Many people far better with numbers than us have concluded Belichick gave himself a better chance to win going for it than he would have punting. Here's one of the best arguments.
It has definitely forced Mr. Buckner and I to reconsider. However, I tend to side with Buckner for the following reasons, some of which he has already stated:
• The numbers factored in consider these were both typical offensive series (Pats and Colts). These WOULD NOT have been typical series. The Pats have a great offense. Also, with it being their last chance, the Colts would have four downs to gain 10 yards, not three, thus increasing their probability to advance the ball downfield. Typical probabilities of them gaining 70 yards vs. them gaining 29 must be adjusted accordingly.
• Momentum is not a word statisticians love. It's similar to the idea of being clutch, which many of us agree is a fool's crutch. However, in this case momentum cannot be denied. The Colts had it by tearing down the field on the previous possession. It only increases once they receive the boost gained by working with a short field.
• For an adequate answer to this questions, probabilities must somehow factor in several intricacies. Did the Pats have the option to run on fourth down? (Not really.) Why? Well, were they missing their top short-yardage back (Sammy Morris)? Yes. Was their defense gassed? Probably. Etc., etc.
So, yes, while many smart people have continued the debate today, I'm not sure simple numbers answer whether Belichick made the correct decision or not. It's much like baseball. Numbers can tell us the correct decision to make over the course of a long season or a long series. In baseball, with so many games, so many at-bats, so many pitches, those decisions should be uniform. But in football, with so few games, so few plays and so few decisions like these, more must be taken into account.
The situation has a much greater impact in football than it does in baseball. Is Brett Favre better than he was 10 years ago? No. But in this situation, is he having a better season? Absolutely. But don't Adrian Peterson, an enormous line and a stout defense help swing the numbers his way?