# Letter: Go for it on fourth down? Not so fast

June 17, 2014

Berkeley's David Romer published research in 2006 encouraging more NFL teams to "go for it" on fourth down ("The biggest blunders in sports," Winter 2014).

But if the "market" (football coaching) has not taken up Professor Romer's terrific idea, shouldn't Chicago Booth's "market" economists hypothesize, and test, more plausible explanations that Capital Ideas' theories about coaches' self-preservation and their disregard for large rewards?

Professor Romer relies too much on "expected values" (objective central tendencies). For him, seven of seven field-goal attempts from the 2-yard line "equals" three of seven touchdown attempts from there, as both equal 21 points.

So, voilá! They are a wash, and the decision rests on subsequent field positions, after the respective attempts.

But in most games, a team is not going to get a whopping seven shots at fourth and goal from the 2-yard line. The team might get only one or two shots. This is a wretchedly low sample for supporting a possibly game-deciding touchdown attempt with a probably of only three out of seven.

In going for the touchdown, the coach is throwing a seven-sided die with three sevens on it, and four zeroes. In just two throws, two zeros will be considerably likely than two sevens.

Technically, the probability of getting two zeros is 33%, two sevens is 18%, and one each is 49%.

In a close game, this random fluctuation of 33% can cost the team a game. And in the NFL's short, 16-game regular season, there might not be enough subsequent statistical time to make up the lost ground.

I would respectfully suggest that Booth researchers entertain, and test, the hypothesis that NFL coaches are not misunderstanding their "expected values." They are understanding their "loss functions" (individualized responses to variation).

Brian A. Kennedy, '85 (XP-54)
Glen Ellyn, Illinois
Retired Treasurer and Finance Division Senior Vice President, Health Care Service Corporation

Romer responds:

Mr. Kennedy argues that the finding of what appear to be large, systematic departures from maximization in a high-stakes business environment is sufficiently surprising that one should look hard for alternative explanations. I agree. In my paper, I considered a range of alternatives, but found essentially no support for any of them. One of the possibilities I examined was the one that Mr. Kennedy proposes—that the randomness of outcomes causes seemingly "conservative" decisions to be optimal from the point of view of maximizing the chances of winning. I found, however, that because scores in football are so high and variable, the assumption that a team should focus on expected points in the early going if it aims to win appears to be almost completely accurate, and thus that Mr. Kennedy's hypothesis cannot explain coaches' decisions. The details of that analysis are presented in Section IV.A of my paper, which is posted on my website

Mr. Kennedy seems to suggest that there must be some explanation for what we observe other than failures to maximize, because we know as a matter of logic that market forces cause firms to maximize. If that is his view, I disagree strongly. The proposition that market forces are strong enough to overcome human beings' lack of unlimited computational ability and their well-documented behavioral biases is a scientific hypothesis, and thus should be confronted with evidence. I do not think my study is definitive, but I think it is a strike against the hypothesis.

David Romer, Herman Royer Professor of Political Economy
University of California, Berkeley

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