Here's what I'm doing: I compare how many Rebs each team got at C (for example), to how many Rebs they got at the other 4 positions, or to the team's overall rebounds above average.
Ok, I see. But, still not convinced that is the best method to obtain accurate results, I've done my own analysis. Basically, for every rebound opportunity so far this year, I've computed the sum of the individual rebounding ratios for the defense and the offense, and compared that to the outcome. I'm using basketballvalue data for this. The results:
- Linear regression:
Code:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 69.73663 2.00587 34.77 <2e-16 ***
drt 0.30864 0.02719 11.35 <2e-16 ***
ort -0.80256 0.04006 -20.04 <2e-16 ***
If I only regress against defense or offense, the coefficients are 0.28 and -0.78, which suggests coaches tend to adapt to the opponent rebounding strength (the coefficient of correlation is small, just 0.07).
- Using a logit model:
Coefficients:
Code:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.84266 0.09811 8.589 <2e-16 ***
drt 1.47949 0.13291 11.131 <2e-16 ***
ort -3.85022 0.19571 -19.673 <2e-16 ***
For a 70-30 distribution, this translates into a 0.31 actual team increase for every extra point in the defensive players' sum, and 0.81 for offense. Essentially, same as above.
- If I estimate actual team rates using the above parameters, and then aggregate all observations into 0.1 wide bins for the expected rate, R-squared is 0.6093. Quite good.
- Correlation is even higher (0.6709) if I use a simple rebounding model for the estimation, where:
playerRate = playerAbility / (sum of playerAbilities on the court)
playerAbility is deduced from the actual player rates and his on-court team rebounding rate. This is similar to the correction MikeG uses in his numbers. Let's plot it (only for bins with more than 100 rebound opportunities):
Conclusions? Yes, I conclude my post here.
Last edited by cherokee_ACB on Wed Feb 13, 2008 4:14 am; edited 1 time in total
Posted: Tue Feb 12, 2008 4:48 pm Post subject: Re: Bottom line
Westy wrote:
So to summarize, what credit should any individual player get for garnering a defensive or offensive rebound, if the baseline for a possession is 1.0?
Both less than 1, defensive rebounds less than offensive rebounds, defensive rebounds much less than 1. Possibly differing numbers for players at different positions. More work needs to be done in order to pin down more specific values. _________________ Eli W. (formerly John Quincy)
CountTheBasket.com
I just put up another post on diminishing returns which uses a method suggested to me by Ben and similar to the one Cherokee_ACB used. I think it does a very good job of visually presenting the impact of diminishing returns on rebounding.
There is another issue with this technique that may lead to it underestimating the impact of diminishing returns
True. But, probably, the lowest (highest) projected rebounding units are the result of teams going small (big). If we accept that position affects rebounding percentages then, in those cases, it's normal that the projection underestimates (overestimates) the actual ratios. It's another issue worth looking at.
Joined: 14 Jan 2005 Posts: 1751 Location: Delphi, Indiana
Posted: Sun Feb 24, 2008 6:32 am Post subject:
I haven't followed this thread very closely, sorry. Eli, in your latest blog post, there's a strikingly weak correlation between (a lineup's) total player DReb% and team DReb%. You conclude that this indicates a diminishing return: Even if you stack your lineup with rebounders, you don't get a lot more (% of) rebounds. I think this is partly true.
What about the opponent's rebounders? If they decide to 'go small', what do you do? You could say, '"We will kill them on the boards"; but you might try to do better. You might go smaller -- which is to say, you'll be playing (with and against) lesser rebounders. Two teams always total 100% of the rebounds.
As small as sample sizes were for team's running with <65% total DReb'ers, it's probably a lot smaller for when the opponent was >70%. I think that to come up with an actual 'marginal value' for the DReb, you have to factor in the opponent's lineup. _________________ 40% of all statistics are wrong.
You're right that that the opponent's lineup should be factored in as well, Mike. Cherokee did that in his study, but mine did not. I will try to look into that more soon. _________________ Eli W. (formerly John Quincy)
CountTheBasket.com
Cherokee: I don't follow your argument. Why does Eli need to worry about position when he's looking at 5-man lineups? Seems like he has that covered.
The opposing player point is a good one, though I'll be surprised if it changes the DRB results very much.
Another way this method may understate diminishing returns is by looking at players only as they function in a single season, which usually means on a single team. For example, if Lineup X is projected at 16% ORB%, these guys clearly aren't expected by this coach to do a lot of offensive rebounding. Thrown together for 400 minutes over the season, maybe they come in at 17-18%. But is that really the best these 5 guys could do, if they became a starting five? I'd guess not. Both are valid ways to look at the question, but I think the latter scenario is closer to the question we're usually interested in answering: when a high/low rebounder is added to a team, how much does that increase/reduce team rebounds? One way to get at this might be to use career rebound rates (prior to season being analyzed) to make your projections.
That said, I think this is excellent work by Eli. Keep it coming. (And it would be great if Eli could post the numbers for each of his buckets: total minutes, projected reb%, and actual reb%.)
Cherokee: I don't follow your argument. Why does Eli need to worry about position when he's looking at 5-man lineups? Seems like he has that covered.
Take Marion, for instance. He averages 3 rebounds more as a PF. Part of that it's because his teammates are worse rebounders, but I believe position has a bigger impact. The regression assumes we should expect his contribution to team rebounding, in absolute terms, to be the same in both positions, and roughly the average of his SF and PF rebound ratins. This is not entirely realistic. It shouldn't come as a surprise then if lineups with Marion at SF underperform in this analysis, and overperform with him as a PF.
I've uploaded a spreadsheet containing all the data I used for the recent study that I did. It includes some formulas so you can see how everything was calculated. The file is around 8mb. Thanks again to Ben for providing the raw data.
Cherokee: I follow you now. Multi-position players will tend to cause this method to understate diminishing returns, except where two players effectively "share" two positions and often play together (in which case the overperformer will be offset by an underperformer in the same lineup). Not clear how big an impact this will have.
Going back to our earlier exchange, it is hard to square the coefficients you and Eli are getting with my position-based analysis, which seems to show a larger diminishing returns effect. To recap, when I look at positions rather than players, each additional 1% of Reb% is associated with a loss of .75 rebounds at the other 4 positions, and thus a total team gain of just .25%. The advantages of the position approach are that it shouldn't be affected by good rebounders being paired on the floor with bad rebounders. It also doesn't have the "Marion" problem you just raised, and avoids the issue of using year X data to "predict" year X outcomes. Do you see problems with my method that are avoided by your and Eli's studies? (Good faith question -- I'm not sure my approach is any better, just trying to understand why we're getting such different results.)
This study didn't mention that the WP's regressed DRebs already account for shot defense, then that's the "why" about the bigger weight. If they decide to rate rebounding, they can make OR*0.7, but they couldn't make regressedDReb*0.3, they would need to do it to the real rebounding portion only. Or they, and any other metric, need to find another way to account for shot defense, and to make DReb much less than the VOP. I think for a metric that confessed it doesn't attempt to account shot defense, PER is overrating DRebs as a whole possession and underrating shot defense action, applying the rebounding rating to this action too.
PER is right about the reb. rating, but WP has some alibi when you account for shot defense. In the end WP is not overrating its rebounds too much more than PER is overrating its owns, they just aren't rating it, and adding shot defense value inside, as a product of a team win regression. But the PER notion that DReb is VOP is not right: Advantage WP.
Another thing about DRebs is that it's true that players with position advantage produce diminishing return on teammates when it comes to account rebounds grabbed, but they also produce increasing return (negative slope in a negative quadrant) when it comes to account opponents's rebounds-allowed. I'm surprised the slope of DR%proyected vs. actual isn't more plane.
Cherokee: I follow you now. Multi-position players will tend to cause this method to understate diminishing returns ...
Do you mean "to overstate"?
Quote:
The advantages of the position approach are that it shouldn't be affected by good rebounders being paired on the floor with bad rebounders.
I already disagreed with this. Pairs like DHoward-Rashard are the biggest problem with your approach. And it's a big problem. If you want to argue for diminishing returns, you shouldn't use data with a bias in favor of your position. Well, at least I'd try not to do that.
Going back to Eli's 2nd issue in his blog post ("If players always played with the same four teammates ..."), I've ran the regressions separately for each team. This way, I focus on the rebounding ratios differences within a roster. Nothing changed. Of course, standard errors are higher and coefficients vary across teams, but averages stay at 0.3 and 0.8.
Last edited by cherokee_ACB on Tue Feb 26, 2008 11:44 am; edited 1 time in total
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