The Patriots had a 13 point lead with just over four minutes to play. Peyton Manning, unfazed, marched the Colts down the field for a touchdown in less than two minutes without using any of Indy's three remaining time outs. With the two minute warning also remaining, Indy decided to kick it deep to New England and trust their defense to get a stop. New England could not convert a third and two from their own 28, and so were facing a fourth and two with just over two minutes remaining, deep in their own territory.
Belichick decided to go for it.
I loved this call. Absolutely loved it. Let's look at the possible outcomes. If you punt, you give Peyton Manning the ball with what amounts to an eternity for him: over two minutes with two clock stoppages (the two minute warning and one timeout). Yeah, you're probably still likely to win, but he's Peyton Manning. Furthermore, there's some evidence that your defense is worn out. I really think this is a shitty position to be in. Maybe that's just the fan in me, but no one wants to see their team playing Peyton Manning when all he needs is one touchdown drive to seal the game.
If you go for the first down conversion and you make it, the game is basically over. You might need to get one more first down, but if you don't and still have to punt, the two minute warning will be long past and the Colts will have burned their last time out. That is an astronomically harder situation for Manning. Furthermore, you've been having your way with Indy's defense all night. The probability of converting that fourth and two is extremely high.
But most importantly, the cost of not converting is just not that high, in my opinion. You're talking about a forty yard difference compared to punting, but that forty yards is highly likely to be made up by Manning in less than a minute, given the way defense is played in that situation. Furthermore, because you are up by six, even if the Colts get the touchdown, it's impossible for them to end up ahead by more than two points. This means that you could win the game on a field goal.
In other words, the worst case scenario for the Pats was not that Indy would get a touchdown. The worst case scenario is that Indy would get a touchdown with no time left on the clock. This scenario is far more likely if you punt than if you fail to pick up the first down (and of course, getting the first down is the ultimate win).
This call took a lot of balls and I think it was the right one. I just don't think that the forty yards you'd net on the punt matter all that much in that situation. Peyton Manning is just so highly likely to make those yards up and still have plenty of time to win it that the price of failure is easily offset by the reward of success.
It didn't work, of course. Indeed, New England then made what I think it was their truly critical mistake (other than wasting their timeouts earlier in the half): they let Indy run time of the clock by tackling Joseph Addai inside the five yard line with about a minute to go. At that point, your best chance to win is to let Addai score and play for the field goal. You just are not that likely to deny Peyton Manning and the Colts with four cracks at the winning touchdown inside the five. Far better to let Tom Brady have a chance to get into field goal position at that point.
Anyway, I wish Belichick's gambit had succeeded because it would make other coaches less reticent to try the same thing. I firmly believe that NFL coaches treat fourth downs too conservatively. Belichick lost this time, but hopefully he's not naive enough to let the result of one play (and the ensuing media backlash) alter his conviction. In the long run, that style of play will pay off.
**EDIT** I should note that the call should have worked. The receiver on the play, Kevin Faulk, bobbled the ball and thus did not receive forward progress beyond the first down marker. Had he not bobbled the ball, he would have gotten the first down. Furthermore, he still may have converted it, but the spot by the officials was not favorable to New England and with no timeouts they were unable to challenge the decision.
**EDIT #2** According to this website, the failure to convert knocked New England from a 77% chance of winning to a 66% chance of winning. If we assume that New England would have won 90% of the time if they had converted, we find that New England needs to convert that play only 50% of the time for it to be the right call. I guarantee that New England is likely to convert that play better than 50% of the time. Almost any NFL team is likely to convert that play better than 50% of the time, and this is one of the best offenses in the league. It was a good call.
**EDIT #3** The website linked above put up this post also defending Belichick's decision.