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.