For Tom Brady's career, he's 14/17 in 4th and short (< 3 yd) situations, with one sack. Let's call that 77%. If they make the first down, they would leave roughly 10 seconds on the clock, counting the 2 min warning, one Indy timeout, and assuming Indy stops them...giving the patriots ~100% chance of winning.
If they don't make the first down (23%), they leave the Colts with 30 yards to drive to win. In their last three drives (excluding the interception and excluding the end when they were running out the clock purposely), the Colts went 79, 79, and 29 yards in 5, 6, and 4 plays, elapsing 2:04, 1:49, and ~1:00. That's roughly 12.5 yards per play, and 19 seconds per play! The Pats defense was completely gone.
If they punt, they leave the Colts with ~65 yards to drive to win; assuming a punt net of 35 yards.
Now, The Math:
1. Go for it. P(winning) = P(firstdown) + (1-P(firstdown))*(1-P(indy going 30 yards in 2:00))
2. Punt. P(winning2) = 1-P(indy going 65 yards in 2:00)
Given the way Indy was crushing the Pats defense, I'm estimating P(indy going 30 yards in 2:00) = 90%, P(indy going 65 yards in 2:00) = 60%.
1. Go for it P(pats win) = .77 + (1-.23) * (1-.10) = 79%
2. Punt... P(pats win) = 1 - .6 = 40%
#1 is clearly the better choice!
#2 doesn't become a competitive choice until you can hold the Colts to a one in four chance of driving the 65 yards. It's the right call for average teams, but not when the Colts have been blowing away your defense.
Conclusion: Bill Belichick made the unconventional but correct decision choosing #1.
(P=1 Conclusion after the fact: Bill Belichick made the wrong decision because his team lost)