Posted by Neil Paine on April 22, 2009
(Before reading this, read this.)
OK, this post is in response to a few questions by our readers over the past day or so...
A Simpler Version
There were some inquiries into a simpler equation than the monstrous one I posted the other day, and it's actually true that not all of the variables I included were significant at the 0.10 level (I'm all but sure this was also the case for Dr. Rosenbaum's model back in 2004 as well). By throwing out some of the less important variables, you can actually use the following simplified equation without a significant loss in accuracy:
SPM = -10 + (0.55*P40) - (1.38*TSA40) + (0.02*TSA40^2) + (0.44*3A40) + (0.44*FTA40) - (1.72*TO40) + (2.25*ST40) + BL40 + (0.44*PF40) + (1.54*VI) + (0.1*MPG)
It appears that although breaking down assists and offensive & defensive rebounds into their own categories is nice, their presence in the versatility index picks up the majority of their value. I'm still going to use the full, more complex version, though, which brings us to...
A poster named "Schtevie" over at APBRmetrics wanted to know if I could include a squared term for player age in the regression, which of course would add a more realistic curve shape to the aging effect (rather than the linear effect that was assumed earlier). And I most certainly can -- in fact, I would have originally, save for the fact that Excel's somewhat lousy -- but easy-to-use -- regression package limits you to 16 variables (and Age^2 would have been the 17th). But because you asked for it specifically, I opened up R and ran the regression this morning, which will now be considered the "official" SPM formula:
If you want a spreadsheet of these results for every player-season in NBA & ABA history (or since 1952, at least), you can get it here.
Another commenter inquired into the possibility of including charges drawn as another variable in the regression, and I replied that I'd like to if I could find the data. 82games.com has tracked charges in the past, but with only one year of full results to draw from, I don't think it would make for a very meaningful regression. So for now, I think we should wait until we see a few more years' worth of charges tracked -- all the while crossing our fingers that the league itself will officially keep tabs on the stat someday.
As always, feel free to ask more questions or tell us your thoughts in the comments below...