I wouldn’t ask the question if I thought everyone was in agreement about the answer. Unfortunately, there are some folks who believe regardless of how low Tyson Chandler’s USG is, that he is the “best” scorer in the league. And you know I’m not lying about that.

To be a little more concrete and topical: the Pistons just traded for Jose Calderon and got rid of Tayshaun Prince and Austin Daye. What should they expect if they ran out a line-up of Calderon (18.2% usage), Stuckey (21.5%), Singler (15%), Monroe (25%) and Drummond (16.4%)? The equation says their 96.1% usage should take their projected offensive efficiency of 109.5 down to 107.5, but it could really be anywhere from 95 to 119.

As a side note, as best I can tell from your site that particular line-up ending up scoring 27 points in 20 possessions, so their efficiency was much higher than expected (obviously in a very small sample, although we’re pretty much always talking about small samples, aren’t we?).

> Date: Tue, 21 May 2013 16:43:06 +0000 > To: akonkel@hotmail.com >

I would encourage you to look at nbawowy for the Heat, and look at lineups where LeBron, Wade, or Bosh are off the court. Look at how the USG of the other 2 remaining on court changes and what happens to their efficiency. It’s truly incredible how good those 3 guys are.

A couple of thoughts though: the R squared becomes outstanding when you bin everything together because you’ve eliminated so many sources of noise. If the question is “can we find evidence of an efficiency-usage trade-off”, then binning is fine. If we care about almost literally anything else in any detail, then it throws away all the information and the uncertainty that comes with it. That being said, I’d be willing to bet that if you found a way to put reasonable error bars on the bin graph, by which I mean the error bars reflect all the uncertainty in those means, the error bars across bins would overlap substantially even if the R squared for your nine points is fairly high.

I find it kind of interesting that your R squared, if memory serves, is lower than what Eli had. You obviously have more observations than he did, so the noise must increase at an even greater rate. I’m not 100% sure what that suggests, but it might influence your thoughts on combining line-ups across seasons.

> Date: Tue, 21 May 2013 07:49:38 +0000 > To: akonkel@hotmail.com >

One big issue is lineup matchups. Some lineups are only used against weaker options. For example, Jamaal Crawford can’t guard a potato sack, so he can’t go against elite backcourts. Also, think of a really high usage lineup. That’s like LeBron + Wade + Bosh, Carmelo and JR Smith, Durant and Westbrook, etc. Those are lineups guys fear, so they put in their best defensive lineups, generally. I need to adjust for the strength of the opposing defense. That will cause some of the noise. It’s also a systematic error, but it’s an error that I think makes low usage lineups seem more efficient than they are.

I’ll look more at your post when I add refinements. Thanks.

In contrast, you seem to feel that RAPM may provide important insights, even if single-season APM has little or no value. That’s a very different perspective, and I suspect not that different from the outlook of most who use/develop +/- statistics. I would think that you might also agree that aggregated +/- data — across multiple seasons and multiple players — could be useful in evaluating and strengthening other metrics. To take your example, if “Kobe Bryant was worth 2 points a game to the Lakers on average from 2005 to 2010,″ that could potentially be very useful. If a boxscore metric said he was only average, that may indicate a flaw in that metric. And if that same metric undervalued SG more generally over those seasons, you almost certainly have an important finding.

What separates the “camps” is not how valuable single-season APM is. It’s whether A) analysts should continue to work with +/- data in basketball, seeking out the signal within the noise, or B) analysts should stop using a “bad stat” and pretending it can have value. Unless I’m misreading you, I think you are still in the “A” camp.