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What Are the Odds?

Quicken Loans has bought an insurance policy with one of Berkshire Hathaway’s insurance companies against a contestant correctly predicting the outcome of each game in the NCAA Division I men’s basketball tournament this spring.

The odds cited are “1 in 4,294,967,296.” As Sheldon once said to Leonard’s mother, “I think I’d like to do the math.”

History tells us that some tournament games are more predictable than others. There’s no history of #16 seeds beating #1 seeds, but it could happen. It’s clearly not a 50% chance of that happening, but maybe it’s 1% or even .01%. On the other hand, #12 seeds have surprisingly good luck against #5 seeds, and the historic trends for #8 vs. #9 are probably close to 50/50.

The odds cited aren’t 1 in 2^64; the quick “back of the envelope” calculation says they’re more like 1 in 2^34. Clearly someone figures picking the #1s to beat the #16s is more like .9^4, not .5^4. It’s when you start looking at the #8 vs. #9 or anything after the first weekend that the odds get much, much longer.

I would imagine “they” (General Reinsurance?) studied the winning scores in various public tournament pools over the past decade and realized how close anyone has ever come to getting all of them right. I just wonder if one in four billion is accurate or not, or how nervous General Re will be after the first round or the first weekend.

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