Game theory in the Super Bowl
Looking through articles about game theory and its uses, I came across this article about game theory in american football. Football, unlike baseball, does not have a huge amount of quantitative data available that is easy to analyse, thus game theory articles are rare. However, this article concerns one of the most famous super bowl plays in recent memory, the Malcolm Butler interception on the goal line two years ago to seal the super bowl for the Patriots.
The situation at that time was that the Seahawks were down by 4 to the Patriots in the 4th quarter with about 1:40 left to play and on the goal line on second down. We all know how it played out, with Pete Caroll calling a pass play that eventually got intercepted. There were many critics at the time of the play call, however this article provides some evidence that the call was justified. On the goal line, there are two plays available, either a run or a pass. In order for an offence to be effective, it must mix up its play calling in order not to be predictable. The equilibrium point is a mixed strategy of the two, the team’s Nash equilibrium.
Interestingly, during the 2014 season. the league as a whole ran about 66% of the time, the mathematical equilibrium with run plays scoring about 57% of the time and pass plays scoring about 57%. For the Seahawks, their optimal strategy would be somewhere higher, about 70%-80% of plays should be runs. Thus we would expect around 1 pass play per 3 play sequence on the gaol line. On the patriots side, they were expecting a run play and thus had stacked 8 players on the line with 4 dropping back. Thus from a game theoretic point of view, Pete Caroll’s play calling strategy was almost optimal and thus he was just unlucky.
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