Game Theory of Super Bowl XLIX
Believe it or not the ending to Super Bowl XLIX involving the New England Patriots and Seattle Seahawks contained more game theory than one could expect. Basic game theory analyzes the possible outcomes based on choices made by the two players. Each choice made by the two players affects the outcome of the combination of both choices. A common example of this is the prisoner’s dilemma. In this game there are two men accused of a crime and they are given the options of confessing the other person did it or remaining silent. If one confesses and the other remains silent then the man that chose to be silent will go to jail for 3 years and the other will get off free. If neither accuses the other then both parties receive 1 year and if both accuse the other then both receive 2 years. Here the most mutually beneficial outcome is for both people to remain silent. However, in this game without multiple runs of the decisions, the prisoners will tend to do what is best for themselves because there will be no consequences based on their decision in another trial.
In the case of the Super Bowl the two players are the coaches of the Patriots and the coaches of the Seahawks. The coaches of the Seahawks can choose to pass or throw the ball over the final three plays of the season in an attempt to score the game winning touchdown. The Patriot’s coaches must make the decision of defending the pass more, the run more or playing a neutral defense. Since this was the final series of plays in the season it is considered to not have multiple trials.
The Seahawks have one of the best running backs in the NFL so a run play has a higher probability of resulting in a touchdown than a pass, however, the Patriots know this as well so they will most likely try to defend the run more. A pass play is more risky and has a smaller probability of resulting in a touchdown than a run, however, since the Seahawks have three plays it is important to consider the combination of plays they can run. If the Seahawks run the ball on the first play, the Patriots will most likely have a strong run defence prepared and continue to play this defense over the next to plays because the Seahawks ran as predicted. But if the Seahawks throw the first play, even if it doesn’t result in a touchdown, it creates doubt in the coaching staff of the Patriots and they will switch to a more neutral defence. This neutral defense will allow for a much higher probability of the Seahawks scoring on a run (the safer option). By this logic it seems obvious that the Seahawks should throw on the first play to allow for a higher probability of scoring on the second as the net probability will increase with a pass on the first play.
Coach Pete Carroll received a lot of grief for his decision to throw the ball on the first play which ultimately resulted in a Patriot interception and Seahawks losing the game. But if we analyze this series of three plays from a game theory perspective we see that Coach Carroll made the correct decision after all based on probabilities. It is important to take this lesson into our everyday lives, the most obvious choice may not be the best choice probability wise so it is important to think thoroughly before making critical choices.
http://www.economist.com/blogs/gametheory/2015/02/applying-game-theory