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Tuesday, November 4, 2008
Tweaking the Plus/Minus Rating


Posted by Kevin Arnovitz

One of the things that makes baseball such a satisfying milieu for stat geeks is the beautiful independence of the plate appearance.  Sure, there are countless variables that go into a plate appearance (i.e. facing Johan Santana is vastly more difficult than facing Adam Eaton, and a plate appearance in San Francisco is more challenging for the batter than one in Houston), but there are fairly simple ways for statisticians to isolate these variables.  In basketball, a shot attempt doesn't offer the same kind of stability when it comes to figuring out a player's offensive value.  As Dan Rosenbuam wrote in 2005 for the New York Times, "Unlike baseball, with its repeated encounters between pitchers and batters, basketball is not a series of one-on-one contests.

In response to this statistical challenge, the "plus/minus differential has emerged in recent years as one of the favored tools.  At the risk of oversimplification, a plus/minus rating measures a player's performance by comparing what his team does when he's on the floor versus what they do when he's not.   It's a good tool&but not a perfect one.  What if the player in question is the weak link in a championship starting lineup?  Won't he have an artificially high plus/minus rating?  And what if the player is a defensive specialist who is on the floor against only the most potent offensive performers? 

Steve Ilardi and Aaron Barzilai are mindful of these concerns:

At first blush, the metric might even seem like the "holy grail of basketball statistics a single measure that captures the precise effect of each player on his team's bottom-line scoring margin. But it, too, has a major drawback: as a mathematical estimate, each adjusted plus-minus rating contains measurement noise, i.e., a margin of error. It's important, therefore, to get this noise (error) level as low as possible.

To mitigate the noise, Ilardi and Barzilai went to work by expanding their samples:

&we've used five seasons' worth of data (provided by 82games.com) weighted very heavily in favor of the 2007-2008 season to disentangle the individual effects of teammates who frequently appear on the court at the same time. As a result, we are able to present below the most accurate (low-noise) adjusted plus-minus ratings ever to appear in the public domain. In addition, we've modeled separately each player's impact on offense and defense, treating these as completely independent variables.

Check out the new numbers here.