Bill Belichick is one of my least favorite people in sports. I love the Colts and do not like the Patriots. The announcers were unanimous in saying the Patriots were crazy to go for it on 4th down in the Colts-Patriots game. I hate to say it, but I think Belichick's move might have made sense.
Looking back at the last two years passing plays on 4th down and less than two yards to go have succeeded around 45% of the time. With Brady this chance is probably higher than 45%. Let SHORT= chance Colts score TD from the Pats 30 and LONG = chance Colts score TD after a punt. Assume that if Patriots get a first down Colts cannot win. Then Patriots should go for it if 0.45 + 0.55*(1-SHORT) > (1-LONG).
The following table computes the Pats' chance of winning if they go for it, minus Pats chance of winning if they punt based on different values of SHORT and LONG. A positive number means Patriots should have gone for it. Note that if Colts have a greater than 50% chance of scoring a TD after the punt, then Belichick made the right move. With Peyton Manning at the helm I would say the Colts had at least a 50% chance of scoring a TD from, say, 70 yards.
