## Monday morning quarterbacks and the limits of game theory

Our colleague Justin Wolfers has written an excellent essay defending the indefensible–Coach Carroll’s controversial play call on 2nd down with 26 seconds remaining in the 4th quarter of Super Bowl XLIX, the disastrous (in hindsight) play call that led to his team’s gut-wrenching defeat in the final seconds of the championship game. In particular, Professor Wolfers takes a well-known solution concept from game theory–the idea of a “mixed strategy“–and applies it to the game of football. Briefly, the idea is that a team on offense should randomly choose between rushing the football and passing the football in order to maximize its probability of scoring …

Although Wolfers’s analysis and counter-intuitive conclusion are theoretically sound, we must also take into the account the probability of a fumble versus the probability of an interception. Which of these two potential perils is more likely to occur? In any case, we should also expect the coach on the defending team to likewise adopt a mixed defensive strategy in order to increase his team’s probability of preventing a score. Given this possibility of both teams playing random strategies, we are back to where we started: do you give the ball to your true-and-tested running back, the best in the league, or do you take your chances with game theory? So, while we are big fans of game theory, we would’ve run the ball, especially when the stakes were so high. (Image below: Wikimedia Commons.)

It’s game day, so solve for equilibrium!

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