For those of you who aren't football fans, there was a call made by the Patriot's head coach to go for it on fourth down and 2 yards to go, deep in their own territory. If they made it, they would have an opportunity to run out the clock and win the game. If they didn't make it, the Colts would have fantastic field position and a golden opportunity to get back in the game.
The result: the Pats did not get the first down, the Colts subsequently scored and went on to a most improbable win.
Well, as you probably guessed, the equilibrium lies in mixed strategies, but the real question is: how often should you go for it on fourth down and 2 deep in your own territory? After some searching, I found a study published that statistically models the mixed strategy equilibria in various scenarios, and it has quite surprising implications.
In general, the results of this model show that coaches are not aggressive enough ... by a long shot. In fact, in this particular situation, the study finds that "Even on its own 10 yard line -- 90 yards from a score -- a team within 3 yards of a 1st down is better off on average going for it". In actuality, the patriots were out past the 20 and only had 2 yards to go.
Belichek is vindicated!!! All those doubters of his strategic master mind take note!!!!!
Disclaimer: I grew up in Boston ... there's some egocentric bias going on here ... Go PATS!
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