First off: yes, the way BB did it was about as dumb as I've ever seen from BB, and certainly contributed to the loss. That said, I think I can explain his thinking. It has to do with a statistical analysis mentioned in Christopher Price's The Blueprint. Basically, that study says two things: (1) Unless you have more than 15-20 yards to go, anywhere between the 10s, if you have any choice in the matter, you're almost always better off going for it on fourth down. [By better off, I mean improving your likelihood of winning the game.] (2) If you're inside your own 10, or on 4th and goal, you're almost always better off punting/kicking. Interestingly enough, IIRC, the author of the paper said that the Patriots were the only NFL team that contacted him about it. Thus, in SB42, Belichick made the statistically correct call, even if it was not the best call for that particular situation. The same goes for his call on 4th and 1.