March Madness: Quantifying the Odds of a Perfect Bracket
The NCAA Tournament starts in full force on Thursday afternoon with first round action in four different cities.
(NOTE: I know that there are four games that the NCAA calls "first round" games on Tuesday and Wednesday night. This is hogwash. These games are functional play-in games for access to the field of 64, which begins play on THURSDAY. They call the round of 64 the "second round." It's not. It is, was, and always will be the FIRST ROUND. Got it? Good.)
Every year, like practically every living, breathing American, I fill out a bracket. And every year, perfectionist that I am, inevitably I am despondent when my first incorrect prediction occurs (typically by around the middle of Thursday afternoon).
I know the perfect bracket is a virtual impossibility, but it's fun to think about, and when that first 13 seed knocks off a 4 seed by 2:30 Thursday afternoon, the dream is over. I'm not even allowed to think about it anymore.
But how ridiculous is the thought of attaining a perfect bracket?
Thankfully, we have the good folks at pregame.com, led by their founder R.J. Bell (one of the best follows on Twitter, if you're into wagering, @RJinVegas). R.J. recently sent out an email that served as an electronic bucket of water to douse my hopes and dreams of the perfect bracket.
The email contained the following "perfect bracket" factoids:
There are 9,223,372,036,854,775,808 possible brackets (9.2 quintillion)
Let me save you the trouble of counting the number of digits after the initial number nine. That's eighteen digits! 9 trillion TIMES a million. That's a lot! And only one of those can be correct.
How big is 9.2 quintillion? Funny you should ask. Here are some facts that illustrate the magnitude of this number:
If everyone on the planet each randomly filled out a bracket, the odds would be over ONE BILLION to 1 against any person having a perfect bracket.
If one bracket per second was filled out, it would take 292 BILLION years to fill out all possible brackets (that's 20 times longer than the universe has existed).
If all the people on earth filled out one bracket per second, it would take over 43 years to fill out every possible bracket.
If all possible brackets were stacked on top of each other (on standard paper), the pile would reach from the moon and back over 1.1 million times.
All possible brackets (on standard paper) would weigh 90,000 times more than every man, women, and child on earth combined.
Even if a person had a 90% chance of winning each game he picked, his odds would still be 763 to 1 against picking a perfect bracket.
The calculations above assume a 64 team bracket, but if you want to count the four play-in games as part of the tournament and expand this analysis to consider 68 teams (We have a word for you people -- communists), then multiply the above figures by a factor of four.
Indeed, the perfect bracket is a ridiculous longshot. Roy McAvoy was right -- perfection is unattainable:
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