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Annals of efficient market theory, NFL coaches edition

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OK kids, here’s a football stats problem.

Situation:  You’re trailing 27-24, four and a half minutes to go, fourth and two at your own 33.  You have one time out left.

If you go for it and make it, your win probability becomes 38%.

If you go for it and get stopped, your win probability becomes 20%.

If you punt, your win probability becomes 21%.

Is it statistically correct to conclude that, if your probability of converting the first down is higher than 5.55%, you should go for it?

What if your quarterback is Aaron Rodgers?

Mike McCarthy is paid $6 million per year to figure this one out.

 

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