Favre’s Not-So-Bad Interception

This post on Advanced NFL Stats (which is generally my favorite NFL blog), quantifying the badness of Brett Favre’s interception near the end of regulation, is somewhat revealing of a subtle problem I’ve noticed with simple win-share analysis of football plays.  To be sure, Favre’s interception “cost” the Vikings a chance to win the game in regulation, and after a decent return, even left a small chance of the Saints winning before overtime.  So in an absolute sense, it was a “bad” play, which is reflected by Brian’s conclusion that it cost the Vikings .38 wins.  But I think there are a couple of issues with that figure that are worth noting:

First, while it may have cost .38 wins versus the start of that play, a more important question might be how bad it was on the spectrum of possible outcomes.  For example, an incomplete pass still would not have left the Vikings in a great position, as they were outside of field goal range with enough time on the clock to run probably only one more play before making a FG attempt.  Likewise, if they had run the ball instead — with the Saints seemingly keyed up for the run — it is unlikely that they would have picked up the necessary yards to end the game there either.  It is important to keep in mind that many other negative outcomes, like a sack or a run for minus yards would be nearly as disastrous as the interception. In fact, by the nature of the position the Vikings were in, most “bad” outcomes would be hugely bad (in terms of win-shares), and most “good” outcomes would be hugely good.

The formal point here is that while Favre’s play was bad in absolute terms, it wasn’t much worse than a large percentage of other possible outcomes.  For an extreme comparison, imagine a team with 4th and goal at the 1 with 1 second left in the game, needing a touchdown to win, and the quarterback throws an incomplete pass.  The win-shares system would grade this as a terrible mistake!  I would suggest that a better way to quantify this type of result might be to ask the question: how many standard deviations worse than the mean was the outcome?  In the 4th down case, I think it’s hard to make either a terrible mistake or an incredible play, because practically any outcome is essentially normal.  Similarly, in the Favre case, while the interception was a highly unfavorable outcome, it wasn’t nearly as drastic as the basic win-shares analysis might make it seem.

Second, to rate this play based on the actual result is, shall we say, a little results-oriented.  As should be obvious, a completion of that length would have been an almost sure victory for the Vikings, so it’s unclear whether Favre’s throw was even a bad decision.  Considering they were out of field goal range at the start of the play, if the distribution of outcomes of the pass were 40% completions, 40% incompletions, and 20% interceptions, it would easily have been a win-maximizing gamble.  Regardless of the exact distribution ex ante, the -.38 wins outcome is way on the low end of the possible outcomes, especially considering that it reflects a longer than average return on the pick.  As should be obvious, many interceptions are the product of good quarterbacking decisions (I may write separately at a later point on the topic “Show me a quarterback that doesn’t throw interceptions, and I’ll show you a sucky quarterback”), and in this case it is not clear to me which type this was.

This should not be taken as a criticism of Advanced NFL Stats’ methodology. I’m certain Brian understands the difference between the resulting win-shares a play produces and the question of whether that result was the product of a poor decision.  When it comes to 4th downs, for example, everyone with even an inkling of analytical skill understands that Belichick’s infamously going for it against the Colts was definitely the win-maximizing play, even though it had a terrible result.  It doesn’t take a very big leap from there to realize that the same reasoning applies equally to players’ decisions.

My broader agenda that these issues partly relate to (which I will hopefully expand on significantly in the future) is that while I believe win-share analysis is the best — and in some sense the only — way to evaluate football decisions, I am also concerned with the many complications that arise when attempting to expand its purview to player evaluation.