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November 10, 2009

A New Approach to APM (Plus Chat)

Filed under: Uncategorized — Kevin Pelton @ 10:59 pm

I’ve written plenty at Basketball Prospectus about adjusted plus-minus, both touting its potential as a rating system and also making note of the limitations created by the high standard errors associated with single-year ratings. It is the latter issue that new adjusted plus-minus numbers made available at hoopnumbers.com by Joe Sill help address.

The math is beyond me, but Sill has utilized a technique known as “ridge regression” or “regularization” that serves to reduce the impact of multicollinearity that can be problematic for adjusted plus-minus (this is a concern when two players tend to share the court for the vast majority of their minutes, making it difficult for adjusted plus-minus to distinguish their impact). This method had previously been suggested by other economists on the APBRmetrics board.

To check his work, Sill used cross-validation–testing ratings from the 2008-09 season through February in terms of their ability to predict results from March and April. (Working within the same season minimizes the effect of aging in muddling comparisons.) What he found was that using regularization nearly doubled the predictive power of adjusted plus-minus.

Besides changing the ratings for a handful of individual players, in practice the other difference made by regularization is that the magnitude of the adjusted plus-minus numbers is compressed toward zero. To me, given the uncertainty that still exists in adjusted plus-minus, that seems appropriate. Keep your eye on hoopnumbers.com for 2009-10 numbers. BasketballValue.com already has adjusted plus-minus (using the traditional regression method) for this season, updated on a regular basis, though right now the standard errors are so enormous that there is little to be gained from APM at this point.

CHAT THURSDAY: After pausing for the World Series, it’s time to get back into a regular routine of chatting at BaseballProspectus.com. I’ll be taking your questions Thursday at 1:00 p.m. Eastern/10:00 a.m. Pacific. As always, you can leave yours now if you are unable to join us live during the chat.

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