Super Bowl Coin Flip
Cullen Roche observes,
I was driving all day long yesterday and heard an interesting statistic on the radio. The last 14 coin flips in the Super Bowl have been won by the NFC. The odds of this happening are 16,000:1. Beyond a statistical anomaly. Anyhow, the commentator, a Vegas bookie, was discussing a bet they had going in which they wager on the coin flip every year. He was talking about how silly the bet is because, obviously, the odds are 50% heads or tails. But Vegas is playing it NFC vs AFC and guess what? 75% of the public is betting on the NFC to win the coin flip!
Roche chalks this up to the “recency effect” and implies that it’s a delusion. It strikes me as simple Bayesian logic. Theoretically, the odds of a coin landing on heads are 1 in 2 and that, since either the NFC or AFC will be represented by heads, the odds of either conference winning the coin flip are equal. Forced to bet on which conference will win and given even odds, then, it’s 50-50 that you’ll win.
Yet, in this case, bettors have additional information: The NFC has won the last 14 flips in a row! A 16,000:1 happenstance! That’s probably just a bizarre coincidence. But there’s at least some tiny chance that it’s something else. So, given even odds, why wouldn’t you bet on the NFC’s winning again?