Football puzzle: punt or go for it?

Click to see larger chart.
I just spent a Sunday mostly watching football. It wasn't as much fun as it might have been. My poor 49ers show signs of life, but haven't reached respectability yet -- and the Raiders are flat out pathetic. Both teams lost ignominiously.

But the day's dissipation reminded me of a set of statistical calculations that I read about last spring in Kevin Drum's blog. With the support of the chart above, he writes:

I'm happy to report (via Tyler Cowen) that David Romer of UC Berkeley has written an exhaustive analysis filled with sigma signs and subscripts that provides a quantitative answer to this burning question: exactly when should you go for it and when should you kick?

The solid line in the chart ... provides the answer. At the 50-yard line, you should go for it if you have less than five yards to go. At the 40-yard line you should go for it if you have less than seven yards to go. At the 35-yard line you should go for it no matter what. Beyond the 33-yard line, as you get into field goal range, the value of kicking rises and the "critical value" necessary to go for it declines steeply (though it stays above four yards all the way to the goal line). The dashed line summarizes actual coaching decisions over the course of the study and shows that, on average, coaches go for it only if they're past midfield and have only about two yards to go. That's much too conservative....

But the bottom line is simple: always go for it if you have less than three or four yards to go. Past midfield, you should go for it even in higher yardage situations until you get into field goal range. But even then, you should go for it if you have less then three or four yards to go.

On the evidence that I saw today, Art Shell might have been aware of this advice -- the Raiders tried to convert on several 4th down situations well outside the normal conservative practice. Mike Nolan took a more conventional approach with the 49ers, punting the ball away.

I'm sure the mathematical probabilities laid out in these studies are true -- but it is pretty easy to imagine how coaches actually make with these decisions and they seem to evaluate other variables. Today, it looked like Shell decided repeatedly to go for it because he considered his team already screwed -- just maybe if they succeeded at an unexpected 4th down conversion, they'd wake up and play like they meant it. Meanwhile, Nolan is trying to normalize the 49ers -- he doesn't want them shaken up; he is teaching consistency of play.

In any case, the statistical calculation misses what certainly is one of a coach's most important considerations in deciding to go for it: if the attempt goes wrong, he's the one who is going to face raving fans and possibly an angry owner. Usually it is the player who drops the ball who gets the vilification, but in this situation the responsibility for an unconventional risk falls directly on the coach. That's not something most coaches can afford to assume. Probably the ones most able to afford the risk are those whose teams least often force them to make a decision whether to punt or go for it.