Football Math

Posted November 16th 2009
Author Ty Fujimura
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The sports world is buzzing over last night’s thrilling and bizzare game between the Colts and the Patriots. Peyton Manning’s Colts capped an improbable comeback by scoring with just 16 seconds remaining to go ahead by one point.

The headline, though, was about the previous possession, in which Patriots head coach Bill Belichick opted to go for it on 4th-and-2 from his own 28 yard line with 2:08 go rather than punt.

Many analysts claim that Belichick made the wrong decision, that he was blinded by ego, that he made an unspeakable gaffe. Did he?

Let’s look at some rough numbers. We can estimate the probability of making it on 4th-and-2 to be 50%, a common success rate on 2-point conversions. The probability of New England winning if they punt is around 70%. If they go for it and fail, they will win about 50% of the time (Even if Indy scores 60% of the time, the Patriots can come back with a field goal). If they go for it and succeed, the probability of winning is around 95% (This number would be higher if Indy had no time outs left; they had one).

So if they punt, they win about 70% of the time. If they go for it, half the time they will have a 50% chance and half the time they will have a 95% chance. Going for leaves them a 72.5% chance of winning — Slightly better than the punt.

Obviously, these numbers aren’t perfect, and more careful analysis would be necessary to make a conclusion about the decision. But in light of the vitriolic reaction the sports press had, the idea that it was a close-to-even decision is enlightening. These pundits are displaying classic risk aversion: They think it far preferable to go for the orthodox rather than assume variance, even if that risk may give you a better chance to win the game.

Usually, head coaches and other decision-makers will favor the safe, because one is rarely canned for it. Only an uber-confident person with a lifetime tenure, as Belichick has, can feel safe making such a decision. If you’re a few rungs up the ladder, with plenty of suits above you, I don’t advise “going for it” in your business choices, even when a risk gives your organization a better chance to win. But if you’re evaluating the decision of someone under your management, consider your risk tolerance before you make an assessment. A smart decision may look awful, or even reckless, at the time. The wise manager can cut through the noise of public opinion and recognize that.

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