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Incremental Analysis, With Two Yards to Go


Published: February 1, 2004

THE academic paper that David Romer began writing 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 California 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.F.L. 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 The Boston Herald. "I don't know much of the math involved, but I 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, /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. - Belichick 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 not 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.

Consider the Patriots' behavior when they need just a couple of yards for a first down or a touchdown. No other team ran the ball more often in those situations this season, according to Football Outsiders, an Internet site that analyzes statistics, even though the Patriots are considered to have one of the weaker running games in the league.

The numbers still favor the strategy because running is far more effective in gaining a few yards than passing is. Yet many other teams including the Giants and Jets, which together won four fewer games than New England this year, tried many ineffective pass plays, in an effort to surprise the defense. It's a little like surprising your opponent in chess by letting him capture your queen.

Belichick also seems to understand an idea that economists call "hyperbolic discounting," which holds that people tend to place too much value on the here and now. Taking advantage of this, the team made two trades during last year's draft that essentially swapped a lower pick in 2003 for a higher one in 2004, noted Aaron Schatz, the editor of Football Outsiders. The Patriots will now enter this spring's draft holding many more high picks than a Super Bowl team typically does.

And Professor Romer's paper is not the only ivory-tower research that has made its way into the coach's head. After Harold Sackrowitz, a Rutgers statistician, was quoted in The New York Times and elsewhere saying that teams try for a two-point conversion too often after scoring a touchdown, he received a call from Ernie Adams, the Patriots' football research director and a friend of Mr. Belichick's since they attended Phillips Academy in Andover, Mass., together. The research director sent Professor Sackrowitz a copy of the team's chart telling coaches when to go for two points, and the statistician critiqued it. "Nobody had any real interest other than the Patriots," said Professor Sackrowitz, who now roots for them in addition to the Giants and Jets. New England did not try a single two-point conversion this year.

In the end, none of these moves is nearly as important as designing a defensive strategy or drafting good players. But Belichick's hyper-efficient approach almost certainly gives his team a small advantage in a game that can easily be decided by minor differences.

The approach has also altered the course of Professor Romer's research. When talking about the Berkeley economist's paper this year, Belichick noted that it did not consider the emotional effect that failing on fourth down could have on a team.

Once Professor Romer read that, he ran the analysis again to see whether teams performed worse after being stopped on fourth down. They did not, just as most economists would expect. Come tomorrow, when Belichick will have some time on his hands, he can read the details on the professor's Web site.

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