Brady said something very important in the interview after the game: "We practice that play all the time and have it down." This was not a rash or rushed decision. Belichick had thought about it, analyzed it, practiced it, and was prepared to pull the trigger. In similar situations in tournament play, it's stong to take a shot on winning on the hand before the final, even if your position on the final hand is diminished if you miss. Usually, if you win on the penultimate hand, it's over, but if you lose, you still have a chance. Very similar circumstances here.