For those who missed the football game and didn't watch SportsCenter this morning, last night's contest between the Colts and Patriots turned on an already controversial fourth-down call.

The Partiots had the ball, fourth and two, at their own 28-yard-line. They were ahead but only by six points, 34-28, following a fourth-quarter Colts touchdown. The clock showed 2:08.

The conventional call was to punt. And although Patriots coach Bill Belichick is famous for eschewing punts on fourth down, it was hard to believe he'd go for it in that situation, so close to his own end zone. But he did. And it almost worked. Brady, throwing from an empty backfield, hit Kevin Faulk right at the first down marker. But it appeared that Faulk bobbled it for a moment; by the time he'd gained full possession, an Indianapolis defender had driven him backwards. The spot put him short of the marker.

At that point, Peyton Manning and the Colts took over, methodically moving down the shortened field and running out the clock. They scored the winning touchdown with just ten seconds left.

The second-guessing started with the Belichick post-game press conference and hasn't stopped since. Maybe it's the shock of seeing Belichick, widely considered the smartest coach of his generation, have a call backfire. Or maybe it's the shock of seeing such a rare decision. Whatever. Nobody seems to think he got it right. "Belichick call unrivalled," writes the *Boston Globe*'s Dan Shaugnessy--employing gentler language than what, I'm sure, callers into Boston talk shows are using this morning.

But statistics show pretty conclusively that football coaches are far too conservative about fourth down decisions--that they should go for it, rather than punt, far more frequently. Apparently, statistics also show that Belichick made the right call here, notwithstanding what everybody thinks. From the website "Advanced NFL Stats":

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 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.

Brian Burke, writing at the *New York Times*, and Nicholas Beaudrot agree.

All of this comes courtesy of Matt Yglesias, who--I know--took little joy in making this case. For what it's worth, I feel the same way. Although my devotion to another Boston franchise is a matter of public record, my pro football loyalties remain with the team I grew up watching in South Florida.

*Update:* Readers are already writing in to suggest that the pro-Belichick analysis fails to account for the specifics of the situation--it was Peyton Manning at QB, etc. Actually, that's not true. I just didn't excerpt those parts. Here's more from Advanced NFL Stats:

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. 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 make punting the better option. At best, you could make it a wash.

And now, here's Beaudrot:

New England has gained a first down on approximately 66% of its attempts with Tom Brady as quarterback. The Colts had no timeouts. If the Patriots gain a first down, the game ends; they can simply wait for the two minute kneel on the ball three times to end the game. If they don't gain a first down, the Colts would still need to score a touchdown to win the game. Let's give the Colts a probability *P* of getting the six if the ball starts at the 28 yard line. So if the Patriots try for the first, their chance of losing is

(Probability of 4th down failure) x

(Probability of Colts scoring a TD from the 28 Yard line) = 0.33*P*

The average New England punt nets about 40 yards. Let's give the Colts a probability *Q* of scoring a TD on a driving starting at the Indianapolis 32. Then, the chance of the Patriots losing is simple *Q*. For Belichick's decision to make sense, we just have to believe that he gave his team a higher chance of winning. In math terms, that would mean 0.33*P *> *Q*. Doing some algebra leaves you with *P* > 3*Q*. In other words, you would have to believe that the Colts odds of scoring a TD on a drive starting 28 yards from the end zone are *more than three times* the odds of the same outcome starting from 68 yards out. The win probability graph for the game suggests that, given 1st-and-10 from New England's 29, the Colts had roughly a 51% chance of winning in the actual situation. We would have to believe that their chances under the punt scenario were below 17% for Belichick to have made a bad decision. Considering the Colts' have scored touchdowns on 30% of their offensive possessions, my guess is that this was a good one.