## You can always call him stupid ex post

I'm sorry I was traveling this morning and had missed the second half of the game last night. Had I been home, I would have seen Bill Belichick's call on fourth and two, which Gary has already emailed me made him an idiot, and which Ed has posted was an act of hubris. Vic Carucci calls it a gutsy blunder, and he writes on the NFL's official web.

I disagreed by instinct. As I told a student after I got to campus who asked about the decision, I said you had to put your head in Belichick's place without regard to what eventually happened. You have to argue ex ante rather than ex post.

Your team has given up two fourth quarter touchdowns in possessions of 2:04 and 3:32. You are playing against arguably the greatest QB ever (arguably, acknowledging that the greatest QB ever could be your own QB.) You are on the road. You have a play that has worked quite well, and you ran it successfully earlier in the game. (Game log) And it's not the first time Belichick had done it this season, Michael Lombardi reminds us. He went 4th-and-1 from his 24 up 19-10 in the third quarter against Atlanta (successful, game log.) So this isn't gut instinct: Belichick has thought the math through.

I was going to write out the math of this in terms of expected values, but Brian Burke has already done this.
With 2:00 left and the Colts with only one timeout, a successful conversion wins the game for all practical purposes. A 4th and 2 conversion would be successful 60% of the time. Historically, in a situation with 2:00 left and needing a TD to either win or tie, teams get the TD 53% of the time from that field position. The total WP (win probability -- the likelihood you would win the game) for the 4th down conversion attempt would therefore be:

(0.60 * 1) + (0.40 * (1-0.53)) = 0.79 WP

A punt from the 28 typically nets 38 yards, starting the Colts at their own 34. Teams historically get the TD 30% of the time in that situation. So the punt gives the Pats about a 0.70 WP.

Statistically, the better decision would be to go for it, and by a good amount. However, these numbers are baselines for the league as a whole. You'd have to expect the Colts had a better than a 30% chance of scoring from their 34, and an accordingly higher chance to score from the Pats' 28. But any adjustment in their likelihood of scoring from either field position increases the advantage of going for it.
Not to say that Belichick had those numbers firmly in his head and thought of it in terms of WP, but he's shown evidence that he's willing to go for fourth downs in his own territory, that the gain in punting would have been to reduce the likelihood of the average NFL team to score the winning TD to 30% from 53%. He certainly knew he would be skewered if his team failed to convert ... which he had to think was a 40% probability. He was confident enough to accept that fate in return for giving his team its best shot at winning the game. In terms of the rest of the season, would you rather have your team lose and the blame placed on your coach for a "bonehead move", or lose and have your defense questioned for its inability to hold a lead?

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