Sports Odds versus Probabilities

NPR this morning announced (listen here) that Quicken Loans will pay $1 billion for anyone who picks a perfect March Madness bracket. The odds of this are very long, but not 9 quintillion to 1, as reported.

NPR seems to have come up with the 9 quintillion to one figure—9 followed by 18 zeros—by calculating the total number of head-to-head matchups that are possible; see for the exact figure. But that is, strictly speaking, the probability of picking the correct bracket if all matchups are equally possible. They are not: we have a high degree of confidence that the second round will have zero 16-seeds playing, because 16-seeds have never beaten 1-seeds in the first round. So we should put very little weight on the probability that any bracket with a 16-seed surviving the first round is the correct bracket.

This is “sports odds,” which take into account the probability of victory for each head-to-head matchup in an iterative fashion (if the probability of 16 beating 1 is low, then the probability of any bracket with 16 surviving is low, and even within those low-probability brackets in which 16 does survive, the probability of the 16 surviving the second round is low, meaning that the probability of any Sweet 16 round with a 16 even lower, etc.). So long as the probability of victory is not equal across all potential teams and all potential matchups, the odds of picking the right bracket are not 9 quintillion to 1. The exact figure is obviously a lot harder to calculate, and the odds are certainly still extremely long against picking the exact bracket, but this is the proper way to think about the problem.

Posted in Research
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