Incremental Analysis, with TwoYards to Go

The academic paper that Daviu Romer began writmg two years ago did not look like something that could determine the outcome of a Super Bowl. Sure, it was an analysis of whether professional football teams punt more often than is rational, but it seemed intended mainly for the amusement of sports fans who happen to be professors.

Professor Romer, an economist at the University of Californiu at Berkeley, used the phrases “Bellman equation” and “dynamic-programming analysis”-in the paper’s title, no less. His footnotes cited work published in Econometrica, Cognitive Science, and other publications that are not exactly must-reads in N.EL. locker rooms. But when his conclusion-teams punt too much-began getting attention last summer, a reporter asked Bill Belichick, the coach of the New England Patriots, about the paper. “I read it,” he said, according to Tire Boston Herald. “1 don’t know much of the math involved, but 1 think I understand the conclusions and he has some valid points.”

Upon hearing that, Professor Romer’s jaw dropped, he said. His paper was available only on his Berkeley Internet site, emlab.berkeley.edu/users/dromer, and the site of a group called the National Bureau of Economic Research. But the most interesting development was yet to come. Two weeks ago, facing a fourth down in the Patriots’ own territory on the very first drive of the game-a sure punting situation in the N.F.L. flelichick decided to go for a first down and made it. The Patriots soon scored a touchdown and were on their way to today’s Super Bowl, against the Carolina Panthers.

Football analysts immediately called the decision an instance of a coach’s instinct triumphing over cold analysis. In fact, Professor Romer said last week, Belichick seemed to be “throwing gut instinct out the window and going on analysis.” The information is right there in Figure 5 of the economist’s paper: on fourth and 1 on your own 44-yard line, the potential benefit of keeping the drive going outweighs the cost of giving the opponents good field position.

The coach may not have been thinking about Professor Romer’s paper at that moment, but he has clearly adopted the methods of a social scientist in a way that few other sports coaches have. Belichick, who majored in economics at Wesleyan University, approaches his job much the way a financial analyst pores over a balance sheet. He seems to view every decision as a chance to perform better cost benefit analysis than his peers do. Richard Miller, a Wesleyan • economist with whom the coach remains in touch, calls the approach “incremental analysis.” In plain English, it involves looking for subtle differences in one small area that can affect an entire system, whether that system is a company, a stock market, or a football game.