David Romer wrote a paper called “Do Firms Maximize? Evidence From Professional Football”.

According to Christopher Price in The Blueprint, Belichick came across “the Bellman equation” in the summer of 2002 in which

David Romer used NFL box scores from the 1998, 1999, and 2000 seasons to attempt—along with mathematical, statistical and economic tools—to debunk the idea that when it comes to fourth down, ti’s better to kick than to go for a first down or touchdown.

Most of the NFL greeted his findings without enthusiasm because, as Bill Cowher suggested, “That one time it doesn’t work could cost your team a football game, and that’s the thing a head coach has to live with, not the professor.”

Professor Romer was surprised that Belichick read his little-known work. Price includes Belichick’s thoughts on the study and I’ve quoted some of them here:

“I think I understand some of the points that were made in there and I think he has some valid points,” Belichick said after reading Romer’s study in the summer of 2002. "There’s sometimes an emotional aspect, and momentum, if you will, to those decisions, but I’m not sure how to calculate that. One of the points he was making was that if you go for it, particularly when you’re inside the opponents’ twenty, even if you come up short, you’ve got them backed up, they got eighty, ninety yards to go. Do the mathematical percentages of them scoring in that situation versus you getting the ball, and so forth and so on, and that’s a valid point. On the other hand to go down there and get nothing out of it, psychologically there’s an impact there on your team.

I think that some of those are legitimate points and you just have to evaluate the situation to your team, the team you’re playing," he added. “I see where a lot of that’s coming from.”

By the way, Christopher Price’s book is well worth picking up. It’s a goldmine of inside Patriots information and a terrific read.