Game Theory and Super Bowl XLIX
In the court of public opinion, Pete Carroll’s call to have Russell Wilson throw the ball as the final seconds of Super Bowl XLIX ticked away has already been judged the most indefensible call in, perhaps, football history. Public opinion, however, is often incredibly wrong, and using tools from game theory, we can see a plausible defense of Carroll’s approach, one that places process over outcome.
In an article in the New York Times, Justin Wolfers, a fellow at the Peterson Institute for International Studies, frames Carroll’s decision in those fateful seconds as a game with set payoffs, a concept we’ve learned in class. In this game, each side has roughly two options. Carroll can choose pass or run the ball (how he accomplishes either of those is a complicating factor, which we ignore in favor of simplicity), and Bill Belichick, coach of the New England Patriots, can play a defense with a loaded box designed to stop the run, or spread his cornerbacks out in a more traditional, pass-prevent formation.
Obviously, there is no dominant strategy for either team. If Carroll chooses to pass, Belichick will choose a pass-prevent option. Usually, the type of play chosen is more or less evident at the time of the snap; Belichick would see pass-play-only personnel enter the game for the Seahawks, and would react accordingly. If Carroll runs, Belichick would stack the box. In a simple game with no dominant strategy such as this, there exists no pure Nash equilibrium, which means a mixed strategy is preferred. A mixed strategy, of course, introduces randomness into the strategy, which is a foreign concept in football; coaches assume choices are deterministic given a set of defined inputs, and the fact that randomness is preferred to a set strategy probably rubs a few analysts the wrong way. Therein lies the power of game theory.