The Sciences

A 3.8-Sigma Anomaly

Cosmic VarianceBy Sean CarrollFeb 4, 2012 2:33 PM

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Every professional football game begins with the flip of a coin, to determine who gets the ball first. In the case of the Super Bowl, the teams represent the National Football Conference (NFC) or American Football Conference (AFC). Interestingly, the last 14 coin flips have been won by the NFC. Working out the numbers, the chances of 14 coin flips in a row being equal is 1 in 8,192. (The linked article says 1 in 16,000, which comes from 2^14; but that first coin flip has to be something, so the chances of 14 in a row are really 1 in 2^13. The anomaly would be just as strange if the AFC had won every time.) That's a better than 3.8-sigma effect! Enough to call a press conference, if this were particle physics. The question is ... is this really a signal, or did we just get lucky? Is it a fair coin and the NFC has just been the happy recipient of a statistical fluctuation, or is there something fishy about the coin? Remember Barry Greenstein's parable about how different people compute probabilities. And let it be a lesson the next time you're excited about 3-sigma anomalies.

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