Why Belichick was right to go for it. Football coaches at most levels seem to forget that the rules allow four tries to attain the first-down line, not just three with a punt/kick down.
But football coaches are managers, and are more highly motivated not to screw-up rather than ultimate outcomes. They can always explain their behavior to ownership by showing they desired to keep it close and followed convention--as all their brethren are conditioned and motivated to do--rather than risk and fail.
More insight here, here, here and here.