We must weigh in on the debate of the day -- should the Patriots have allowed the Giants to score that late TD? Should the Giants have scored or stopped at the one-yard line?
As repugnant as he is to us and human-kind generally, Belichek made the right decision by letting the Giants score a touchdown with 57 seconds left rather than run the clock down to about 20 seconds and then kick a chip-shot field goal for a 18-17 lead. And it seems that at least someone (reportedly Eli Manning) on the Giants knew that the best decision they could make would be to not take the free TD and instead kick what should have been the winning field goal (albeit there would have been about 20 seconds left for the Pats).
But here's where things went wrong. If the Giants actually had the strategy that they were not going to take the free touchdown, WHY HAND THE BALL OFF AT ALL?!?!?!?!?! This is one of my biggest pet peeves. If you are just killing time before kicking a field goal, and you don't need to gain any more yards (and the Giants were already at the 6 yard line), why not just have the QB take a knee? Why are you taking completely unecessary risk by handing the ball off (possible fumble) then having the running back burrow into the defensive line (who will be doing nothing other than trying to create a fumble)? By handing the ball off to Bradshaw, the Giants were creating a situation where the only thing that could happen was something bad -- a fumble, or the Pats get the ball back.
(NOTE: You could make a decent argument that the Giants should have just taken the touchdown and trusted their defense to stop the Pats, as they did. But it's clear that they were stuck in some no man's land of decision making, so this assumes that they had decided the best option was to kick the field goal).
Again, if you decide that you want the field goal, nothing good can come from handing the ball off. I hope you're sitting down for this because I'm about to tell you a hard truth -- NFL players are not necessarily very bright. They are world-class at doing one thing: being super-athletic. Decision making is not their strong suit, so a coach's job is to put players in a situation where they have to make as few decisions as possible.
If you need evidence of this point, just look at a few plays earlier when Hakeem Nicks caught a pass for a first down and could have let the Giants run the clock down to zero before kicking a FG if he goes down inbounds. He went out of bounds. Or look at the Bradshaw TD -- he knew he shouldn't have scored, but instinct took over and he couldn't help himself. Or look at Marian Barber III's epic meltdown in Denver earlier this year when he could have iced the game by staying inbounds, but instead went out of bounds and allowed Tebow to come back, win the Denver fans' affection, and make John Elway want to kill someone.
(Another side note: You could argue that Marian Barber killed the Steelers' season with that play as well. If Chicago wins that game in Denver, the Broncos don't make the playoffs, Ike Taylor never gets abused by Demaryius Thomas, and maybe the Steelers -- who easily could hang with the Giants or Pats -- have a different fate).
The point is this: No matter how many times you tell players not to do something stupid, they'll do something stupid. Or something bad will happen. So your job as a coach is to minimize the risk of catastrophic failure.
Or just pray for a little help from above.