Karen DeCoster at the Mises blog says that this is why the Patriots head coach does so well.

his mathematical and economics background have fed his penchant for strategy, deep analysis, and cost-benefit decisions. Where other coaches only see an individual's outward performance, Belichick lays out his plans based on deeper analysis. He measures the player's direct cost to the team and the various opportunity costs of keeping the player. The benefits of that player's performance are weighed against the assorted costs to determine whether ot not that player will advance the performance of the team, as a whole, while at his position. Apparently, he finds that using simple, incremental analysis adds to his problem-solving ability, which he relies on for both personnel and gameplan decisions. Belichick, in my opinion, though not necessarily the finest coach in the NFL, is the game's greatest master in terms of the particulars of planning and gameday management, and he accomplishes this as an economist and field academic.

Belichick went to Phillips Andover and Wesleyan. In a blog of a thesis done at Virginia, Jason Detwiler mentions Belichick's understanding of David Romer's paper on going for it on fourth down.

Steelers head coach, Bill Cowher, commented on Romer�s application of the Bellman equation: �Basically, you have to recognize that you're not doing everything by a sense of what the odds are,� Cowher said. �When you drive the length of the field, you want to come away with points because, if you don't make it, there's a tremendous momentum you have to take into account.� 8
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Bill Belichick, head coach of the reigning Super Bowl champion New England Patriots commented: "I think, basically, he was saying that if you get down there and don't score, you're putting the other team 80, 90 yards away from the goal line anyway, and the chances of them scoring aren't very good," Belichick said. "You'll probably get the ball back in good field position. And the percentages added up to his conclusion, which was to go for it."

Cowher coaches on the basis of emotion, Belichick does math (maybe even Bellman equations.) You can argue who is the better coach.