Thanks for Storyteller and Varlos for elaborating on the benefits of going for it. Those are the sort of mental calculations I went through quickly when I evaluated (before the play occured) that I had no problem with the call.
In general, “conventional” football is way to conservative. It’s designed to protect the coach’s ass by making it seem like he made the safe decision even when he made the wrong one. Coaches regularly give up a fraction of a chance to win the game in order to deflect fan anger later if they lose. One of the great things about Bellichick is that he doesn’t give a shit about all that, and he can objectively evaluate the merits of going for it even if the fans can’t. So the move he made deviates from the norm - and deviating from the norm and then not having success definitely gets you quite a fan reaction - but it was the smart play given the circumstances.
No, this is overly simplistic. Obviously going for the first down with a lead with 2 minutes left carries certain benefits (ie running out the clock) that doing the same thing in the middle of the first quarter would not. Additionally you need to factor in how good your team is at converting a 4th and 2 type play, how good their defense is at stopping it, how likely your defense is to stop their offense going 35 yards vs 70 yards, etc. There are many variables that can change whether or not it’s the right decision.
But the variables were all favoring going for it here. The Pats have the best 4th and 2 converting offense in the league. The Colts are as capable of any team of scoring on a 70 yard drive with 2 minutes to work with. Your defense is worn down and isn’t stopping them, and that was just proved by them running a quick scoring drive a few minutes ago, and your defense has not gotten substantial rest since then. New England was likely to convert the 4th and 2 play. The Colts were likely to score if they got the ball again. The specific situation dictated attempting to retain possession of the ball.