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Going For It: Applying The Bellman Equation To Football

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Berkeley economist David Romer wrote an interesting paper in 2005 entitled Do Firms Maximize? Evidence From Professional Football in which he posits that football coaches are far too reliant on kicking on 4th down. Romer believes that teams should be going for it far more often in order to maximize their team's chances of winning. Statistical modeling of his theories has shown an increase of just over one victory per NFL season. Some coaches appear to be early adopters of some of these philosophies, but none have been remotely as aggressive as they should be to optimize their statistical chances of victory. How do we know?

The Bellman equation says so:

Ei Di(gt) Vi = Pgt + Bgt Ei Di(gt+1) Vi - egt

Romer's general guidelines can be summarized as follows:

A team facing fourth-and-goal within five yards of the end zone is better off trying for a touchdown.

At midfield, go for any fourth down within five yards of a first down.

Even on its own 10-yard-line -- 90 yards from the end zone -- a team within three yards of a first down is marginally better off, on average, going for it.

Revolutionary. It would certainly change the game of football and it might offer a significant advantage to early adopters. Adapting team and fan psychology to your new strategy would be crucial.

If you scroll down to Trend #3, you'll see an interesting article on Pulaski Academy in Arkansas where head coach Kevin Kelley decided to stop punting in 2005 after reading Romer's paper. To good effect. Coach Kelley hates punting

How would this fare at the college level? Aside from the psychological aspects to be considered for both your team and the opponent, I'd venture that the net wins to be gained would be even higher than professional football since college offenses generally exhibit much higher levels of production vis a vis the average college defense. I think this is groundbreaking stuff and though I don't endorse Romer's guidelines totally, I do think he's far closer to empirical reality than most modern coaching folkways and mores. This is a first step in applying Moneyball type statistical modeling to football; I'm excited by the possibilities.

Your thoughts?