Doing the math: Belichick's 4th-and-2 call was statistically better decision

The New York Times's 5th Down Blog has done the math, and it turns out that the Patriots had a better chance to win the game by going for it on 4th and 2 from their own 28 than they would have if they'd punted:

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 win probability 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 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.

We don't pretend to understand the 5th Down's math. But we're certain that Belichick's decision would've made more sense if, well, he had a 5th down.

GAME RECAPS:

NY TIMES: Colts pull off improbable win as Patriots' gamble backfires 

AP: Belichick's 4th down gamble fails 

BOSTON HERALD: Colts capitalize on fourth-down failure