Tuesday, February 7, 2012

Roll Over, You Pats!

This past weekend's Super Bowl XLVI (that's forty-six) provided yet another confluence of probability, tactics, and sports.  That's never a bad thing.

I'm speaking, of course, of the decision on the part of Patriots coach Bill Belichick to permit the Giants to score on second down and goal from the Patriots' six-yard line, with about a minute left in the game.  The Patriots put up only token defense, so that when Ahmad Bradshaw took the handoff from Eli Manning, he was able to waltz into the end zone.  Almost literally: Bradshaw had a moment of indecisiveness as he reached the one-yard line, but soon backed into the end zone for the touchdown.

Even before that play began, color commentator Cris Collinsworth had already suggested that the Patriots might permit the Giants to score easily, because the Patriots only had one timeout remaining.  They would therefore be able to stop the clock after second down, but not after third down.  Since the play clock starts at forty seconds once the ball is set, the Giants would attempt a field goal on fourth down with only about ten to fifteen seconds remaining on the game clock.  Collinsworth reasonably contended that the Patriots should prefer trying to score a touchdown with a minute left (plus their one timeout) over trying to score a field goal with ten to fifteen seconds left (without any timeouts).

(It's worth pointing out that then-Packers coach Mike Holmgren had been roundly criticized for making a similar tactical decision fourteen years earlier, in Super Bowl XXXII against the Broncos.  Times change.)

And now, once Bradshaw had scored, Collinsworth decried Bradshaw's touchdown as a tactical error.  Well, setting aside the tendency of sports broadcasters to exaggerate practically anything, was it a tactical error?  Which outcome is better for each team?

Well, first of all, there's the intuitive argument that if one team wants you to do something, then your best strategy ought to be to resist that.  So if the Patriots are parting the Red Sea, maybe your best bet is to lie down.  And indeed, the Giants had considered that.  Manning later reported that he was telling Bradshaw to go down in the field of play.  The Patriots, for their part, said that it was immaterial, that they would have shoved Bradshaw into the end zone, but that tactic would not have worked if Bradshaw had taken a knee: Any subsequent bump by a defender, even the lightest touch, would have made Bradshaw down by contact at the one-yard line.

But let's not let psychological ploys decide the question.  Which tactical choice is the right one here?

The Patriots have two choices—allow the touchdown, or play straightforward defense—but there are more than two possible outcomes.  If the Patriots play defense, there are still multiple possibilities:
  • The Giants might score on second down anyway.
  • Or they might score on third down.
  • Or they might score a field goal on fourth down.  (We'll assume they wouldn't try to score a touchdown.)
  • Or they might fail to score at all, either because of a turnover or a missed field goal.
If the Patriots allow the touchdown, and we assume for the time being that the Giants don't refuse that touchdown, then the Patriots would have to score a touchdown in about a minute, with one timeout remaining.  Let's say they're able to do that with some probability qTD.

On the other hand, if the Patriots play defense, then there are those four possibilities:
  • If the Giants score on second down, the Patriots still have to score a touchdown with about a minute remaining, and one timeout.
  • If the Giants score on third down, the Patriots have to score a touchdown with about a minute remaining, but no timeouts.
  • If the Giants score a field goal, the Patriots have to score a field goal with ten to fifteen seconds left, and no timeouts.
  • If the Giants fail to score at all, the Patriots can simply run out the clock.
If the Giants score on second or third down against straightforward defense, the Patriots are left in pretty much the same situation as if they just let them score on second down, modulo that timeout.  So as it stands, they're just a bit worse off if they play defense.

Now let's take a look at those last two cases.  If they don't score on second or third down, the remaining possibilities are a turnover, a missed field goal, or a made field goal.  Out of those, I'd guess the made field goal happens nineteen times out of twenty.  In the remaining cases, the Patriots just have to sit on the ball, which I'd also guess would happen nineteen times out of twenty (remember, they might have to avoid the safety).  So the question roughly boils down to, which is more likely: Scoring a touchdown in a minute, or one of the following happening—scoring a field goal in ten to fifteen seconds, securing a turnover, or the Giants missing a field goal?  If it's the touchdown, the Patriots should let the Giants score.  If it's any of the remaining three choices, they should play straightforward defense.

Given that Lawrence Tynes hadn't missed a field goal of thirty yards or less in forever, the Giants were going to play possession football, and the Patriots would have no timeouts left for a field goal attempt, I'd go with letting them score, just as Belichick did.  But there's no way this is a foregone conclusion.  Sometimes, it's just a close call.

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