Belichick has math on his side

Two sources have concluded that Bill Belichick, in a theoretical sense, made the correct call last night when he went for it on fourth down.

Brian Burke, who writes the Web site Advanced NFL Stats, used a play simulation to figure that the Patriots had a 79 percent chance to win by going for it and a 70 percent chance to win by punting. He then further explains his position.

Belichick also gains support from the ZEUS computer program, which produces probabilities for football coaching decisions. In an e-mail to the Fifth Down blog at nytimes.com, ZEUS developer Frank Frigo explains why Belichick was right:

A very interesting and controversial decision with the Patriots last night. I read the Advanced NFL Stats analysis and concur with Brian Burke’s general framing of the problem and his support of Belichick. Here are three ways ZEUS breaks down the problem. In each scenario, an extended simulation is performed beginning with the exact circumstance on 4th-and-2 and finishing at the conclusion of the game.

Scenario 1: The custom case for the specific offensive and defensive features of the Colts and the Patriots.

Going for it: 77.3% (Probability of Winning for the Patriots)
Punting: 75.7%

Scenario 2: The case for two N.F.L. average and equal teams in every offensive and defensive category:

Going for it: 78.6% (Probability of Winning for the Patriots)
Punting: 76.4%

Scenario 3: The break-even point on the decision occurs when the team with the ball is about 5 percent weaker than N.F.L. average on offense and 5 percent better than N.F.L. average on defense, while the opposing team is 5 percent better than N.F.L. average on defense and 5 percent worse than average on offense.

The results of Scenarios #1 and #2 clearly point in favor of Belichick’s decision, although not by nearly as wide a margin as we might have expected. Additionally, the analysis in Scenario #3 really cements the case for “going for it.” Applying this benchmark and comparing it with the far different characteristics of the Patriots and the Colts makes the call all the more clear.

Thumbs up to Belichick on a courageous and correct call last night.

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