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Optimizing Isn't Easy Even for Belichick

Long time followers of TSE know that I have an ongoing interest in decision making in sports and how it may relate to decision making in broader contexts.   In an effort to deal with high levels of complexity, many managers in sports appear to adopt managing templates from other successful managers rather than attempting to decide on the spot regarding the optimality of a decision.  Maybe this is a way of condensing complexity or a risk averse reaction to possible criticism of unorthodox moves.   Some managers, however, such as Bill Belichick or Jim Harbaugh, seem less bound by a template and more willing to seek optimal, if unorthodox, strategies on a case by case basis.

Sunday's New England/Baltimore AFC Championship game illustrates that such optimization by even someone like Belichick is very difficult.  Keith Goldner at Advanced NFL Stats provides a lengthy analysis of eight fourth down decisions by the Patriots.  At least by a simple model using league averages, Belichick went the wrong way (and surprisingly, the conservative way) seven out of the eight instances.    Goldner isn't bashing Belichick.  In fact, he makes clear that several of these are relatively tight decisions complicated by factors not in the models.  For example, the fact that the Patriots were a sizable favorite changes the analysis some.  A team that has a sizable positive point differential increases the likelihood of an upset by engaging in riskier strategies that spread the distribution out more, even if they average point differential is not impacted.  In addition, blustery days like Sunday make the calls in the "no man's zone" (the fringes of field goal territory) more difficult.  Also, although not mentioned my ANS, the manager's forecast as to the offensive capability of the opponent matters.

The decision that caught my attention during the game was the 4 and 8 for the Patriots from the Ravens 34 with 11 minutes left in the 3rd quarter and the Patriots leading 13-7..  A 51 yard field goals had a low likelihood of success.  The ANS calculator shows a positive expected points in going for it over punting and by a decent margin.  The league average success rate in this length situation isn't great, only 38 percent, but the Patriots are not an average offensive team.  In addition, a punt is likely to gain few yards, so a team who punts gives up a chance at possession with a very small likely gain.  A big, unmodeled influnce, though, is the 7 points for the Ravens.  They had not looked very potent on offense.  A 90 yard drive would seem less likely than league averages which are small.  This would seem to be the overriding influence on Belichick.

An interesting related aspect of this game is just how much the win probabilities turned on a few plays right before and right after this punt.  One can see that "threshold" or highly non-linear impact of a few key plays.   Wes Wekler's drop on third down sticks out.  With that catch and the increased likelihood of a NE touchdown with them going up 20-7, the whole course of the game is changed.  Of course, the plays on first and second down turned out to be about as important along with the first few plays of the Ravens drive.