APBRmetrics

Eli W · Joined: 01 Feb 2005 Posts: 401

I took the method from my last study on diminishing returns in rebounding and applied it to scoring, which is basically just another way of investigating the usage vs. efficiency tradeoff. I used some of Dean's stats from Basketball on Paper and lineup data from BasketballValue. I think the big advantage to the method I used is that it narrows things down to situations in which players were forced to increase or decrease their usage, which removes most of the usual confounds from players upping their usage in games/matchups when they were playing better (more efficiently) due to having a weak defender on them or just being "hot."

http://www.countthebasket.com/blog/2008/03/06/diminishing-returns-for-scoring-usage-vs-efficiency/
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Eli W. (formerly John Quincy)
CountTheBasket.com

Neil Paine · Joined: 13 Oct 2005 Posts: 774 Location: Atlanta, GA

That's some phenomenal work there, JQ. I'm not a huge fan of the low R^2, but I like the methodology a lot... In fact, changing the WARP formula to use the 1.25 tradeoff instead of 0.6 creates results that "feel" more believable (Calderon is no longer side-by-side with, say, Kobe -- JC dropped to 17th-most-valuable, and Kobe jumped up to 3rd).

Also, I'd love to hear Dean's thoughts on this new research, and whether it means we can now assume the typical player's usage-efficiency tradeoff is +/- 1.25, not +/- 0.6.

Harold Almonte · Joined: 04 Aug 2006 Posts: 616

I'm not sure, but I feel that this +/-1.25ORtg. each -/+1% usage is not linearly proportional all the way at the player level. I also feel that the way a player's usage is built has something to do. A player like Calderon with an A/TO higher than 3, and a lot of his usage built by that, and a player like Kevin Martin with a lot of his usage built by FTA, won't change eff. vs. usage like an average player.

HoopStudies · Posted: Thu Mar 06, 2008 7:38 pm Post subject:

I need to read what Eli did, but I will say that the 0.6 number I generated was a quick and dirty thing. I never use that since I generate individual values and use those. If Eli finds a different number, it's not a big deal. I hope he puts some range on it so that we can be confident it's not 0....

I'll try to look at it soon.
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Dean Oliver
Author, Basketball on Paper
The postings are my own & don't necess represent positions, strategies or opinions of employers.

Neil Paine · Joined: 13 Oct 2005 Posts: 774 Location: Atlanta, GA

So, I'm guessing you're not at liberty to disclose how you generate individual values... or are you?

(Sorry, I had to try! Smile

)

HoopStudies · Posted: Thu Mar 06, 2008 7:48 pm Post subject:

Ben F. · Joined: 07 Mar 2005 Posts: 391

Really great job, Eli, as always.

One thing I wonder about the graph - how big is the sample size for the farthest right point on the graph? Because without that point the graph looks like it's saying adding usage to a lineup gets you very little, and it doesn't matter how much you add. Whether it's +10% usage or +2% usage, you only get around +1 ORTG. Yet +12% usage jumps you way up, to close to +3 ORTG. That seems odd, so I wonder if there's any sample issues with that. If so, what does it mean that adding a lot of usage above league average doesn't get you much? And if not, why the sudden jump?

Eli W · Joined: 01 Feb 2005 Posts: 401

Guy · Joined: 02 May 2007 Posts: 109

Nice work, Eli. A few random thoughts:

Is the sample big enough to look separately at lineups with high vs low projected efficiency? It would be especially interesting to know what happens to low-usage/high-projected-efficiency lineups (since these are the players who should be shooting more, in absence of diminishing returns).

I think your projORtg should probably reflect actual usage in that lineup (if you have it), not the season average. For example, if a .90 usage lineup gets to 1.00 by giving all the 'extra' shots to its most efficient shooter, then the no-diminishing-returns efficiency expectation is a bit higher. (However, don't think this would change your results materially.)

It seems to me it's the low usage part of your graph that matters more, which is where the tradeoff is even larger (looks like a coefficient of approx .35). The important question is not how much more efficient, if at all, Kobe would be at average usage, but how much better he makes his teammates by employing 31% of the possessions. Looking at your graph, it looks like reducing the usage of four players from .80 to .69 (.0275 per player) increases efficiency by about .05. That means an extra 2.5 to 3 points a game, if I've done the math right. Pretty impressive. The fact that reducing the usage of high-usage players seems to pay only a small dividend is further disincentive to shift more shooting to low-usage players.

Eli W · Joined: 01 Feb 2005 Posts: 401

Eli W · Joined: 01 Feb 2005 Posts: 401

Guy · Joined: 02 May 2007 Posts: 109

Eli W · Joined: 01 Feb 2005 Posts: 401

Ok, I found the separated regressions that I ran. I'll try the breakdown Guy suggested later.

For all 5387 low-usage lineups (csum%TmPoss < 1), the OLS coefficient was 0.56 with a SE of 0.12 and an R-squared of 0.004. Weighting by possessions, the coefficient was 0.32 with a SE of 0.08, R-squared of 0.003. Using only the 240 low-usage lineups that played at least 50 possessions together, the coefficient was -0.23 with a SE of 0.19 and an R-squared of 0.006.

All 2729 high-usage lineups: coefficient of 0.24, SE 0.24, R-squared 0.0004. Weighted by possessions: coefficient of 0.096, SE 0.103, R-squared 0.0003. The 315 high-usage lineups with at least 50 possessions: coefficient of 0.40, SE 0.17, R-squared 0.02.
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Eli W. (formerly John Quincy)
CountTheBasket.com

DLew · Joined: 13 Nov 2006 Posts: 222

This is really great work Eli. I quite enjoyed it. I hope that Henry links it on Truehoop.

Could you do the same thing with multiple seasons worth of data to determine how robust the findings are?

Eli W · Joined: 01 Feb 2005 Posts: 401