It's fourth and goal, and your team is down by three points with seconds left in the game. Do you kick a field goal and try to eke out the win in overtime, or do you go for the touchdown to seal the deal? That was Baltimore Ravens coach Brian Billick's dilemma last December in a game against the 0-13 Miami Dolphins.

NFL teams are notoriously hesitant to go for fourth-down attempts, even when the stakes are much lower. Last year, teams attempted an average of 16.7 fourth-down plays during the entire 16-game regular season. The Ravens tied their game with a field goal but lost in overtime.

Of course, Billick's team might have failed on its fourth-down attempt. But the data suggest that teams would be better off going for far more fourth downs than they do. Do coaches know something the statistics aren't telling, or does the discrepancy show that coaches have more on their minds than winning the game?

The question of going for it on fourth down was the subject of a 2002 study by economist David Romer of the University of California, Berkeley. He analyzed 732 regular-season NFL games from 1998 to 2000, focusing on plays from the first quarter.

Consider a team facing fourth and goal. It will almost certainly score if it kicks a field goal. But, on average, the team is better off going for it if the odds of making a touchdown on the play are better than three in seven. (The extra point on a touchdown is essentially automatic, with NFL kickers converting more than 99 percent of their collective attempts in 2007.) Even if the team fails to score the touchdown, it is not necessarily in bad shape, because the other team would gain control of the ball close to its own end zone, which could translate to a safety for the first team or good field position when their offense takes over again.

Romer assigned a value to fourth-down attempts at all points on the field based on the odds of making the play compared with the other team's chances of scoring on its possession. (Because fourth downs were rare, he estimated their value from statistics for third downs.)

He found that for an average team near the 50-yard line, a fourth-down attempt would net more points than kicking as long as the distance to a first down was less than four yards. At the opponent's 33-yard line, that distance was 9.8 yards; at the 21-yard line, four yards; and within the five-yard line, the average team should always go for it, according to Romer's reckoning.

The comparison with teams' actual behavior was striking: Out of 1,068 fourth downs where the stats favored going for it, teams made only 109 attempts. "The bottom line is very clear," Romer says. "If the goal is to win football games, teams should be a lot more aggressive in going for fourth downs."

Naturally, NFL coaches tend to see the fourth-down call as more art than science. They have questioned how well an economics model captures real-world matchups, in which teams have particular strengths and weaknesses and are playing before thousands of rowdy fans.

Moreover, the benefits of going for it more frequently on fourth down might not be as dramatic as Romer's analysis suggests. "It would dramatically transform the way the other team played defense against you," says Aaron Schatz, president and editor in chief of the Web site Football Outsiders, which he says would alter the success rate of fourth-down attempts.*

That may be partly why NFL teams have not flocked to the strategy. Between 2002 and 2006, the frequency of fourth-down attempts has held relatively steady at about 14 percent, jumping to 17 percent last year, according to Schatz's colleague Jim Armstrong.

Coaches may also be wary of sticking their necks out by going for plays perceived as risky. "Everybody in the football analysis world believes that coaches do not go for it often enough on fourth down," Schatz says, "and yet, they don't go for it often enough on fourth down."

Billick, when asked at a press conference following the Dolphins game why he didn't go for the win, responded: "Had we done that after what we had done to get down there and [failed to score], I can imagine what the critique would have been today about the play call." He was fired later that month.

To Romer, the sheer infrequency of fourth-down tries suggests something deeper going on. "Maybe they would rather sacrifice some probability of winning in order to not have the probability of winning rest as much on individual plays," he says. Like the rest of us, he says, "they like having the illusion of control."

* Correction (9/3/08): This article originally referred to Football Outsiders as a Fox Sports blog; the Web site is currently associated with ESPN.