The Two-Person Game that Lost Super Bowl XLIX
Super Bowl XLIX was the most watched program in American television history, with over 120 million viewers tuning in for the game’s dramatic and controversial ending1. The Seahawks were down 4 points with 26 seconds left. However, it was only second down, and the Seahawks had the ball on the one-yard line with one of the best running backs, Marshawn Lynch, in the game. In what is considered by many football fans as one of the biggest mistakes in Super Bowl history2, Pete Carroll, the head coach for the Seahawks opted for a passing play, instead of letting Lynch run the ball, which was then intercepted by Patriot’s cornerback, Malcolm Butler, and lost the game for the Seahawks. In an article for Upshot, an online section of the New York Times, economist Justin Wolfers argues that if we approach that final play as a two-person game and apply principles of game theory, Pete Carroll’s decision to call a passing play was reasonable.
In fact, our textbook, Networks, Crowds, and Markets: Reasoning About a Highly Connected World, represents this decision, whether to run or pass in a football game, as a two-person game that can be played with a mixed strategy. In Networks, Crowds, and Markets, the game gives the offense the options to pass or run and the defense the options to defend the run or defend the pass. The corresponding payoff matrix for the game benefits the offense when they choose to pass or run and the defense chooses to defend the opposite option. On the other hand, the matrix benefits the defense when they choose to defend the option the offense chose to play. The model then assigns a probability to the likelihood with which each team will play their each of their respective options. The two team’s mixed strategies then consists of all of the possible probabilities, ranged from 0 to 1, they can assign to play either option, and the success of each strategy is determined by calculating its expected value.
Wolfers claims that a solution to Carroll’s dilemma in the 4th quarter of the Super Bowl can be obtained by modeling it as a more complex version of this model proposed by the textbook. To do this, Wolfers first argues that contrary to popular belief, the Seahawks would not have succeeded if Carroll had played the pure strategy of always running the ball with Lynch. Wolfers makes the assumption that the Patriot’s best response to the Seahakw’s pure strategy of always running Lynch would be formidable enough to prevent Lynch from scoring for all three downs of the last play. The underlying reasoning for this assumption is that even a running back of Lynch’s caliber can not get passed a defense designed to specifically stop him. Furthermore, a precondition to Lynch’s success in the regular season was that he was running against defenses that played with a mixed strategy and thus only defended against his runs a fraction of the time. Since the Seahawks could not run Lynch every time, Wolfers implies that Carroll had to play with a mixed strategy which would require him to use passing plays some proportion of the time. While this model is an oversimplification of the very complex decision making process that goes into the last play of the Super Bowl, it does at least provide a justification for Carroll calling a pass play. So although Wolfer cannot say that Carroll’s decision to pass was correct, he can say that if the play were to be “run in a dozen parallel universes, with each coach continuing to play the same mixed strategy”, the outcome of the game could have been drastically different.
Other Sources:
1. Super Bowl XLIX. https://en.wikipedia.org/wiki/Super_Bowl_XLIX
2. Schein, Adam. “Super Bowl XLIX: Patriots-Seahawks proved to be classic, tragic”. Feb. 2, 2015. http://www.nfl.com/news/story/0ap3000000467747/article/super-bowl-xlix-patriotsseahawks-proved-to-be-classic-tragic