March Madness: Netting the Odds of Rounds 1 and 2

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The first two rounds of this year’s NCAA men’s basketball tournament have featured a number of surprising upsets. With #1 seed Kansas falling to #9 Northern Iowa, and no-scholarship Cornell advancing to the Round of 16, teams are busting brackets with abandon. But how unusual are these results really? What are the odds?

Taking a look at a few specific games gives us our first clues.

  • In the first round, #14 seed Ohio defeated #3 Georgetown. The odds a #14 seeded team will defeat a #3 seeded team in the NCAA tournament are 1 in 6.67. Not too outlandish.
  • #15 seed Robert Morris took #2 Villanova to overtime before losing. The odds of a #15 beating a #2 in any given game are 1 in 25, and with four such games per tournament, we could expect to see it, on average, 16 times or so in a century.
  • Even what might seem like the biggest upset wasn’t really all that big: the odds a #9 seed will defeat a #1 seed, as Northern Iowa did in defeating Kansas, are 1 in 12.4twice as likely as the Villanova upset that almost happened.

Individually, then, none of these upsets was outlandishly unlikely.

However, things start to look different when we multiply the odds of all the results together to get the big-picture odds. How likely was this year’s situation after Round 1? After Round 2? By that measure, compared to last year, this year’s first two rounds start to look like outliers.

  • Last year’s Round 1 had fewer upsets than this year. The odds a first round will go exactly the way it did in 2009 are 1 in 4,710,000. (For reference, the odds of all the higher seeds winning in the first round are 1 in 13,000.)
  • The odds a first round will go exactly the way it did this year, by contrast, are 1 in 30,700,000That’s 6.5 times less likely than last year’s results.
  • The exact picture at the end of Round 2 last year had a likelihood of 1 in 2,860,000,000. (one in nearly three billion.) Sounds unlikely, but…
  • The odds of this year’s picture after two rounds are only 1 in 1,520,000,000,000—that’s one in over one-and-a-half trillion. So overall, this year’s tournament through two rounds has been 530 times less likely than last year’s.

 

Upsetting? Absolutely, if you dream of a perfect bracket or watched your favorite team lose. Is there a silver lining? Yes, indeed. For those who have not had too many of their picks drop out, the chances of getting a better than usual payout are better than in other years. The fewer winners at the end, the greater the winnings of each individual winner. Although most years it is unlikely anyone picks a perfect bracket, in every pool there are winners. This year’s will be well compensated.

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