Against an offense like the Rams, it's a no brainer to go for it.
Our defense was shot at that point, I'm not about to put a championship all on a coin toss.
That's a good point, and if you study soccer there's an even bigger reason why it's smart to go for it.
In soccer, considering that it's such a defensive sport, where your typical score is 0, 1, or 2 the percentage of goals scored in the 90th+ minute is up there compared to goals scored at any other point in the game. You have 89 minutes of defensive playing, and then there's all these goals that take place in that last minute.
The strategy behind it is simple. One team tends to quit and plays for over time or the tie. The other doesn't. They catch them sleeping.
Football's no different. If there's 10 seconds on that clock, you should always be looking for the win. You don't quit because not only do you depend on a coin flip in OT, but the chances that the other team is breathing a sigh of relief and might be waiting for the clock to run out, are in your favor. In addition, considering the chances of success at the end of the game is heavily in favor of the offense when they have a QB that doesn't get rattled easily, and defensive players are more tired, it's yet another reason to go for it, rather than giving them a break, to catch their breath.
In this case Pats had the ball. They had everything to gain by going for it. The only risk they had was turning over the ball in their own territory, but when it came to Brady, that's not a greater risk than the 50% the coin flip gives you. Chances are good Bill already knew this about Brady by the time they got into the Super Bowl, even if the majority of people didn't.
