It's fourth-and-goal in the first quarter of an important National Football League game. The fans rally for the coach to go for it, but they know he probably won't. As usual, the kicker trots out.
Obviously the conservative coach knows something the fans don't. He's analyzed the numbers and is making a sound judgment.
Actually, the decision is consistently botched, according to a new study by David Romer of the University of California, Berkeley.
In a series of case studies, Romer found coaches to be overly conservative, opting for field goals in situations where, on average, choosing to go for a first down or a touchdown would up the odds of winning by 3 percent.
In particular, Romer found that when faced with fourth-and-goal on the 2-yard line early in the game, going for a touchdown is the much wiser choice. While the field goal is a near certainty, getting a touchdown in that situation has about a 43 percent chance of success, he calculates. And failing to score a TD at least leaves the opponent deep in its own territory.
But in nine case studies of this situation, the teams booted against the odds.
After doing a whole bunch of complex math, and considering things like momentum and field position in more than 700 real NFL game situations, Romer concludes that whenever the chance of a touchdown is statistically 18 percent, that's the better choice.
The study used data only from the first quarter of games, when the contests were still close and the outcome uncertain.
Just like life
Romer details his findings in the April 2006 issue of the Journal of Political Economy. You might wonder why NFL coaching decisions are the topic of an article in a journal of this sort.
Because in a professional football game, the desire to win is very strong, the decisions can be based on statistics, and the market for coaching services is very competitive. Coaches make an average of about $3 million a year, Romer says, and turnover is about 20 percent each season. Because fourth-down decisions are common, data on the outcomes isn't hard to come by. It is, apparently, ignored.
Romer thinks his study provides valuable insight into what he sees as a strong tendency toward conservative decision making in general.
"Much of the previous evidence of systematically conservative behavior involves highly stylized laboratory settings with small stakes and inexperienced decision-makers devoting relatively little effort to their choices. Thus previous work provides little evidence about the strength of force pushing decision-makers toward conservatism," he writes. "The results of this paper suggest that the forces may be shockingly strong."