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Game Theory in the NFL

With twenty six seconds left in Super Bowl XLIX, the Seattle Seahawks had three downs to advance the ball one yard and win the game. Instead, they threw an interception, in one of the most unforgettable moments in sports history. Head coach Pete Carroll was criticized relentlessly for the play call – despite having one of the best running backs in the league (Marshawn Lynch), he ran a passing play. After the initial media firestorm, many voices defended Carroll, citing game theory as justification for his call.

Justin Wolfers wrote an article for the New York Times titled “Game Theory Says Pete Carroll’s Call at Goal Line Is Defensible.” He claims that Carroll wisely used a mixed strategy, randomly choosing when to run and when to pass, with a particular probability assigned to each. The logic behind this is that the Patriots were expecting a running play, so they set their defense up to guard as heavily against the run as possible, thus decreasing the payoff for a run and increasing the payoff for a pass. This is generally how teams operate in close yardage situations in the NFL – running the ball 57% of the time and passing it 43% of the time seems to be the Nash Equilibrium that analysts have discovered yields the best outcomes for most teams. This applies even teams with imbalanced passing and rushing attacks because the opposing defense adjusts accordingly to their strengths and weaknesses.

While all of this is technically true, football is not a matching pennies game. The options at the disposal of an offense are far more complex than simply running and passing, and just because the Patriots were defending the run doesn’t necessarily mean it was impossible for the Seahawks to run for a touchdown. Data analysts can crunch numbers over the long run, but there were only three plays left in the game – far too small of a sample size for a generalized strategy. Game theory was at work, but as an unsolvable problem. Ultimately, there is no way of knowing what the best strategy would have been.




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September 2015