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David Romer’s paper

Posted by Doug on May 10, 2006

I have an intuitive "proof" that coaches are generally too conservative on fourth downs. It goes like this. The next time you're watching a football game, pay attention for a situation where your team in on defense and it's fourth-and-1-or-2 somewhere around midfield. While the replay is on your screen, the announcers will spend a second or two discussing the possibility that they might go for it. You're not sure what's going to happen. When the TV cuts back to live action, you see the punter trotting onto the field. If you're like me, this is a huge relief. I am always nervous when I think they might go for it and relieved when they don't. That's my gut telling me that going for it is the right move there. Does your gut tell you the same thing?

I'm going to devote the next few (or several, depending on how it goes) posts to the topic of fourth down strategy. Readers of this blog are probably familiar with various studies indicating that coaches ought to go for it more often. The first such study I encountered was in a book called The Hidden Game of Football which I'm sure many of you have read.

A few years ago, this paper by Berkeley economist David Romer got a lot of publicity. It used to be titled It's Fourth Down and What Does the Bellman Equation Say? A Dynamic-Programming Analysis of Football Strategy, but he has changed the name to Do Firms Maximize? Evidence from Professional Football. It was just published last month in The Journal of Political Economy. The abstract says:

Examination of teams' actual decisions shows systematic, clear-cut, and overwhelmingly statistically significant departures from the decisions that would maximize teams' chances of winning.

The decisions he's talking about are whether to go for it or kick on fourth downs. As you can guess from the abstract, Romer concludes that coaches kick too much --- both field goals and punts --- and go for it too little on fourth down. The point of his paper, at least from the standpoint of a reader of the Journal of Political Economy, is to test whether firms truly do exhibit profit-maximizing behavior as is routinely assumed in economic theory. Romer starts by equating profits with wins:

the problem of maximizing profits [in football] plausibly reduces to the much simpler problem of maximizing the probability of winning

He then demonstrates rather convincingly that teams' fourth down decisions are not optimal from the standpoint of maximizing their probability of winning, and spends the last few pages of the paper wondering why. He points to several studies which indicate that people will under certain circumstances prefer options with less risk even when the expected payout is greater for the riskier option (and I mean the expected payout after taking into account the risk). In other words, people often value conservatism for conservatism's sake. Romer says:

previous work provides little evidence about the strength of the forces pushing decision-makers toward conservatism. The results of this paper suggest that the forces may be shockingly strong.

In my opinion, it's painfully obvious why coaches make these decisions. This is not an indictment of the paper --- I'm sure it's written in a style that's appropriate for the journal in which it appears --- but I didn't have the patience to fight through all the jargon in the last section of the paper. So Romer may have alluded to this, but I wasn't sure. The reason NFL coaches behave so conservatively in this situation is because they are behaving in such a way as to maximize not their probability of winning but their quality of life. For an NFL coach, quality of life certainly is largely determined by winning percentage and is also highly dependent on job security which is in turn largely determined by winning percentage. But the payoff of straying from "the book" is nowhere near worth the cost. Romer states:

This evidence suggests that a rough estimate of the potential gains from going for it more often on fouth downs is . . . an increase of about 2.1 percentage points in the probability of winning. Since an NFL season is 16 games long, this corresponds to slightly more than one additional win every three seasons.

Imagine you're an NFL coach. You have the option of winning an expected 6 games this year or winning an expected 6.33 games and fielding approximately 1,846,344 questions per day about your decision to go for it on fourth-and-one from your own 22 on your first drive. Those .33 wins aren't going to save your job. But unless your owner understands what you're doing and is also willing to ignore the legions of fans and writers who don't, your nonstandard decisions could cost you your job. Romer is obviously not claiming that you'll always make it if you go for it more often on fourth down; he's saying that, in the long run, the benefits you'll get when you do make it exceed the costs you incur when you don't. A coach employing the strategies suggested in this paper would frequently make the right choice and have it not work out. Ask Barry Switzer how fun that is.

Of course this brings up the question of how the non-optimal default fourth down strategies got into "the book" in the first place. I suspect that, given the game conditions in the early days of football, punting on fourth down was almost always the optimal decision. The conditions of the game changed slowly enough that no one noticed when some critical threshhold was reached that should have caused the default decisions to change. But I'm really not sure about that.

I'll spend the next day (or more) describing the mathematical details of Romer's method and its implications. [EDIT: here is the link to the next post in the sequence.]