Game to Game Wins Produced Correlation for 2009-2010 Season and a fun little equation

I really wanted to get this post out last night but life sometimes intervenes. I was all set to start writing and then my wife’s computer went belly up (stupid Vista). I was up till 3 am working on it, using what my wife calls the black and white little nerd screen.

Now, I get to write it during my lunch break. In fact it’s a fun little challenge in trying to write something coherent and good in less than 45 minutes.

The last couple of weeks have been extremely productive (both professionally and hobbywise). I’ve been learning a lot and doing a lot. The first is obviously a result of my recent life changes. The second is the the fault of  Andres Alvarez, his mad skills (All Powered by Nerd Numbers).  He’s placed game to game Wins Produced splits at my disposal and placing this kind of data at my disposal even when I’m swamped, is like leaving cookies for the cookie monster.

I know I should stop but I can't help myself

 

So as a result, I’ve been taking these numbers out for a spin (WARNING: This is a math intensive zone feel free to go read and review the Basics if you need to). The results have been very surprising. Now my fun time right now is somewhat limited (so I’m not going to hit every bullet today and my a.a. milne  post stays on the queue) but I really wanted to get this particular fun fact out there for the world.

A common discussion in this and the other WOW blogs is that the WP coefficients are off. I decided to check this by looking at the game to game correlation between between Wins Produced margin (Sum of Home team ADJP48*MP -Sum of Visiting team ADJP48*MP for each game) vs. the actual point margin for each game. I figured that if there was skew it would show up upon detailed inspection (and we could then work on correcting/refining  it). I looked at all the splits for the 2009-2010 season . The results are as follows:

How about that, it lines up perfectly. I get the fun equation, Point Margin =0.0377 + 15.5 WP margin (I then round to get a whole number). This has an Rsq of 99.8%. Alternitavely,  WP margin= (Point Margin -0.0377)/ 15.5.
The absolute average absolute error is .32 points and a maximum absolute error of 2 points (for every game after rounding).
Out of 1230 games I got:

A 2 point differential 6 times (.48%)

A 1 point 392 times (31.8%)

and spot on 67.6% of the time

:-)

We really need to work on improving those coefficients!

70 Comments

  1. EvanZ
    12/3/2010
    Reply

    Arturo, WP matches up with wins at the team level, but whether the credit is distributed appropriately at the player level is a (long-standing) question.

    Just to give a clear example of how you can see this…What if we hypothetically split the credit for a rebound among all 5 teammates? The WP will still roughly match team wins, but each player’s WP48 will change.

    There is no “right” answer to this dilemma. Dave gives full credit for a rebound to the player. That certainly has some logic to it. Does the player deserve full credit? Did his teammates not contribute to him getting that rebound (i.e. through defense, blocking out, etc). That’s more of a philosophical question in my opinion.

  2. entityabyss
    12/3/2010
    Reply

    Hasn’t there been many posts about this rebound thing? This just will never be settled, I guess.

  3. Austin
    12/3/2010
    Reply

    It looks like EvanZ already covered it, but I would like to reiterate: no one thinks that the WP coefficients are off on the team level. The dissent all concerns the individual level.

    In other words, some people think that you can’t just apply team coefficients to individuals.

  4. 12/3/2010
    Reply

    Evan,
    The point I was making had to do with the argument about the weight/value of a rebound. The value of the rebound as it relates to wins (or point margin in this case) properly tracks. I’m not even using position adjustments in the calculation so I really wasn’t going for the value discussion (although I’ve covered that extensively, search for WORP or value or the short supply of tall people).

    The year to year correlation remains strong for wins. In fact, I think some of the recent findings on dimishing returns lend further credence as a lot of the variation year to year would be expected to come not from the player but from the roster shifts. We can come to a reasonable conclusion on player value based on the data (depending on your definition of value) and you can reasonably build a team around the numbers (just remember that you can have to much of a good thing and that you should not hire any members of the Portland training staff :-) ). I really need to get to v.3 of Build me a winner.

  5. Guy
    12/3/2010
    Reply

    Arturo:
    I’m sure you agree that this discussion can only be productive if everyone engages the actual arguments made by the other side, and not strawmen. As Austin and Evan allude to, none of WP’s critics dispute that a rebound is worth .03 wins at the team level. And none disputes that the team sum of WP48 is essentially equal to point differential. In fact, they INSIST that this is true, and that one can create a dozen other metrics that do the same thing, which is why they see the famous .95 R^2 as trivial rather than a vindication of WP. (After all, if you are going to include points made and points allowed in your metric, as WP does, how hard will it be to “predict” point differential? :>) So nothing in your post even addresses, much less refutes, the criticisms actually being made.

    Now, it’s totally kosher to argue that every extra player rebound does add a team rebound, if that’s your view. But let’s all engage the actual arguments being made. Knocking down strawmen doesn’t advance the discussion, and in my experience often has the opposite effect.

    One other note: I think you expressed the diminishing returns finding incorrectly. Recall that in the other thread we discovered, using Dr. Berri’s own research, that every extra win produced by a player (according to WP48) actually subtracts .3 wins from his teammates. This is a reason to make major adjustments in your assessment of players’ productivity, not to give “futher credence” to WP48. In fact, you may discover that the diminishing returns is so much larger for big men than guards that you don’t even need the position adjustment any more.

  6. 12/3/2010
    Reply

    Guy,
    When you come to a potluck it’s often a good idea to bring a dish. In fact it’s an odd cultural norm. Something that is considered rude is to just eat and insult everyone else’s food. Now I love discussion and arguing (a lot in fact) but I keep seeing these long critiques that boil down to “I don’t like how rebounds work in Wins Produced.” In short, please start bringing some food to the potluck, you’re being rude (as in show some analysis, some proof, heck anything other than three paragraphs of ‘See you’re wrong’.)

  7. ilikeflowers
    12/3/2010
    Reply

    So the rebounding coefficient is wrong position has now been modified to a diminishing returns speculation? This is a more reasonable stance at least. Of course it would be nice to see the diminishing returns effects upon all the model components as they impact all the other model components (as has been mentioned over the years at wow BTW – nothing new here either). So, if this latest rehash of all the same ole same arguments from the last five years about rebounding leads to a comprehensive examination of all diminishing returns then it’ll actually be worth something this time. It would be nice to see the actual shape of the various diminishing returns curves. Not a trivial task, but certainly doable.

  8. 12/3/2010
    Reply

    Diminishing returns was discussed in some detail in Stumbling on Wins. It was also noted in some detail in The Wages of Wins. Although I don’t want people to think I am just plugging these books (actually, I’m okay with that), before attacking this work you might want to read these two books.

  9. Guy
    12/3/2010
    Reply

    flowers: if you are interested in diminishing return rates for various stats, you might like this article (suggested by EvanZ): http://basketball-statistics.com/blog1/2009/12/06/the-diminishing-returns-of-rebounds-and-other-stats/. You are right of course that this is a long-running debate. But that’s only true at WOW and its sister sites. In the rest of the analytical world, the debate is considered settled (in favor of DR).

    nerd: I hardly know where to start. I’ve offered lots of statistical evidence on this issue, linked to powerful studies, and provided countless examples of diminishing returns at work. I’ve even told you a simple way to prove me wrong, that should take about 5 minutes for someone with your datasets: find some great rebounders who didn’t “happen” to have below-average rebounders for teammates. Yet no one has risen to the challenge. I have to conclude that you and I just have very different standards of evidence and logical reasoning. A good example is your recent post on Camby: The guy leaves your team, and the team remains just as good, and then he goes to a bad team which becomes even worse. Your conclusion is that Camby is one of the greatest players in the NBA. Oddly enough, I would look at that evidence and conclude Camby is much less valuable than WP thinks he is. So maybe it’s not productive for you and I to engage, since the kinds of statistical evidence I find persuasive don’t seem to move you, and your preferred evidence (“Dr. Berri says so”) doesn’t do a lot for me. I think the tone of the conversation on Arturo’s site has been quite positive and respectful, and I wouldn’t want to be part of changing that.

    • ilikeflowers
      12/3/2010
      Reply

      That’s great news! So, where is your model that makes use of your reality? Let’s add it to the smackdown. Time to put up.

    • ilikeflowers
      12/3/2010
      Reply

      In particular your (communitiy’s preferred) model is needed so that we can empirically examine its ability to predict player/team performance when players switch teams. Presumably, since you have a more accurate measure of reality (i.e proper valuation of rebounding) your model will prove especially superior in these cases.

    • ilikeflowers
      12/3/2010
      Reply

      Sorry for the multiple posts, but I did follow your link and I am already familiar with that work. It isn’t addressing what is needed. The effects of adding a great rebounder/scorer/assister/etc… on all of the team stats is what I’m talking about. Presumably other players can focus more on something else if there are those who are better at a particular aspect than they are. This is important because your claim that rebounding is overvalued in the wow model necessarily means that it is overvalued relative to other stats. Therefore the effect of each stat on all the others is necessary in order to establish that it is overvalued in a model that is measuring total win contribution from all the stats. If I add a tremendous rebounder to a team what is the impact on all of the other player’s stats? Does scoring efficiency go up or down? Do assists go up or down? And so on. Same for adding a high usage high efficiency scorer or a high usage low efficiency scorer.

  10. some dude
    12/4/2010
    Reply

    With all due respect, ilikeflowers, one does not need to provide their own model to discount another model.

    That’s like saying one must present an explanation for existence when one discounts the claim of God (and yes, many theists do use this improper argumentation).

  11. […] don’t think anyone has strong objections to this point (at least according to Arturo’s new post and the comments there) (with the exception that is supposedly doesn’t include defense, which […]

  12. Colour_Hysterical
    12/4/2010
    Reply

    @ some dude: I think what ilikeflowers was referring to, is what nerdnumbers was saying, namely that it becomes pretty tiresome when someone continues to discount something again and again and again using the same argument, when said argument involves no real foundation.

    • some dude
      12/4/2010
      Reply

      He keeps discounting it with the same argument because no one has yet to address it. And no one has stated the argument has no foundation. In fact, the argument has been largely ignored.

      can you explain why his argument has no foundation?

      I haven’t seen him claim to have a better model or even another model (or support for another model). But he doesn’t need one. The onus is not on the critic to provide something “better” or something “right.” The onus is on the original claimer to counter any legit claims or evidence against their own model. That is how it works. And no one has demonstrated his argument is incorrect or silly (by silly I mean argument that can obviously be thrown out by any rational person).

      When someone demands the critic give something better or more right, then there is nothing but the appearance of a lack of support for their own claims.

      • ilikeflowers
        12/5/2010
        Reply

        I already addressed his points. He continues to ignore mine both about the clear critical flaws in claiming that his evidence demonstrates that wow overvalues rebounds (he’s comparing oranges and citrus) and about a better model (from his better respected community) to settle the dispute, on this thread and on others. What point of his did I miss?

        As regards a model, if someone claims without equivocation that a coefficient is wrong then they must know at least the likely range of values. Contrary to what Guy has claimed about dberri being ‘stuck’ defending the wow position other coefficients have been tried with little impact (0.7 has definitely been tried and I believe other even smaller coefficients were examined as well – it was a while back).

        Guy is not making a nuanced argument he just says that the rebounding coefficient is wrong, period.

    • Guy
      12/4/2010
      Reply

      No foundation? LOL. Look, I’ve made a simple claim that is easily refuted if I’m wrong. I’m saying that virtually all “great rebounders” — defined as 3.0 or more Reb48 above average, at least 1800 MP — have teammates who are below-average rebounders. And that virtually all “bad rebounders” (-3.0 compared to position average) have above-average teammates. If there is not a large diminishing returns effect, then there will be plenty of good rebounders whose teammates are average or better (it should be close to 50%). So here’s the challenge for nerdnumbers, hysterical, or anyone else who still — against a mountain of evidence — believes there is not a very powerful diminishing returns effect: find some of these players. Time to put up, as flowers likes to say.

  13. […] the WoW Smackdown numbers. Wins Produced correlates very well with team wins (discussed by Arturo yesterday), so I’m using the current team WP figures (gathered from Dre’s Automated WP site) to […]

  14. Maybe one explanation
    12/5/2010
    Reply

    Maybe one explanation for the fact that there aren’t other good rebounders on a team with a great rebounder is because teams need more than just good rebounders, so they only employ one “great” rebounder.

  15. EntityAbyss
    12/5/2010
    Reply

    I’ve realized why this argument keeps going on and on and on and on. The reason is because you have guys who use box-score stats versus guys who essentially use plus-minus stats. The reason this doesn’t work is because the guys who use plus-minus stats believe that those must tell the story (and with good reason, when you think about it).

    The problem with that is, randomness happens. Plus-minus stats don’t correlate over time, so not only are plus-minus (different line-ups are included in this) don’t plus-minus stats correlate with wins, it doesn’t correlate with itself.

    The reason for this – randomness happens. People always try to explain things, because they feel certain things must have an effect. The data seems to show that randomness is the cause. If I average 30 points when player A is on the court and 25 when player B is on the court, and their stats are the same, you’d think that player A is the reason I scored 30 points. It makes sense in your head, but it can also just be luck. The very next year, I could average 25 with player A and 30 with player B. Why? Once again, because randomness happens. Over the course of a year, you can have different results with different line-ups, but that doesn’t mean it’s because of the line-up. It’s because randomness happens. Even if you put fans, another team, coach, and other different things, you can’t know what to expect. The problem is the plus-minus guys (once again, good reason) are sure that these things must have a play. The data suggests that this is random.

    That’s why plus-minus stats don’t correlate so well as years go by. I remember when Allen Iverson was on Detroit, before he got injured, they had a pretty good record on non-Sundays, but lost around 7 or 8 straights games on Sundays. The idea was that Sunday just wasn’t their day. The truth could’ve simply been that by chance, they just lost on Sundays.

    This doesn’t seem to make sense, but the data suggests it. Plus-minus doesn’t predict well. WP does. Why? The reason is because over the course of a season, box-score stats stay consistent. Who’s on the court at the time doesn’t seem to matter. It may look like it does, but it’s just luck. So you could have team with really good rebounders and bad rebounders on it. You could put all the bad rebounders together and outrebound teams and put all the good rebounders together and not outrebound teams. Why? Because randomness happens. At the end of the year though, you’ll get around the same stats, depending on minutes and pace.

    So in the case of Rodman. It’s possible that if you have a line-up with him in it, that line-up will rebound bad, and if you replace him with a bad rebounder, they’ll rebound well. The end result though at the end of year, will be your team rebounding better overall with Rodman getting more minutes. Yea, Rodman will have an effect on his teammates getting rebounds, but if they get their minutes, they’ll get their rebounds. Might not be when Rodman’s on the court. That doesn’t suggest that he’s the main reason, even though he’s the change.

    It just doesn’t make sense, but it works. That’s the thing with wins produced. It doesn’t make too much sense to certain people, but it works. The reason is because people think too much and put too many factors on certain things. We put coaching, fans, chemistry, heart, line-ups… to explain things that seem to be explained by one thing – randomness.

    So when it comes to line-ups, you won’t see the correlations you’re looking for. What will be consistent is stats at the end of the year and WP for players. I don”t know why. I just know that it’s just like that. plus-minus stats won’t correlate, but WP will. The reason is because randomness happens at times, all the time, but at the end, it all evens out.

    Sorry for the long post. (also, if you think Miami’s struggled because of “chemistry issues”, consider that maybe all 3 of the big 3 started off bad).

    • some dude
      12/5/2010
      Reply

      Okay.

      1. I personally am not a big fan of +/- but I do try to use all the advanced metrics to some degree.

      2. Your Rodman example makes no sense at all. How could you attribute every single great rebounder having inferior rebounding teammates be chalked up to randomness? I’m sure that that’s statistically converging to zero. The argument laid out about Rodman is that the increase to the team’s total stats (specifically rebounds) is less than what WP would predict. That’s the point and the data, according to everything arturo had posted previously, confirms Guy’s claim in this regard, not the other way around. And the one thing that cannot explain this is randomness because it’s consistent among all similar rebounders! finally, the argument that the team is better without Rodman is a straw man because the argument is only that his impact is overstated, not that it’s negative.

      3. Miami is a terrible example. B-R.com just ran a Monte Carlo of the likelihood that Wade and Bron are randomly on slumps and basically the answer was it was impossible. Here’s a case of people ignoring the statistics because they disagree with their viewpoint.

    • some dude
      12/5/2010
      Reply

      One more thing:

      And duh that WP is consistent over time since most players don’t move every year and are the same player for most of their career. Pretty much any way you set up WP based off all the box score stats will be consistent over time. The issue isn’t its consistency (in fact, if it was inconsistent over time since it measures box score stats, that would be an indication that it’s definitely not valid but consistency does not prove validity), the issue is whether it gives the proper allocation of a win to the individual players. I believe Guy’s argument is that it overstates the impact of a rebound (at the individual level) and that’s something I’ve always agreed with. And his argument has been pretty sound. He’s saying the WP formula at the team level needs tweaking, not that it is invalid.

  16. entityabyss
    12/5/2010
    Reply

    1. With regards to rodman, it may seem like giving the player 1 rebound suggests that he is getting credit for the entire rebound and therefore increasing the team’s rebounding by 1. Not exactly what is being stated. Being that diminishing returns for individual PLAYERS (not the team and not line-ups) don’t change much when adding a good rebounder, giving that player the total rebounding and accepting the small diminishing returns to each player seems to work best. Your argument on its effect on the team doesn’t change that each player’s rebounding numbers (and WP) will stay consistent. So no, if rodman wasn’t there, some1 on the team would’ve probably got it, but him being there doesn’t reduce each player’s rebounding numbers by much, so giving him the credit won’t change each player’s numbers much. That’s what WP does. It evaluates players. That’s why the team adjustment has .99 correlation to the player’s WP without it. At the end of the day, WP will still be accurate and consistent over time for players.

    If B-R believes that both Lebron (and wade’s efficiency is almost back to normal. Idk why he came up) and Bosh aren’t slumping, let’s see. Let’s see if they return to form (with respect to shooting efficiency, rebounding, TO, and assists)

    Also, there’s not much of a change you could make to WP for each player’s numbers. Giving the whole rebound to a player doesn’t mean the other team would have otherwise got the ball (although it certainly seems that way), but rather the value the player gives to the team. The effect of diminishing returns effects all players, but the effect is very small. That’s why player’s rebounding numbers (and WP) don’t change much. I understand where your argument’s coming from, but giving the value of a rebound to the player who got it, seems to work best. If not, WP wouldn’t be consistent over time.

    It’s a stat for effects players have on wins. It’s not perfect, but even if you do perfect, the results will not be much different. Also, the ways you’re suggesting to perfect it might not work. When a player takes a shot, his teammates don’t get credit for the shot they could’ve got, and when a player rebounds, same thing is told. At the end of the day, the same story is told.

    • some dude
      12/5/2010
      Reply

      “So no, if rodman wasn’t there, some1 on the team would’ve probably got it, but him being there doesn’t reduce each player’s rebounding numbers by much, so giving him the credit won’t change each player’s numbers much.”

      But they obviously do change much. That’s the point and what the data suggests. The reason WP is consistent is because of the lack of turnover among teams. Rodman is a great example because if the individual contributions to rebounding are as great as WP claims it to be, then the team’s total rebounding should be higher. But they’re not and it’s not even close to the WP predictions.

      “If B-R believes that both Lebron (and wade’s efficiency is almost back to normal. Idk why he came up) and Bosh aren’t slumping, let’s see. Let’s see if they return to form (with respect to shooting efficiency, rebounding, TO, and assists)”

      Coming back doesn’t prove it was a slump, it proves they figured out how to play together. The point was that it’s not just some random slump and that it is a structural issue, but those issues can be fixed.

      To the rest, you’re looking too micro. Just because someone’s rebound only dips slightly, the collective of the team demonstrates a large shift. And that’s what does happen. The point is that WP says 1 rebound by the player adds 1 to the team, but we never see that in the actual totals. That means that they’re being given too much credit, no matter how much you want to claim something else happening. There’s really no way around this that I can see.

  17. entityabyss
    12/5/2010
    Reply

    Also (sorry for the double post), I find it funny that lebron started off slow because of “chemistry”. Kevin Durant started off slow too (which dberri brought up). Must be some new “chemistry” issues that just popped up in OKC.

    • some dude
      12/5/2010
      Reply

      K-Durant has reverted closer to his statistical norm if we look at all 3 years. There’s a big difference.

  18. Guy
    12/5/2010
    Reply

    This is perhaps hopeless, but let me try narrowing this discussion to a set of specific claims that can be tested against evidence. The first claim of WP/WOW is that each additional/fewer rebound for a team is worth .034 wins more/less — I think everyone agrees on that. The disputed claim is that each additional/fewer rebounds a player records yields approximately one more/less rebound for his team. I say “approximately” because Dr. Berri acknowledges “some” diminishing returns (“DR”), but says they are not very significant for measuring players’ productivity (if he has been more specific and I missed it, I will happily defer to that more specific estimate). So we won’t be sticklers: if WP says a player adds 3.0 Reb48 to his team, and it turns out to really be 2.7, we’ll still call that a “win” for WP. Fair so far?

    Now, some (like abyss) seem to concede there may be huge diminishing returns on rebounds, but WP still “works” anyway — although he has no idea why — because it predicts wins. Since this is not the argument actually made by the WOW authors, let’s set this argument aside. If we can all agree there are in fact large diminishing returns on rebounds, then we can discuss whether WP somehow still “works” despite such a crucial assumption being wrong.

    My first claim is that there is effectively no evidence that players with high reb48 actually deliver anything close to the number of rebounds that WP assumes and that we would predict in a world without diminishing returns. Not “weak” evidence, or “unconvincing” evidence — but no evidence whatsoever. This is simply an assumption that has been made. (Just as Iverson fans might assume that every extra point scored by a player yields an extra point for the team.) So one thing that WP defenders might do is try to find or develop some evidence that each extra rebound produced at a position does increase team rebounds by something close to one. Instead of diversionary talk about WP predicting wins, or being stable from year to year, actually address the issue at hand and provide evidence.

    But some will say it’s not their job to produce evidence against diminishing returns, it’s my job to produce evidence to the contrary. I don’t think either side should avoid the obligation of backing up its claims with evidence, but I’ll do my part. The main evidence for diminishing returns is this:
    1) When high-rebound players are in the same lineup, they get fewer rebounds than expected; when low-rebound players are in the same lineup, they get more rebounds than expected.
    2) Every single one of the high-Reb48 players that WP loves has played with teammates who, collectively, are bad or terrible rebounders. Rodman, Lee, Wallace, Camby — every single one, without exception. This is true for essentiall all “great rebounders.” Conversely, so-called “bad rebounders,” like Bagnani, invariably play with good rebounders. This cannot be a coincidence, and is the logical consequence of diminishing returns. In a world without diminishing returns, some of these great rebounders would have average or better teammates, and their team would have the additional rebounds that WP predicts. The fact that this never happens is proof of DR.
    3) When high-rebound players change teams, the Reb48 rate for other players tends to fall.
    4) Team rebounding performance plays a very small role in predicting team WP. For teams, what produces a high WP is mainly efficient shooting and preventing opponents from shooting efficiently. Both are MUCH more powerful predictors than Reb48 of team Wins Produced. In the NBA, great teams are only a little bit better than bad teams at rebounding, but they are MUCH better at shooting and defense. This means that rebounds plays a relatively small role in explaining wins and losses in the NBA. (That doesn’t mean “no role.” I’m not saying rebounds don’t matter. Just that they matter far, far less than shooting and defense.) And remember, this is not my theory — this is what Wins Produced tells us at the team level.

    However, at the player level the story looks very different. Here, rebounds plays a huge role in determining each player’s WP48. WP48 for players correlates much more highly with Reb48 than points-per-shot, or whatever efficiency metric you prefer. Even for shooting guards, WP48 correlates more with Reb48 than shooting efficiency! So at the player level, WP is telling us that rebounds matters more than anything else, and is by far the most important element separating good and bad players. But at the team level, WP tells a very different (and IMO correct) story: that rebounding is not what mainly separates good and bad teams. Both stories cannot possibly be true. And mathematically, the only way WP can tell such radically different stories is if there are huge diminishing returns on rebounds, such that players with very high rebound totals are always offset by low-rebound players, and vice-versa.

    So, that’s the evidence. The challenge to WP believers is to disprove any or all of those three claims. Don’t tell me “that can’t be true because WP predicts wins,” or “you must be wrong because WP correlates from year-to-year.” Those aren’t germane, and using those arguments is just an admisstion you don’t have a leg to stand on with regard to DR and rebounds . And once again, if DR is not a reality, finding evidence to knock down my 4 arguments will be a piece of cake. There will be lots of great rebounders with average teammates. Reb% will be the best predictor of team WP48, just as it is of player WP48. But if you can’t find the evidence, then maybe you will at least consider the possibility that every NBA GM, every coach, and every single statistical analyst of basketball (other than Dr. Berri), are correct in recognizing large scale diminishing returns on rebounds.

  19. 12/5/2010
    Reply

    The argument that there not much variation in rebounding data appears to be incorrect. To compare the variation in two series we refer to the coefficient of variation (or the standard deviation divided by the mean). If we look at data from 1990-91 to 2009-10, we see the following results.
    Offensive rebound percentage: 0.106
    Defensive rebound percentage: 0.0392
    Adjusted field goal percentage: 0.0429
    Offensive efficiency: 0.0374
    Defensive efficiency: 0.0343

    It appears the variation in defensive rebounding is at least as high as the variation in offensive and defensive efficiency (and I assume people think offensive and defensive efficiency matters in the NBA). We should also remember that there must be variation in defensive rebounding for it to have a statistically significant impact on wins (which regression analysis shows that it does).

    As for “studies” that show a “large” diminishing returns effect… the only “studies” I have seen (other than what is reported in Stumbling on Wins) were offered by Witus and Nichols. These supposedly “powerful” studies are clearly flawed. Witus and Nichols offered regressions with only one independent variable. So nothing was controlled for. These regressions were misspecified. And you cannot interpret regression coefficients when the regressions are mis-specified (and describing a study as “powerful” doesn’t get around this point).

    That being said, there is a diminishing returns effect to defensive rebounds (as noted in Stumbling on Wins). And there is a diminshing returns effect to Wins Produced. This was noted in Wages of Wins (so it was never assumed that this doesn’t exist). The question is… what do we do about this? Sport Skeptic (see link above) wrote a great essay explaining why it would be difficult to include diminishing returns in the Wins Produced calculationm (one issue… there is diminishing returns with respect to points, field goal attempts, free throw attempts, defensive rebounds, blocked shots, and assists).

    And I agree with Sport Skeptic’s argument. That being said, in Stumbling on Wins (see this was all talked about in our last book, which I suspect people have not bothered to read) we did re-calculate Wins Produced with various weights on rebounds. We tried 0.5 for both ORB and DRB (although there is doesn’t appear to be any diminishing returns effect for ORB). We also tried Hollinger’s weights. The correlation between WP48 and what we see with these new weights is 0.95. So it doesn’t seem to make much difference.

    My argument is to treat WP as a measure of “how” productive a player has been. If you want to know “why” a player has specific numbers, then you need to consider factors like coaching (sometimes matters), age, injury (a big fact0r), diminishing returns, etc…

    One last note… when it comes to field goal attempts and points you see much larger diminishing returns issues. So this is yet more reason why Hollinger’s Player Efficiency Rating is incorrect. That means all the people who wish to harp on diminishing returns… well, you now need to run over to Hollinger’s posts and start leaving the same comments there that you keep leaving here. That should keep you busy for awhile.

  20. Guy
    12/5/2010
    Reply

    Let’s penetrate the fog a bit and see what Dr. Berri is really saying. The standard deviation on DReb%, according to his data, is .0392 * .73 = .0286. So a team that is one SD above average, the 83rd percentile in the NBA, will add approximately .0286*42 (opportunities) = +1.2 points per game. For offensive efficiency, he reports the SD is .0374*.5 = .0185. So a +1 SD team in offensive efficiency (83rd percentile) will add approximately .0185*2 (pts) *80 (FGA) = +2.96 points. So the variance in offensive efficiency explains two-and-a-half times as much of point differential as variance in rebounds. Which is exactly what I claimed. So this is great: now we can all agree at least that rebounds play a much smaller role than shooting (or defense) in winning games in the NBA.

    (For those interested, the coefficient of variation is an incorrect way to measure the impact of each statistic on wins and losses. Dividing each SD by the mean, when dealing with totally different statistics and different magnitudes of impact on wins/losses, is arbirtrary and misleading. For example, Dr. Berri’s coefficients seem to show that offensive rebounds have 3x as much variance as defensive rebounds — but both have the exact same standard deviation (and the same opportunities per game)! So we know that those two variances are equal in importance.)

    And it’s also great to see that diminishing returns in Wins Produced is now acknowledged. Dr. Berri’s own work shows that the addition of an above-average player will reduce the productivity of his teammates to the extent that 30% of his WP is lost. That is, replace a .100 player with a .300 player on an average team, and instead of gaining 16 wins the team will actually gain 70% of that, or 11 wins. Now, I suspect that this understates the actual extent of diminishing returns for big men. But at least as a starting point, you could just regress all players’ WP48 30% toward the mean — that would be far more accurate than the current values.

    The fact that the WP48 rankings don’t change much if you reduce the values of rebounds by 50% is a curious argument indeed. First, it would still have an enormous impact on the magnitude of players’ impacts: players now credited with producing 18 wins a season would only be producing 9 or 10 — quite a difference in how we value them and analyze their impact on a team. This effect is hidden when you report only a correlation (clever, eh?). But second, it reveals the separate problem in how WP values shooting. Because the total value of all FG shooting in WP equals zero (more than 80% of the wins produced for an average player comes from rebounds), rebounds still plays a huge role in WP even if you reduce the coefficient for rebounds by 50%. If you rank every player in the NBA based mainly on their Reb48, and then cut the value of a rebound in half, guess what happens — you still get the same rank ordering! So I’d put this particular finding in the “indictment of WP” category, rather than the “defense of WP” category.

  21. Guy
    12/5/2010
    Reply

    And I’m still waiting for someone — anyone! — to find me a “great rebounder” who did not suffer from diminishing returns, and whose teams enjoyed the full benefit of his WP-measured rebounding. Surely there must be at least one of these great rebounders who didn’t have the misfortune to be saddled with “bad rebounders?” The silence is becoming deafening…..

    • 12/5/2010
      Reply

      Guy,
      Really, stop it. No one is arguing that there are no diminishing returns. There are DR for every stat.

      This does not change the fact that adding a better player improves your team.

      For the rebounding/shooting arguments you’re just wrong. Player producing average production for every stat would deliver .100 WP48 (not .000 WP48). So shooting wins do not add up to zero (they can’t). An average player (.100 WP48) playing 1920 mp delivers 4 wins to his team. A below average shooter still adds wins to a team (just not enough). The centerpiece of this discussion is that rebounding is always viewed as a net positive, it adds value (possesions) at zero cost while the act of shooting in itself is a net negative act until the point where you score the points. I see your point but my rebuttal is tough nookies. That’s the way the game is setup.
      Blame Naismith

      You won’t get straight value for any stat but the correlation between having extraordinary rebounders/shooters etc. to winning is clear. If you’re better than average you produce wins. The DR discussion is an interesting one but let’s move it forward. We accept that it exists for all stats and we should be working on quantifying it (and in fact we’ve always accepted it). It’s certainly not linear though and the effect varies based on how good/bad your team is. This is why WP works as a model because for the most part the linearity of player value would be expected to hold. It’s only in extreme situations that the accrual of value leads to glaring shortfall on return (see Heat,Miami). The opposite is also true as if a scarcity exists increased returns will happen (this means that a good player moving to a bad team will be expected to generate more wins).

      And as a final point:

      Here’s a list of above average rebounders playing on above average rebounding teams.
      That’s 10% of all teams since 1979.

  22. 12/5/2010
    Reply

    Guy,
    Of course offensive and defensive efficiency matter more than rebounds. Rebounds are only a part of a team’s offensive and defensive efficiency measures.

    And I am not using the coefficient of variation to measure the impact of anything on wins. I was using it to measure the level of variation in rebounds and other stats. You claimed there was no variation in rebounds. We can now see you were wrong (and your inability to admit you were wrong — or in other words, your silence on how wrong you were — is indeed quite deafening… seriously, who talks like this?)

    And since the diminishing returns story was told in The Wages of Wins (with Wins Produced), no one is suddenly admitting this was true. It was part of the original story told more than four years ago.

    Here are my questions for Guy:
    1. Did you read the Wages of Wins? I assume — given your interest in all this — that you must have. But then again.. you missed the part on diminishing returns. So maybe you didn’t.
    2. Have you read Stumbling on Wins? Again, one would think you must have. But then again… if you did you missed quite a bit that is relevant to what you are talking about.
    3. Are you Guy Molyneaux? Just curious about that point.

  23. some dude
    12/5/2010
    Reply

    Arturo – are those above average rebounding teams including the best rebounder or not? And what do you mean by “above average rebounders.” Doesn’t every NBA team have an “above average rebounder?”

    Do you mean great rebounders (RP48 > ??) because the way you defined the list confuses me.

    • some dude
      12/5/2010
      Reply

      Arturo, that list includes the rebounder. For instance, I did the Denver nuggets from 2007. Camby had the RB48 of 16.5 but you have the team at 10.44. If you remove Camby and his minutes from the totals, the team RP48 is 7.56. Which again proves the point.

      That list isn’t what he asked for. You have to remove the said player from the totals to come up with how well his teammates rebounded.

      • 12/6/2010
        Reply

        SD,
        I did it the other way before. The point was that the above average rebounder leads to above average rebounding for team

        • some dude
          12/6/2010
          Reply

          Well, I don’t see how you came to that conclusion (even though it may be true).

          But the issue isn’t whether above average rebounders play on above average rebounding teams. That obviously happens. The claim made was that all great rebounding big men end up with below average rebounding teammates, thus overstating their impact since we know these teammates rebound better when you eliminate the great rebounder.

          I don’t know why you keep arguing against a straw man rather than address the argument made. Your chart answers a question that wasn’t asked. You have to remove the rebounder from the numbers.

  24. Guy
    12/5/2010
    Reply

    Let’s review the bidding. I provided four very specific claims for believing there are large (not small) diminishing returns on rebounds, which should be extremely easy to refute if I’m mistaken. Dr. Berri kind of attempted to refute one of these, which is that rebounding plays a small role in explaining team wins relative to shooting efficiency (and opponent shooting efficiency). His evidence turns out not to refute the claim at all, but rather to support it. I did assume he meant eFG% when he said “offensive efficiency,” since I was clearly talking about shooting efficiency separate from rebounding. If you do the same analysis with eFG%, you get the same result I provided above: a 1 SD change in eFG% has 2.5 x the impact on point differential as a 1 SD change in Dreb% (2.91 points vs. 1.18 points). If there is data out there more perfectly consistent with the claim I was making, I can’t imagine what it would be. So I think Dr. Berri for his supporting evidence.

    Now, Dr. Berri does say that he wasn’t trying to explain wins, he was simply rebutting my claim that “there was no variation in rebounds.” I plead guilty to assuming Dr. Berri was actually responding to my argument, which was about the relative importance of rebounds in producing team wins. But of course I never did make the claim he was rebutting (and indeed, went to quite a bit of trouble to make clear I didn’t believe it: “This means that rebounds plays a relatively small role in explaining wins and losses in the NBA. That doesn’t mean ‘no role.’ I’m not saying rebounds don’t matter. Just that they matter far, far less than shooting and defense.”). What remains unclear is whether Dr. Berri now agrees that rebounds are less important than shooting efficiency in explaining team wins, but are much more important in explaining player WP48, and why there should be such a discrepancy.

    Arturo:
    On rebounding/scoring, I was refering to the pre-position-adjusted productivity of players. The average Win Score at each position (the productivity of an average player) is very close to the average Reb48 at each position, so rebounds account for most of the production. But this is a rather arcane point, so I’ll retract it. The important claim by Dr. Berri is that changing the coefficient to .5 “doesn’t seem to make much difference.” So I would ask simply: what was Marcus Camby’s WP48 last year under the new coefficients? Or David Lee’s? That will tell us whether it “doesn’t make much difference.”

    You’ve made another stab at addressing my claim that great rebounders always have below-average rebounders for teammates, but again haven’t been able to find real evidence. I feel guilty sending you on any more wild goose chases, so I should warn you that I’m pretty sure these players don’t exist. (But if you want to continue, please adjust for pace.)

    You say we all agree there are diminishing returns, and that would be great if it were true. But it seems to me some people think the effect is quite small, and doesn’t require any change to WP. But my view is the effect is huge. And I don’t agree there are diminishing returns on shooting, beyond those already accounted for in FGA. So I really don’t think we all agree (which is OK).

    Bottom line: 1) still no one has prevented any evidence for the proposition that each player rebound adds something close to one extra rebound for his team. And 2) no one has provided evidence to rebut any of my four claims suggesting very large diminishing returns (any of the claims I actually made, that is).

    • 12/6/2010
      Reply

      Guy,
      As for the argument against DR being huge in general and for non-linearity in terms of WP?

      Garnett & Allen 2008 Celts
      Gasol 2008 Lakers
      Shaq multiple times

      All moved and all performed and improved their new teams and old teams more or less as predicted. These are huge WP moves and DR was not a significant factor.

      • some dude
        12/6/2010
        Reply

        Arturo, you’re bringing up extreme examples. Garnett and Allen and even pierce (since he missed so much time) came to a team openly tanking with D-league quality players and Rondo in his 2nd year now. I’ve already mentioned that at the extremes you won’t see the DR effects which is why David Lee going to the all time worst rebounding team in NBA history will improve the rebounding significantly. The argument revolves around the averages or heck within 1-2 Standard deviations, not teams at the margins.

        Lakers improving drastically in 2008 with gasol is questionable. Prior to Bynum getting hurt, LAL were the #1 seed in the West and Bynum. In fact, Bynum’s 2008 WP48 was .367 and Pau’s was .241, so according to you the Lakers pre-gasol and Bynum injury were BETTER than the Lakers with Gasol in 2008. Not only does this refute your claim of gasol in 2008, but um, do you really believe that Lakers would have been better off with Drew over Pau in ’08?

        Shaq – which ones? Suns were worse off replacing Marion with him. Is boston any different through 2 months this year than through 2 months last year or the year prior? Cleveland’s rebound rate was virtually unchanged with Shaq an they had a worse efficiency split.

        I’m having trouble seeing how your examples prove or disprove anything at all.

  25. 12/6/2010
    Reply

    Guy,
    You never answered my questions. In Stumbling on Wins we answer your question, but use Ben Wallace (another productive rebounder who can’t score) as the example.

    And yes, shooting efficiency has a larger impact on WP48 than rebounds. It is the story on shooting efficiency that drives the WP story. Not the rebound story.

    One last point… you did claim before that there is no change in rebounds across teams. Again, you were wrong. Again, you failed to admit this. You also failed to admit that your “powerful” studies weren’t so powerful.

    In the end, this seems like a waste of everyone’s time. You might wild claims. We waste our time shooting these down. You admit nothing and just keep the argument going. Do you really have no better way to spend your time?

    • some dude
      12/6/2010
      Reply

      When did he claim “there is no change in rebounds across teams.” I don’t see any such claims. Please quote it. Looks like a bunch of straw men arguments.

      And I see no reason why he should answer your questions when you’re simply trying to use misdirection or a veiled attempt at an ad hominem fallacy.

      Speaking of Ben Wallace, can you explain to me why despite replacing his minutes with 3 worse players & rebounders in Webber, Mohammed, and Maxiell that the Pistons rebounded the same the next season? Every single holdover from 2006 team increased their rebounding percentages….

  26. 12/6/2010
    Reply

    Some Dude,
    What an odd response. Guy has said more than once that there was very little difference between team rebounds. In fact, he once said it directly to you (within the last few days)!!

    Here is part of what he said (again, this was to you and this was not the only time he argued that rebounds don’t vary much across teams):
    Right now the top 8 teams in point differential are .26 OBR% and .75 DRB%. And the bottom 8 teams are .28 ORB% and .73 DRB% — no difference at all!

    Again, that was directly in response to something you said. Guy put forward a simple argument. Rebounds really don’t vary much across teams. Well, I just showed today that the variation in defensive rebounds is the same as the variation in offensive and defensive efficiency. And offensive rebounds have a much greater variation.

    In looking over Guy’s comments here (and there have been quite a few that seem to say the same thing), he has also wondered about what would happen if we had different coefficients (did it in Stumbling on Wins) and about diminishing returns on Wins Produced (did that in Stumbling on Wins also).

    He does keep suggesting the same silly test. How about this test? Let’s look at how a player’s defensive rebounds are impacted by his teammates? Wait, did that in Stumbling on Wins also.

    In the end, I think Guy needs to read the book. And then he needs to find something better to do with his time. If I am not mistaken, he has made this same argument about rebounds for several years (assuming this is the same Guy who has shown up at my website). The issue has been debated to death. We all agree that diminishing returns exists. The size of the impact has been estimated (in a fairly extensive study). The impact of diminishing returns has also been estimated for Wins Produced. I argue the impact — which has been estimated — appears “small”. But if you or Guy (or anyone else) want to believe it is “huge”… well, I am okay with that.

    • evanz
      12/6/2010
      Reply

      The size of the impact has been estimated (in a fairly extensive study).

      Can you be more specific about which study showed the effect of diminishing returns of defensive rebounding? Are the results in a published article? I have read Stumbling on Wins (in fact I’m looking at it as I type this), and the extent of the discussion is basically what you have said here, “The analysis says…that the effects are small.” What analysis? What does “small” mean in numbers? Thanks.

    • Westy
      12/6/2010
      Reply

      Also, above you note, “The correlation between WP48 and what we see with these new weights is 0.95. So it doesn’t seem to make much difference. ”

      Is this correlation in player rankings? Is the remaining 0.5 value for rebounds assigned to the 4 fellow defenders? I guess I don’t see how, if some portion of the value for a rebound is shifted to the other players on the floor, the player rankings remain consistent. Has this research been released publicly outside being discussed in the book?

      I guess I’d be interested in seeing a Top 20 players list in the WP48 system and then in the system built on the premise that each rebounder gets 0.6 (or 0.5) and the other 4 defenders split the remainder of the rebound. I’d guess there would be some noticeable shifts.

  27. some dude
    12/6/2010
    Reply

    “Some Dude,
    What an odd response. Guy has said more than once that there was very little difference between team rebounds. In fact, he once said it directly to you (within the last few days)!!
    Here is part of what he said (again, this was to you and this was not the only time he argued that rebounds don’t vary much across teams):
    Right now the top 8 teams in point differential are .26 OBR% and .75 DRB%. And the bottom 8 teams are .28 ORB% and .73 DRB% — no difference at all!”

    He said “very little difference between team rebounds,” not “no difference,” which is your claim.

    His “no difference at all” was in reference to the current top 8 vs current bottom 8 teams, which was correct at the time. It was not a statement to say there is “no difference at all” among all teams. You are putting words in his mouth. I am very well aware of the conversation Guy and I had.

    I can’t tell if you’re honestly having a hard time interpreting the sentences he put forth or if you’re trying to mislead. I hope it’s the former.

    “Again, that was directly in response to something you said. Guy put forward a simple argument. Rebounds really don’t vary much across teams. Well, I just showed today that the variation in defensive rebounds is the same as the variation in offensive and defensive efficiency. And offensive rebounds have a much greater variation.”

    But the fact that the variation is the same doesn’t change anything. What matters is how much of that variation explains wins. as Guy pointed out:

    Let’s penetrate the fog a bit and see what Dr. Berri is really saying. The standard deviation on DReb%, according to his data, is .0392 * .73 = .0286. So a team that is one SD above average, the 83rd percentile in the NBA, will add approximately .0286*42 (opportunities) = +1.2 points per game. For offensive efficiency, he reports the SD is .0374*.5 = .0185. So a +1 SD team in offensive efficiency (83rd percentile) will add approximately .0185*2 (pts) *80 (FGA) = +2.96 points. So the variance in offensive efficiency explains two-and-a-half times as much of point differential as variance in rebounds. Which is exactly what I claimed. So this is great: now we can all agree at least that rebounds play a much smaller role than shooting (or defense) in winning games in the NBA.
    (For those interested, the coefficient of variation is an incorrect way to measure the impact of each statistic on wins and losses. Dividing each SD by the mean, when dealing with totally different statistics and different magnitudes of impact on wins/losses, is arbirtrary and misleading. For example, Dr. Berri’s coefficients seem to show that offensive rebounds have 3x as much variance as defensive rebounds — but both have the exact same standard deviation (and the same opportunities per game)! So we know that those two variances are equal in importance.)

    When are you going to address this? So while they have similar variance, one explains wins at the team level a lot less! So if that’s the case, doesn’t that mean it should explain wins at the individual level a lot less!? And econometrics does agree with his claims about different stats and magnitudes, as well.

    At the end of the day, Mr. Berry, you seem to believe peddling your book is more important than defending the work, unfortunately. When someone tries so hard to sell something “in a book” rather than in the open, it’s often very difficult to look past it, kind of like Neil Boortz and his Fair Tax Book absurdity.

    Gee, and telling people they should do something better with their time than criticize your statistical analysis when you’re a professor of economics and supposed to be about free debate and exchanging of ideas, etc. *shrug* I think it’s unfortunate that you must stoop to such forms of debate. And seriously, do you think that by insulting Guy that it will convince him to buy your book if he hasn’t yet read it?

    And one last comment. The “debated to death,” argument is one that have been used against the abolishisnists and against guys like Galileo as well. It is not a valid argument

    “The peculiar evil of silencing the expression of an opinion is, that it is robbing the human race; posterity as well as the existing generation; those who dissent from the opinion, still more than those who hold it. If the opinion is right, they are deprived of the opportunity of exchanging error for truth: if wrong, they lose, what is almost as great a benefit, the clearer perception and livelier impression of truth, produced by its collision with error.” – John Stuart Mills

  28. Guy
    12/6/2010
    Reply

    Arturo:
    I neglected to say earlier that I agree stongly with this statement you made: “The DR discussion is an interesting one but let’s move it forward. We accept that it exists for all stats and we should be working on quantifying it.” That’s a good idea, and I appreciate the spirit behind it. Let’s look for areas of common agreement where possible, and build on those. Rather than debating yes/no, let’s try to figure out “how much?” If we can establish that, then everyone is free to call it “small,” “big,” or anything in between, as they wish. However, we should recognize the possibility — I imagine you agree — that the rate of DR may vary quite a bit from one statistic to another.

    And perhaps there is more agreement than I recognized that for rebounds, or at least defensive rebounds, the diminishing returns seem quite significant (since no one seems to disagree with the specific claims I made.) It appears that on average, teams only gain about 30% of a player’s Reb48 above average. Do you agree that it’s somewhere in that general ballpark, or do you have a different estimate?

    Above, Dr. Berri identifies a crucial piece of common ground for our discussion: “And yes, shooting efficiency has a larger impact on WP48 than rebounds. It is the story on shooting efficiency that drives the WP story. Not the rebound story.” At the team level, as I wrote, that is true: shooting efficiency drives WP much more than differences in rebounding. And that is consistent with what we see in the standings: the top teams are distinguished much more by their shooting efficiency (and defense) than rebounding. Now, the big question I have for you is this: why is WP48 for players driven mainly by rebounding, when that doesn’t seem to be what’s creating actual wins and losses? If you check your data, you will find WP48 correlates much more with rebounds than shooting efficiency. If you run a regression to predict WP48, using rebounds and efficiency as independent variables (and include other elements if you want), you will find that rebounding plays the largest role. Don’t you think this mismatch between what actually matters for team success, and what WP says matters at the player level, signals a potentially significant problem?

    Some Dude: Thanks, you did all the heavy lifting for me while I was asleep. Cool. I think if we stay focused on ideas and evidence here, and do not make things personal (and don’t get distracted by the frantic “pay no attention to the man behind the curtain” routine), we can have a productive dialogue.

    • bduran
      12/7/2010
      Reply

      ” If you check your data, you will find WP48 correlates much more with rebounds than shooting efficiency. If you run a regression to predict WP48, using rebounds and efficiency as independent variables (and include other elements if you want), you will find that rebounding plays the largest role.”

      Didn’t Dr. Berri say that adjusting the coefficient on rebounds did little to effect player rankings? Doesn’t that show that rebounds do not drive the WP48? Did you do any of the things that you suggest? It seems like you tell people what to do to answer a question, but also tell them what the answer will be. So i’m guessing you’ve done what you’re asking already?

      • Guy
        12/7/2010
        Reply

        I assumed Arturo would want to verify any claims I made anyway, and that his results would have a lot more credibility with many commenters here. But yes, in my analysis of players’ WP48, rebounds play a much larger role than shooting efficiency. For example, at PF last year (min. 1200 minutes) , the correlation of WP48 and Reb48 was .91, while the correlation with points/FGA was .30. A 1 SD gain in rebounding produces an increase in WP48 of .103, while a 1 SD gain in points/FGA raises WP48 by .023 — so rebounds had almost five times the impact of efficiency in determining WP48 at PF (in 2009-2010). What really surprised be was SG, where the correlation with REb48 (.67) was again much higher than for efficiency (.44).

        I’m sure the relative impact of rebounding varies by position, but as best I can tell it’s generally very high and plays a larger role overall than efficiency — even though efficiency is in fact much more important for winning (as Dr. Berri notes above).

        • bduran
          12/7/2010
          Reply

          Guy,

          I’m sure people would want to verify your claims, but in my experience making claims and providing no support makes people want to ignore claims. Clearly you don’t want to be ignored. Thanks for the info.

          Points per shot ignores FT possessions so that probably explains at least some of the difference. I still don’t know how rebounds could drive WP48 if cutting their value in half doesn’t change the rankings much.

        • Guy
          12/7/2010
          Reply

          BDuran: Fair point on providing the evidence. FT possessions will have a trivial effect I think (using eFG% to measure shooting efficiency yields similar results).

          Yes, Dr. Berri does say above that using the Hollinger coefficients (.3/.7) “doesn’t seem to make much difference.” In SOW he cites Ben Wallace in 2001-2002 as an example, saying Wallace would still lead the league in WP48 using Hollinger’s coefficients. I ran the numbers, and Wallace’s WP48 declines from .433 to .337. That’s a loss of .097 WP48, equivalent to an average NBA player, and a loss of about 6 wins to the team. I leave it to others to decide how accurately “doesn’t make much difference” describes a 22% decline in productivity.

          As for why cutting the value of rebounds doesn’t change the rankings much, paradoxically, it’s precisely because rebounds play such a huge role in determining WP48. If rebounds explain most of WP48, and scoring plays a small role, then reducing the value of rebounds for all players can’t change the rankings very much — the top players will still overwhelmingly be high Reb48 players (position adjusted). If rebounds determined 100% of WP48, then you could change the coefficients to .1, .7, or 3.8 and you’d always get the same ranking. Think about it this way: if the final exam counts for 80% of your grade and the mid-term 20%, and the professor decides to reduce all the final exam scores by 50%, the final exam will still acount for 67% of your final grade. Rebounds are the final exam.

          So the lack of change in the rankings with new coefficients is actually additional evidence that player WP48 is too dominated by rebounds, rather that evidence on the other side. (Which is why it’s always surprised me that Dr. Berri keeps making it.) And even so, changing the coefficients will dramatically change many players’ WP48.

          • bduran
            12/7/2010
            Reply

            eFG% also ignores FT attempts. It just adjusts FG% for the effect of the 3 pt shot. I would think that the effect of FTs would be non trivial since possessions are so important (Ignoring FT attempts essentially gives points at no possession cost), but I don’t know for sure.

            As for Ben Wallace, of course cutting the coefficient drops productivity, who would argue otherwise?

            You certainly make an interesting point about changing the coefficient, however, if I disagree with the statement that the coefficient change is necessarily evidence that RB48 dominates WP48. Obviously, if RB48 was onlya small part, then changing the coefficient wouldn’t matter much either.

            It’s certainly easy to find a not great rebounder that WP48 loves. Manu Ginobili has a slightly below average rebound rate according to hoopsdata, but last I checked had a +.300 WP48. Tony Parker is just average and is close to .200 WP48. Matt Bonner has always been a subpar rebounder, but is consdiered above average by WP48 when his shot is falling. These are just guys I can think of from my favorite team.

  29. Guy
    12/7/2010
    Reply

    “As for Ben Wallace, of course cutting the coefficient drops productivity, who would argue otherwise?”

    BDuran: Well, Dr. Berri appears to. He frequently says it makes little difference if you change the coefficients. But it greatly reduces the productivity of some players, while increasing the productivity of others.

    Ben Wallace, by the way, is a great example of diminishing returns and the way WP48 can misvalue players. In 2002, WP credits Ben will adding 320 rebounds for Detroit (above an average C-PF). And what was Detroit’s team total? -163! So Wallace’s teammates were — allegedly — a jaw-dropping 483 rebounds below average, or 6 boards per game. And note that this bad luck followed Wallace every single year, regardless of the team he played on — he was always saddled with poor-rebounding teammates. Quite the coincidence, wouldn’t you say?

    Good point that the coefficients also wouldn’t change things if Reb48 had a minimal weight in WP. Of course, we know that isn’t true. Let’s just agree that the small change in rankings is not evidence either way, but is completely consistent with an overweighting of rebounds.

    I certainly agree that average rebounders can post high WP scores. But I’m not sure what your point is. No one has said WP values only rebounds and nothing else, only that it weights rebounds far more than anything else, and far more than their actual role in determining team wins. None of that is contradicted by your examples.

    You’re welcome to test any measure of efficiency you’d like — Arturo has all the data you need for last season presented here. I’m confident that none of them will approach Reb48 in terms of predicting player WP48 (and remember, we already know that efficiency should be much, much stronger). When Reb48 and WP have a correlation of .8 to .9 (as we see at C and PF), we know that rebounds are the story.

    More broadly, I’m wondering if we’ve now reached a rough consensus that there is a large diminishing return effect in rebounds, and that therefore WP does indeed significantly overweight rebounds. Arturo, are you on board? Flowers? Can we move forward with trying to measure the extent of the problem?

    • ilikeflowers
      12/8/2010
      Reply

      Wow. Given all the posts, I really don’t know what more to say. Your conclusions from your evidence are just illogical. In other words no, I’m not on board that WP significantly overweight’s rebounds. As for moving forward, we are precisely where we were years ago, waiting for relevant work on diminishing returns based upon various factors (position/stat/magnitude) with regards to wins. If this otherwise unproductive rebounding myth rehash motivates that then at least it will have been worth something. There’s really not anything more to say on it until then.

      • Guy
        12/8/2010
        Reply

        Illogical evidence? Interesting. OK, just answer this: why can’t we find even a single great rebounder who hasn’t experienced large diminishing returns on rebounds — not even one — if the effect is only small in general? Wallace, Camby, Garnett, Rodman, etc. — every one saw huge diminshing returns. Or, why is that not a fair test of the propostion if that it is your view?

    • Guy
      12/8/2010
      Reply

      That’s a disappointing response, reservior. I patiently and politely presented a substantial amount of evidence for a very large DR effect on rebounds. No one provides any contrary evidence, even though disproving my claims should be extremely easy if the diminishing returns effect truly is small. Even Dr. Berri stops by, apparently reads a lot of my comments, but is not able to rebut a single piece of the evidence presented. And at the same time, no evidence has been provided to support the position that player rebounds create nearly as many team rebounds — indeed, over five years the total amount of evidence preresented for that position remains at zero. Yet this is your only reply, to try to dismiss and marginalize the problems I’ve raised? I would have hoped that evidence counted for more, and faith in the Wizard a little less…..

      • Gabe
        12/8/2010
        Reply

        “I would have hoped that evidence counted for more, and faith in the Wizard a little less…..”

        sigh.

        Khandor is also exceedingly polite and patient, and he also presents what is, in his opinion, substantial evidence that supports his positions…

  30. Guy
    12/8/2010
    Reply

    Ah yes, the world-weary “sigh” response — very strong evidence indeed, Gabe. Really, if you guys are so confident in your position, why is it that you don’t present evidence for it? I mean, even after all these comments, no one has identified even a single “great rebounder” who didn’t suffer from huge diminishing returns on rebounds. Dr. Berri himself shows up, and the best he can do is present some statistics that turn out to be 100% consistent with the claims I made (once we cleared up his confusion about the relationship between variance and wins). If there were strong evidence that diminishing returns on rebounds truly is “small,” don’t you think Dr. Berri would be the one to have it? He took the time to come here and disagree, so why wouldn’t he share relevant evidence if he actually has any?

    • Gabe
      12/8/2010
      Reply

      I think sighing is a fair response to your —> “faith in the Wizard” dig.

  31. Westy
    12/8/2010
    Reply

    Guy,
    You note, “…cutting the value of rebounds doesn’t change the rankings much.”

    But it would if you distributed a portion of the rebound’s value amongst the teammates who helped generate it, correct? Sharing the value of the coefficient is different than just moving it up or down.

    • Guy
      12/8/2010
      Reply

      Westy: That’s correct. And you could even quarrel with the claim that the rankings don’t change much, depending on what you think “much” means. In 2002 (the year Dr. Berri focuses on), using Hollinger’s coefficients reduces Ben Wallace’s WP by about 6 wins (22%). But Kobe’s WP goes down by only 1.6 wins (13%). And Reggie Miller sees his WP INCREASE by 2.3 wins (29%). So the notion that it makes little difference which coefficients you use I don’t think bears much scrutiny.

  32. Nick
    12/9/2010
    Reply

    Well said Guy and somedude!

  33. […] the defensive effort that lead to the rebound I’ve played with these myself over time. The point margin analysis really nailed it for me though. 1230 samples using the marginal WP to Point Margin linear […]

  34. Mike
    3/3/2011
    Reply

    Reading this, I’m not really sure why someone didn’t at least attempt to answer Guy’s questions…or didn’t run a regression themselves to see what the correlation was between WP48 and Reb48.

  35. Eric Cartman
    4/20/2011
    Reply

    This discussion was really sweet. Someone actually claimed that WP “predicts better than +/- ” which is pure comedy in itself and then we have the anti-WP guys actually believing him and then start claiming that good prediction doesn’t matter. The jokes just seem to write themselves

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