(Brian Burke, a former Navy pilot who has taken up the less dangerous hobby of N.F.L. statistical analysis, operates Advanced NFL Stats, a blog about football, math and human behavior.)
New England Coach Bill Belichick is taking a lot of heat for his decision to attempt a 4th-down conversion from his own 28 with a late 6-point lead against the Colts. Indianapolis came back to win in dramatic fashion, 35-34. Was the decision a good one?
With 2:08 left and the Colts with only one timeout, a successful 4th-and-2 conversion wins the game for all practical purposes. A conversion on 4th-and-2 would be successful 60 percent 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 percent 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 (WP stands for win probability)
A punt from the 28 typically nets 38 yards, starting the Colts at their 34. Teams historically get the TD 30 percent 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 30 percent 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. You can play with the numbers any way you like, but it’s pretty hard to come up with a realistic combination of numbers that makes punting the better option. At best, you could make it a wash.
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