Wednesday, March 17, 2010

Rating Interceptions Probabilistically

Just as it's hard to emphasize the process instead of the results in medicine, it's hard to correctly weight the role of luck in determining the outcome of a given play in sports. But, especially in sports with small sample sizes like football, it is crucial to isolate just the effect that the player himself had on the play.

One way to do this is by having watchers rate the expected value that a player contributes to a given play. For example, instead of just seeing a binary 0 or 1 interceptions on a given play, a continuous rating system should give more information.

So, give 0.5 expected interceptions for a throw that would have been picked off 50% of the time by an average defense / rest of offense (as wideouts play a role, too), 0.05 for a ball that probably wouldn't have been picked off unless the wide receiver hadn't tipped the ball off his hands, or 0.9 for a ball that was basically thrown right to the defender. Of course these ratings will be rough and subjective. But by and large they will be better than the status quo raw stats.

For example, this interception would be rated as ~ 0.9 expected interceptions, this one would be rated as ~ 0.02 interceptions, and this non-interception would be rated as ~ 0.6 expected value interceptions. You then divide the number of expected value interceptions by the number of passing attempts, possibly regress for the style of offense, and you'll have a much more reliable measure of the propensity of the QB to throw an interception than the raw interception stats.

This is what most scouts already intuitively do. But this rating method quantifies it so that the knowledge is more transparent and accessible. I'm willing to bet that this expected value measure, if adopted, would predict the QB's actual interceptions in the following season better than his actual interception total from previous seasons. Is anyone willing to bet against me on that?

This generalizes to other sports statistics, like the expected outs from an outfielder's throw to a runner speeding to home plate, the expected goals of a shot in soccer, or even the expected points from a jump shot in basketball (i.e., air balls are like 0, and points that hit off the rim more than once before going in are less than a swish). It generalizes beyond sports too, to emphasizing the process over the results as an important part of any performance analysis.