Wednesday, March 18, 2015

The odds of picking a perfect NCAA tournament bracket are not as impossible as you may have heard

I've seen in several places that the odds of filling out a perfect NCAA tournament bracket are roughly 1 in 9.2 quintillion (9,223,372,036,854,775,808).  That's just not true.

The math is sound.  There are 63 games, each with two possible outcomes.  That really big number I already typed out once is equal to 2^63.  If you want to know the chances of correctly predicting 63 consecutive coin flips, that's your answer.

The thing is, NCAA tourney games aren't coin flips.  The worst-case scenario you have for picking any given game is 50/50, but a lot are much easier.  When 34-0 Kentucky plays 17-17 Hampton tomorrow night, I'd guess there's about a 99 percent likelihood (maybe more) that the Wildcats emerge victorious.

If choosing every winner was that simple, a perfect bracket would be too--you'd have a 54 percent chance (.99^63).  Obviously most games are harder to get right than that.  For the sake of simple math, I'll estimate there's a two-thirds probability of picking each one correctly on average.  Under that premise, the calculation becomes 1.5^63, which makes the odds of predicting a perfect bracket "only" 1 in 124 billion or so.


Pretty big difference, huh?

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