from the [not]-everything-works-in-[game]-theory dept.
Justin Wolfers writes in the New York Times that Seahawks coach Pete Carroll's reasoning behind the play that led to the Patriots' interception that clinched Super Bowl XLIX is defensible in terms of game theory. The key insight of game theory for an NFL coach is that when you think about what choice you should make, you need to also consider the response from the opposing coach, understanding that he is also thinking strategically. There is no play that cannot be stopped if the defence knows it is coming. If the Seahawks were to sign a blood oath promising to have Mr Lynch run the ball, the Patriots could simply throw all 11 defenders at him and stop him in his tracks.
“This line of thinking suggests that you should not necessarily call a run play, even if you’re blessed with a great running back. Likewise, it’s not clear that you should definitely pass,” writes Wolfers. “Rather, your choice should be somewhat random — a choice that game theorists call a ‘mixed strategy.’” The logic is that if you always choose to run in this situation, then you make the opposing coach’s job too easy, as he will set a defensive formation aimed at stopping your running back. Instead, you need to keep your opponents guessing, and the only way to do this is to be unpredictable — essentially playing the football equivalent of Rock-Paper-Scissors. According to Wolfers this leads to the intriguing possibility that if that fateful final play were to be run in a dozen parallel universes, with each coach continuing to play the same mixed strategy, the actual plays called would differ, as would their outcomes. “And so the same teams pursuing the same strategies under the same circumstances might have yielded a different Super Bowl champion.” The only reason Carroll is being raked over the coals is because the play happened to end in an exceedingly improbable interception. Not one of the previous 106 passing plays that NFL teams launched from the one-yard line in 2014 was picked off.