game theory in football

http://www.slate.com/id/2092863

This article talks about Virgil Carter, who actually attended Northwestern's business school, attempted to model football plays using game theory and matrix forms. Unfortunately this was extremely difficult due to the number of plays in football and slow processing times of computers. By averaging these results, he was able to learn the "expected value" of having balls at certain parts of the field. He concluded that the expected value is essentially linear, starting at -2 points at your own goal line, moving to +2 at midfield, and rising to +6 at the opponents' end zone

As a football nerd and wannabe-sabermetrician this is incredibly interesting to me. Then again, there is a lot of room for statistical improvement in football. It is widely known among sabermetricians that coaches go for fourth-down conversions much less than is optimal, simply because they are highly risk-averse. They can't often be "blamed" for punting on fourth-and-four, whereas they will be blamed by sportswriters and fans if they try a pass on fourth-and-four that fails. Many coaches, though, cite "momentum" as the reason for their risk aversion - and obviously, this is something that cannot really be quantified through sabermetrics.

Modeling football plays with payoff matrices and the like would be extremely difficult to generalize. But I think it has the potential to be very beneficial for a team-to-team basis. In a team's playbook, some plays will work great against one team, but horrendous against another team. This could be due to matchup problems (WR vs. CB or OL vs. DL) or the study of film to realize what a team does well and what it doesn't do well. If a team could model its plays based on how well the opposing team responds to those types of plays, then the overall playcalling would be greatly increased in terms of effectiveness.

But like I said earlier, game film can ruin any payoff matrix. If a team does certain plays that do well and then try them on another team, chances are it will not succeed, because the opposing team will have seen that play and how they operate it and will devise a way to stop it. So perhaps the better way to look at it would be devising payoff matrices for situations, as opposed to single plays in the playbook. What is the payoff for going for 4th and 3 with a draw play up the middle? What is the payoff for going 4th and goal with a play action pass? Situational matrices may be more practical, then determining the payoffs for doing a 20 yard out at mid field.

bill belichick (new england patriots coach) actually read some of this guy's stuff or something like it.

http://money.cnn.com/magazines/fortune/fortune_archive/2005/10/31/8359159/index.htm

seemed to work pretty well.