Was Belichick’s decision to go for it on 4th down against the Colts a bad one?

During last nights Indianapolis Colts vs. New England Patriots game Bill Belichick risked everything on one play. In a controversial call, late in the 4th quarter, deep in his own territory, Belichick decided to go for it on a 4th down and 2 yards to go rather than punt the ball away.

Was this a bad decision on Coach Belichick's part? Conventional logic says to put it away, but it turns out that after a statistical analysis New England's decision to attempt a 4th down conversion was the right one.