Sunday, November 15, 2009

Don't Lose Your Edge, Bill!


Predictably, the talking heads have already begun raking Bill Belichick over the coals for his decision to go for it on 4th-and-2 from their own 28 yard line with 2:08 on the clock. However, if you look at the math, the Pats' head coach appears to have made the correct decision.

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 no timeouts one timeout. If the Patriots gain a first down, the game ends; they can simply kneel on the ball three times slowly walk to burn a few seconds, then take a knee on each down to end the game. If they don't gain a first down, the Colts would still need to score a touchdown to win the game. Let's give the Colts a probability P of getting the six if the ball starts at the 28 yard line. So if the Patriots try for the first, their chance of losing is
(Probability of 4th down failure) x
(Probability of Colts scoring a TD from the 28 Yard line) = 0.33P
The 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 higher chance of winning lower chance of losing. In math terms, that would mean 0.33P > Q 0.33P < Q. Doing some algebra leaves you with P > 3Q P < 3Q. In other words, for the Patriots to have made the right decision, we only have to believe the Colts odds of scoring a TD on a drive starting 28 yards from the end zone are less than three times the odds of the same outcome starting from 68 yards out. The win probability graph for the game suggests that, given 1st-and-10 from New England's 29, the Colts had roughly a 51% chance of winning in the actual situation. We have to believe that their chances under the punt scenario were below 17% above 17% for Belichick to have made a bad good decision. Considering the Colts' have scored touchdowns on 30% of their offensive possessions, my guess is that this was a good one.

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).
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