Nash equilibrium American football decision making
American football is a very strategy riddled game. While a players performance is important, the decision making a player makes is highly scrutinized as well as the coach’s. In a personal project of mine I recently began looking into the different meta game strategies that have been developed by coach’s. What I found was nash equilbrium. Consider the following situation: its third down with 2 yards left. Your best running back averages 5 yards per play and so far he has not run anything less than 3 yards against this team all night. Any fan of the sport would claim that it would be ridiculous to not make a run on this play. But for some reason the coach decides that the team will run a pass play and it to the dismay of the fans it fails into a turnover. The coach gets labeled as a failure for calling such a ridiculous play but what the fans don’t realize is the underlying nature of the game of football.
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Consider the above analysis of an offense running or passing. In our case the numbers work out a little differently but the underlying decision making is still there. The coach’s know that if they always run the same play in a specific position then the defense will be able to run a strategy that will most likely be able to mitigate the offenses advancements. Thus, they must run in mixed equilbirium in order to ensure that their actions are not predictable. Along with that they are also able to force the other team to run in a mixed equilibrium as well, thus creating a better likelihood of success of their plays.
While it may seem that at times there is an ‘obvious decision’ to be made by a coach on what he should run on a play, it may be smarter to run a different play as it maintains the game at a mixed equilbrium which ends up being a state of stability that both teams would rather not leave.