Football Economics

Published by patrick honner on

This is a nice, short profile of David Romer, an economist and lifelong sports fan who briefly turned his attention to football some years ago.

In 2002, Romer wrote the first serious academic paper asking the question “When should football teams go for it on 4th down?”, applying rigorous analytical from economics and mathematics.

belichickHere’s the simple summary:  a touchdown in football is (usually) worth 7 points, and a field goal is worth 3 points.  A team will often face the situation that, on 4th down, they can either kick a field goal with a relatively high probability of success (say 80-90%), or they can go for it on 4th down (which has something closer to a 40-50% success rate) and continue to try for the touchdown (not a guarantee).

Romer’s conclusion was basically that teams should go for it on 4th down far more often than they do.  This is essentially an expected value argument:  if, by going for it, you get 7 points about 40% of the time, that’s an average of 2.8 points per attempt; if, by kicking the field goal, you get 3 points about 80% of the time, that’s an average of 2.4 points per attempt.  So in the long run, going for it will produce more points.

However, the fact is that teams rarely go for it on 4th down, usually only trying this strategy in desperate times.  So what account for the difference between the theoretical conclusion and the practice of professionals?

patrick honner

Math teacher in Brooklyn, New York


Tao · September 6, 2010 at 5:26 pm

Expected value arguments ignore the effect of short-term variance. However, in football the short-term variance of 4th down conversion attempts can lead to the loss of a game. Football teams are graded by end-of-season win/loss, not total points scored.

An example: assume you are on a game show in which you have already won $250,000. The host now gives you the chance to swap your winnings for “the box” which contains $1,000,000 or nothing with equal probability. Should you switch? An expected value argument would say “yes”, but we need to consider other factors. Namely, how often will we get to make this choice? Most likely, a person will only be on this show once. Thus, the short-term utility of $250,000 in hand might be much more than $500,000 expected or the risk of ruin might outweigh the marginal utility of an additional $750,000 (and in this case, the “short-term” might be the rest of your life).

MrHonner · September 6, 2010 at 9:42 pm

You make a good point regarding expected value and variance, and presumably it is an issue that Romer–a world-renowned economist and knowledgeable sports fan–addresses in his paper.

While football teams (and coaches) are ultimately graded by win-loss record, football games are indeed determined by total points scored.

Furthermore, it would be hard to make the case that a particular game was lost on such a play.

Jeffrey Luk · October 2, 2010 at 9:18 pm

Despite the accurate calculations that conclude that going for a 4th down will better the score, when a team fails to past their fourth down marker they turnover the ball. When you turnover the ball, the opponent gets the ball at where ever you turned it over. While when you go for a field goal or punt, you’ll keep the opponent from having good field position where they’ll try to get a field goal or touchdown of their own. I hope this answers why many teams refrain from going for fourth downs even if it betters their scores because defense is the best offense.

MrHonner · October 3, 2010 at 7:55 am

Jeffrey, field position is a very important (and underrated, I think) strategic element of the game. Indeed, good defensive teams might consider field position as important as trying to score, sometimes. But keep in mind, that turning the ball over doesn’t guarantee that your opponent will score.

Turning the ball over on your own 20 yard line is almost certain to guarantee points for your opponent, but consider the case when you are on your opponent’s 40, 30, 20 yard line–a punt in that situation won’t make much difference. If you go for it and don’t get it, your opponent still has to go 60, 70, 80 yards to score; if you do make it, then you’ve still got a chance. And if the likelihood that you make it is, say, 50% (on a 4th and 2, for example), that’s worth thinking about, I’d say.

Jeffrey Luk · October 6, 2010 at 10:27 pm

So why do teams scarcely go for 4th downs? I mean we’re definitely not the first ones to calculate the statistics. Many times it has to do with the physiological part of the game. Despite the slight advantage of going for 4th downs, many teams doubt they’ll get it because they believe you need only 3 downs to get a 1st down if you’re in a rhythm. So when you’re not you have less confidence and begin to doubt yourself. I also believe it’s a matter of professionalism. Going for 4th downs seem to reckless and when you don’t reach the 1st down, you’re liable for that. People generally remember bad outcomes versus good results. Why do you think so?

MrHonner · October 6, 2010 at 11:41 pm

Romer, the author of the paper in question, wonders the same thing–if the analysis suggests that teams should try it more often, why don’t they? I think you make some relevant points, especially this one: no coach is going to lose his job because he did the conservative thing (punt), but some coaches might lose their job if they do what’s perceived as the risky thing and they fail.

This reminds me of a phenomenon I’ve read about (and experienced) in the business world–people quickly learn that they have more incentive to do things the way they’ve always been done than to try something new and innovative.

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