returns are observed that this stat must be overvalued with respect to the model as a whole. That is a possibility. It is not the only possibility though and it does not conclusively follow that it must be so. And to address this, you must actually look at the sum of performance in all of the game, not just in one category, else you are no longer evaluating the same model.

  One thing that Dave has been very clear about is that he’s an academic. Part of the process of academia is to share ideas so that *others* can take them and use them and improve upon them. It’s very common to see someone take someone’s model and show how their modifications improve it, and you have full rights to do so. By making it public (as he has) you have this ability.

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  Eli W // March 3, 2008 at 8:51 pm

  You emphasize that my critique does not address the predictive ability of Wins Produced. That is true. My critique is of the theory that went into the construction of WP, based on some empirical research that I’ve done. I think models should be evaluated on both levels - does the theory by which they were constructed make sense, and do they ultimately succeed at prediction.

  For some research into the predictive ability of Wins Produced, I recommend looking at the performance of Wins Produced and Alternate Win Score in tables 4, 5, 6 and 7 of this paper ( http://sonicscentral.com/apbrmetrics/viewtopic.php?p=18776 ). Alternate Win Score is an adjusted version of Win Score that is similar to what I am proposing. While my research suggests weighting player DRB as contributing 0.3 team possessions acquired and ORB at 0.8, Alternate Win Score weights DRB at 0.3 and ORB at 0.7 (AWS also has an adjustment for missed shots which is an area that I haven’t done any research on). Overall, AWS is closer to what my research suggests than Wins Produced is (which weights both DRB and ORB at 1). And those tables show that AWS predicts future team wins better than Wins Produced for every time period looked at.

  But regardless of that, it’s important to evaluate a model on its own terms. And Dave went to great lengths in the Wages of Wins to spell out the theory of how WP converts player statistics into team wins. I think I have found evidence suggesting that player defensive rebounds don’t contribute 0.033 wins because they don’t contribute a full possession acquired to the team, since much of the time the team would have acquired possession anyway (by a teammate grabbing the defensive rebound). Do you disagree with this line of reasoning?

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  Kent // March 3, 2008 at 9:58 pm

  Eli,

  Your research on diminishing returns in rebounding is very interesting. Have you done any work on how adding a high rebounder to a team influences other statistics? You point out compellingly that team rebounds do not increase by the full margin of the incoming player. But do other statistical categories benefit as a consequence of allowing other players to shift focus from rebounding? I think Jason is implicitly assuming this could be true.

  (On a related topic, is there any research on how adding a guy with high assists totals impacts shooting % of team?)

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  Animal // March 3, 2008 at 10:26 pm

  Sheli, what do you have against snake mittens?

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  Jason // March 3, 2008 at 10:36 pm

  Eli, if you are not aware of the go arounds about the Lewin and Rosenbaum, it’s been discussed many times before. This is not new news.

  Eli, perhaps it’s just your style, but your “do you agree with this line of reasoning” sounds more alike you’re trying to get me on cross examination. I’ve been on witness stands before as a scientific expert and don’t find that style particularly favorable to discussing science.

  Do I think that the observation that there’s diminishing returns in defensive rebounds is interesting? But I do *not* think you’ve come close to showing that a defensive rebound does not contribute what it does to the team. What you suggest is that the *allocation* of that rebound to a single player *may* be flawed *IF* you are counting rebounds as a single isolated category. Since that’s a conditional statement hinged on a conditional statement, I do think that the better method is to construct a model of total efficiency and see how that measures rather than to deconstruct the components. You’re free to disagree, but that’s my opinion and *as a model of total performance* I think that it’s a more defensible position to take.

  Again, the trick is to see if you get better predictive ability with the newfound knowledge. If you don’t, this suggests something else, and something much more interesting than these tiring “hah! you’re overvaluing rebounds” things have ever suggested.

  Forest. Trees.

  for what it’s worth, a defensive rebound *does not* gain a possession in the WP model. It marks the end of an opponent’s possession, but the actual possession would have come eventually anyhow. What it marks and measures is a defensive stop. You can divide this value among teammates in some manner (equal or otherwise) or assign it to one player, but the value of the defensive stop is not overvalued even if you believe that someone *else* would have grabbed that rebound. *That* is what your data suggest. Perhaps that’s what you meant, but that’s not what your last post said.

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  Brad // March 3, 2008 at 10:49 pm

  Jason,

  Is the predictive evidence of win score just that it is autocorrelated? If so, couldn’t that just show the persistence of a player being misvalued? For example, a player’s role could primarily be rebounding and that could remain his role year to year. The autocorrelation in his win score wouldn’t validate win score as a predictive measure.

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  Eli W // March 3, 2008 at 10:50 pm

  Kent, I haven’t looked at that. It’s worth investigating, though I doubt it would “cancel out” the diminishing returns effect. Especially since the effect is much larger on defensive rebounds than offensive rebounds.

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  Animal // March 3, 2008 at 11:03 pm

  TG Randini, where have you gone?

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  Eli W // March 3, 2008 at 11:30 pm

  Jason, I was just pointing to one aspect of that paper as it related to your specific question about predicting future wins. If you have any criticisms of how that part of their study was done I’d be interested to hear them - I know people objected to the use of adjusted plus/minus as a baseline for prediction, but I hadn’t heard people complain about them using team wins (which is the only part I was endorsing).

  I understand that your position is something like Kent said - rebounds may contribute to wins in ways other than those directly spelled out in the Wins Produced model. That may very well be true, and nothing I’ve done has disproved that. My research has just suggested that the specific route by which Wins Produced calculates the contribution that defensive rebounds make to team wins is flawed. There could be other pathways that neither myself nor Dave has anticipated. But as I said, I doubt that would “cancel out” the diminishing returns effect in rebounding. For one thing, my research suggests a larger effect on ORB than DRB. But it would be a pretty big coincidence if the positive side-effects of DRB’s were much greater than those for ORB’s (which is what would be needed for the values that WP places on both to be right).

  You’re right that I was simplifying in saying that a DRB acquires a possession rather than that a stop + a DRB acquires a possession. The distribution of credit between those two is another interesting issue, though I haven’t done any research on it myself.

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  Jason // March 3, 2008 at 11:34 pm

  Brad, the predictive value is that if a team has the highly rated ones, they do better than if they do not have such players. If a previously highly rated player arrives and the team does better (or departs without being similarly replaced and the team does worse) then this is not an issue of autocorrelation.

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  Brad // March 3, 2008 at 11:42 pm

  Jason, thanks for your reply. I understand now. I hadn’t realized the predictiveness was also being done on the team level. My copy of the book is in transit. I”m looking forward to reading it.

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  Westy // March 4, 2008 at 9:56 am

  Good discussion Jason and Eli.
  I enjoy this agreeable back and forth, and definitely think this is how progress gets made.

  What Eli has shown is a potential problem in the individual player valuation as described by WP. Even if there were no improvement at the team win prediction level, this improvement would be valuable to the WP formula. This is because although the model was created to predict team wins, it is being used to make statements about the relative value of individual players. If a certain subset of players is being mis-evaluated, the model should be updated or not used to make claims about players. The claim that scorers are overranked is not being disputed. However, their relative place in the hierarchy of players in the NBA could be incorrect if the individual valuation application of this model is inaccurate.

  I would also note that yes, the academic response would be to adjust the model, make our own additions and publish it as a response of sorts. For better or worse, I guess that is what Rosenbaum is trying to do. However, speaking only for myself, we are not academics. And to a large extent, I have little time to do more than keep up with the discussion. By offering critiques, my hope would be that others involved would recognize methodologies still could be improved and do that themselves. I would hope that everyone’s end goal is to produce the best model, not necessarily their own.

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  Jason // March 4, 2008 at 10:54 am

  “Even if there were no improvement at the team win prediction level, this improvement would be valuable to the WP formula.”

  If both models had *equal* predictive value, this could be true. But in any case of inequity, this is not substantive to the issue. If the model is created to evaluate team success and predict team success, I do not believe you can ‘mis-evaluate’ players but come up with better team predictions. If the model outperforms another model, it really does not matter whether or not individual diminishing returns are noticed for a particular statistical category. That breakdown is irrelevant. It’s almost guaranteed that the model misses things, that though it’s mostly a linear additive formula, there are probably aspects that defy this.

  Westy, Eli appeared to be generally peeved that Dave is not taking his observation and hopping back to change things. Maybe I misread his intent and affect, but that’s how it appeared. It sounded very much like a “I’ve shown this, now you have to do this or your model is wrong” sort of statement. Another aspect that seems somewhat disingenuous to me in the “I just want to make it better” issue is that the focus of all these diminishing returns critiques focus on rebounds. That seems to be the most common critique whether it is backed with evidence (as Eli has tried to do) or backed with blanket assertion. If diminishing returns are an issue, re-formulating based on knowledge of it in rebounds, but ignoring it in all other cases doesn’t seem to be much more than a knee jerk to satisfy the assertive criticism that the value of a rebound ‘just doesn’t sit right with many people. The cross of the model sounds like legal cross, not a scientific cross, focusing on people’s particular wording ind describing their reasoning rather than the data generated.

  It appears to me that people are picking on rebounds specifically. Guy once upon a time said that we didn’t see it in other aspects and enumerated turnovers to be one, though when I asked him for data, he amended that pronouncement. I suspect that there are diminishing returns to other aspects because the game has fixed boundary parameters of time and because the makeup of the game is such that there’s a division of labor inherent in the way most teams play. The question really isn’t whether or not there are diminishing returns, but whether or not these adversely impact the model such that trying to control for them makes for better predictions (or, in the case of this particular model, aren’t already adequately controlled–I suspect that the position adjustment actually accounts for far more of this ‘overvaluing’ discrepancy than most seem to think and disarticulating the rebound’s value without considering this doesn’t do anyone any service).

  My guess, and it’s a guess, is that there’s a more optimal non-linear solution, but how much more optimal is not something I’m willing to wager on. The approach of constant values makes the model relatively easy to work with and, if it’s good enough, it has merit there. My guess is that deciding that rebounds must be adjusted and then simply giving a fractional value again in a linear fashion is *also* “wrong” in many ways.

  But that’s not the model. The model is one of total individual performance summed to make team performance.

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  Mountain // March 4, 2008 at 11:16 am

  I agree that this is a useful thread, worth getting to. Solid points from several voices.

  It may conclude a chapter.

  Where to go from here? Into the value of rebounding on other aspects of team performance.
  Into diminishing returns of shot attempts. And separation of individual credit for stops from rebounds within data constraints.

  I look forward to hearing more on these points.

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  antonio // March 4, 2008 at 11:17 am

  Jason, while I know you have problems with Rosenbaum’s paper in how it compares different models in how they predict future wins, how would you go about comparing the models to see which one predicts future wins better? I am sort of just making an obvious question off of what Eli said -

  “I know people objected to the use of adjusted plus/minus as a baseline for prediction, but I hadn’t heard people complain about them using team wins (which is the only part I was endorsing).”

  So what was your problem with the team wins portion of the paper?

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  antonio // March 4, 2008 at 11:19 am

  I think the model of WoW should just be compared to the AWS proposed in Rosenbaum’s paper. While it is not the exact values Eli came up with, he himself said they were close enough. Whichever one predicted future wins better would be a better model, correct? And than from there, diminishing returns in other aspects of the game could be looked at to improve whatever model performs better

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  Mountain // March 4, 2008 at 11:24 am

  Jason: “The question really isn’t whether or not there are diminishing returns, but whether or not these adversely impact the model such that trying to control for them makes for better predictions (or, in the case of this particular model, aren’t already adequately controlled–I suspect that the position adjustment actually accounts for far more of this ‘overvaluing’ discrepancy than most seem to think and disarticulating the rebound’s value without considering this doesn’t do anyone any service).”

  My reaction to this statement is to restate my strong preference for using PAWS over WP or WS for measuring and comparing players.

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  Westy // March 4, 2008 at 12:01 pm

  If diminishing returns are an issue, re-formulating based on knowledge of it in rebounds, but ignoring it in all other cases…
  I completely agree. I think it should be addressed in each category. I would note, though, that it appears the diminishing returns are more significant in the case of rebounds. As well, based on the values being considered, the valuations for rebound-heavy low-usage players are significantly off in the current ranking (seemingly further off than any errors caused by disregarding diminishing returns in other categories), and thus, important to fix first.

  The approach of constant values makes the model relatively easy to work with and, if it’s good enough, it has merit there.
  And I also agree with this. I like keeping a simple model available. But really, I’d call even PER a relatively ’simple’ model. My only goal would be to see the current linear model improved by adjusting the constants as necessary to optimize the model with the data collection (box score info) we have available.

  Where to go from here? Into the value of rebounding or other aspects of team performance.
  Into diminishing returns of shot attempts. And separation of individual credit for stops from rebounds within data constraints.
  Yes, please. All of the above.

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  Mountain // March 4, 2008 at 12:03 pm

  Rebounding is done quite disproportionately by bigs and does make them or them in their role/ place on the court more valuable than perimeter players in their role / place if mainly scoring and assists -and their value- (but also everything else) are not in general as disproportionately distributed in favor of perimeter players as the WP results show.

  But the court is shared by 5 teammates dividing up the work and credit and generally 2-3 guys will do much of the rebounding work and get that credit and that credit is a lot about position and role.

  Use WP for what it shows / does best - win share distribution on a specific historical team.

  Use PAWS or PER for comparison of player performance. PAWS is by position, PER’s treatment of rebounds tends to even the playing field from the role/place on court rebounding aspect. (But maybe the value of rebounds should vary by position?)

  If cross-position player comparisons are done these metrics are better tools to me than WP.

  As for predicting win impact of adding a player to a new team I’d like to see more summary level data on the performance of the WP model on that (beyond the specific highlighted cases) and compared to the performance of other models/metrics out right now or that could be created for that specific challenge.

  A non-linear model would be a next level to explore as Jason notes. Worth it? Have to see to know.

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  Mountain // March 4, 2008 at 12:06 pm

  to clarify in my previous post it should have been …

  Into the value of rebounding “on” other aspects of team performance.

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  Jason // March 4, 2008 at 12:24 pm

  Antonio: Team wins is a fine way to evaluate the models that are (at least alledged) to assess team wins. I can’t think of a better way to assess team wins than by team wins. Off the top of my head, I don’t recall what sort of sample they used to compare the models. A single year (or single progression–I believe they looked at predictions for a couple or three years) is flawed and the sample should be multiple progressions. (This of course means that one cannot simply assign residuals to get to the total wins since this should not be consistent across the total of the sample)

  If I recall correctly, the predictive value of several models was actually rather close. I don’t recall how statistically significant the differences were though I do recall one way they assessed this, by counting the possible pairwise comparisons and seeing which ones “did better” and simply using the fraction as an assessment, something that really tells us very little in cases where models perform almost identically. Without some measure of statistical significance, a statistical comparison isn’t worth much.\

  Westy: you wrote: “As well, based on the values being considered, the valuations for rebound-heavy low-usage players are significantly off in the current ranking (seemingly further off than any errors caused by disregarding diminishing returns in other categories), and thus, important to fix first.”

  This seems like you have evidence that these rebound-heavy low-usage players do not contribute to victories as the model suggests (e.g. when one joins a team, they do not add to the win total as their WP would predict). Do you have such evidence? That there’s a diminishing return on defensive rebounds and they do not increase this particular statistical category is *not* such evidence. The only way to measure their impact on wins is to measure their impact on wins. If this is off, then the observation of diminishing returns suggests *why* this may be true, but it cannot lead the conclusion without evidence that the prediction is actually off.

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  Mountain // March 4, 2008 at 1:40 pm

  The metric study Eli mentions
  covered all teams, major personnel change or not. A study that focused on metric performance just on the set of cases with a significant personnel change- say a top 5 on team player- could help isolate metric performance on this aspect.

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  Mountain // March 4, 2008 at 2:12 pm

  At the apbrmetrics board I’ve mentioned the idea of deriving adjusted 4 factor ratings for players for their personal actions and team affects. Do that for every player offense and defense and combine them you would have a model that portrayed pretty comprehensively what a player did directly themselves in their countrpart matchup and their actual data-based team impact (where and how much) instead of relying on league wide estimates of positive impact or unit or diminishing returns by stat.

  Every team is still different and roles can vary too but such an approach might do better at predicting where and how much team 4 factors change or at least give numbers about difference from ‘expected if things transferred fully’ and studying why the numbers moved more one way or another could help understanding the unique nature of that team context and chemsitry or evaluate the wisdom of the 5 man lineup choices.

  You could sum the personal and the team data with linear weights or perhaps go non-linear.

  An ideal comprehensive non-linear model would link from physical attributes to skill abilities to the expression of them in personal performance and team impact data.

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  Westy // March 4, 2008 at 2:57 pm

  This seems like you have evidence that these rebound-heavy low-usage players do not contribute to victories as the model suggests…
  Just to clarify, I stated this based on the constants Eli was suggesting (0.3 and 0.8). If these should turn out to be more accurate (than 1.0), the current WP valuations would be off with respect to this type of player.

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  Brad // March 4, 2008 at 9:29 pm

  According to 82games, when the defense is in advantage (2 or more players vs. 1), the off. rebounding is 32% (with a frecuency of 28%). That’s from FGMissed, with the defense not as organized like from FTs. The defensive part of a rebound (the boxing out) can be as or more important than the mere act of jumping, and even the floor advantage and the bound of the ball. By the way, a 30% of def. rebounds are uncontested.

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  Harold Almonte // March 5, 2008 at 9:07 am

  Brad. That’s an old post of mine in other site. I need to clear up that although there’s logic behind the difficulty factor, odds, or whatever name given to that; it’s arbitrary and unfair to apply to one action, and not to other ones. If this is the case, an easy layup from an assisted fast break would worth much less than a double contested also assisted jumper. To block a PG would be more easy and worth less than to block a Center, etc. Then, it’s not fair to stay simple judging one action, and complex judging another one. The root problem of rebounding in all metrics is that there are margins (made - miss) for everything, but not for rebounds (neither for scoring: points allowed-included in WP, forced misses-included inside regressedDR). If these possession differential margins exist at the team level, for sure exist at the player level too.

  The game has other logic things which are debatible to be includded in a player individual metric, the most debatible of them is the team change of posession after a FGMade as a lost (if you don’t apply a fair inbounding compesation, and you don’t do the viceversa at the defensive side).

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  Eli W // March 8, 2008 at 7:43 am

  “Another aspect that seems somewhat disingenuous to me in the “I just want to make it better” issue is that the focus of all these diminishing returns critiques focus on rebounds. That seems to be the most common critique whether it is backed with evidence (as Eli has tried to do) or backed with blanket assertion. If diminishing returns are an issue, re-formulating based on knowledge of it in rebounds, but ignoring it in all other cases doesn’t seem to be much more than a knee jerk to satisfy the assertive criticism that the value of a rebound ‘just doesn’t sit right with many people.”

  I’m definitely interested in researching every area in which diminishing returns could have an impact. Have to start somehwere though, so I began with rebounds. I’ve followed that up with some research on diminishing returns for scoring:

  http://www.countthebasket.com/blog/2008/03/06/diminishing-returns-for-scoring-usage-vs-efficiency/

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  The Return of the Birdman « The Wages of Wins Journal // March 11, 2008 at 11:00 pm

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