The following paragraph has been edited for clarity, in addition to flipping the sign in the equations written to reflect what I actually wroete
On 4th down, with 2 yards or fewer to go, New England has gained a first down on approximately 66% of its attempts with Tom Brady as quarterback. The Colts had
(Probability of 4th down failure) xThe average New England punt nets about 40 yards. Let's give the Colts a probability Q of scoring a TD on a driving starting at the Indianapolis 32. Then, the chance of the Patriots losing is simply Q. For Belichick's decision to make sense, we just have to believe that he gave his team a
(Probability of Colts scoring a TD from the 28 Yard line) = 0.33P
Tom Brady is sitting in the postgame press conference doing yeoman's work trying to explain this to a roomful of stunned sports reporters in a language that they can understand. I don't envy him in this moment.
Update: Okay, the Patriots made one error
3rd and 2 at NE 28
(Shotgun) T.Brady pass incomplete short right to W.Welker (J.Powers).
Timeout #3 by NE at 02:08.
4th and 2 at NE 28
(Shotgun) T.Brady pass short right to K.Faulk to NE 29 for 1 yard (M.Bullitt).
The punt team should not have come on the field, forcing the Patriots to call a timeout. With the time out in hand, New England could have challenged the spot on the 4th down play, or allowed the Colts to score quickly so they could try for a comeback field goal (speaking of which, why didn't they let the Colts score a TD on the first play from scrimmage so they could try for a comeback field goal).