Billionaire Bracketology

If you haven’t heard, Quicken Loans and Yahoo! Sports (with a hefty helping of Warren Buffet) have teamed up to run a March Madness bracket where anyone who picks all 63 games correctly wins — I shit you not — ONE BILLION DOLLARS.

Or, fine, a nuclear warhead from Kerplakistan, whatever.

Or, fine, a nuclear warhead from Kerplakistan, whatever.

This is an astronomical sum of money to be bet on a sporting event — imagine going to Vegas and slamming down the GDP of the Solomon Islands on black.  To be fair, though, Warren’s hedging his bets by spreading the bet over every game in the NCAA basketball tournament.  All sixty-three games of it.

Let’s assume everyone who enters the tournament chooses the winner of each game blindly.  Quicken Loans is limiting the number of entrants to 15 million, so the chance of anyone at all winning by blind luck is a 0.5063 × 15,000,000 = 0.00000000016% chance.

Ah, but we have more information than luck!  Every team in each of the four sections of the tournament is seeded 1 through 16.  If we assume this alone gives us enough information to pick every game with at least 2/3 probability, then the chance of someone — anyone — wins the billion-dollar bucket is a whopping 0.6763 × 15,000,000 = 0.016%.

So it’s unlikely any average person wins this.  Ever.  But!  Let’s assume (for sake of argument) that I am smarter than the average person.  Well then:

The contest is free to enter, so just by filling out a bracket and picking teams by, I don’t know, jersey color and degree of mascot alliteration (i.e. randomly) I can expect to win 0.5063 × $1,000,000,000 = $0.0000000001.  If I can use the seeds of teams to increase my odds to 2/3, then I’d expect to win 0.6763 × $1,000,000,000 = $0.01!

The kicker, of course, is that as a veteran bracketologist (second place in my pool to a girl who actually did choose by color last year, what what), I can safely assume I’ll be able to pick games correctly 75% of the time.  I’m that good, obviously.  I don’t even have to watch any college basketball this season, such is my mastery of sabremetrics and theorycrafting (full disclosure: I did, once this season, listen to another man watch a North Carolina game).  And with my superior March Madness skill set, fueled by in-depth statistical analysis and this one blog I read on Grantland, I can already expect to win 0.7563 × $1,000,000,000 = $13.45, thereby offsetting (a fraction of) the beer I’ll need to sit through any of the actual tournament games themselves while I wait for college football season to roll around again.

I’ll take my check by direct deposit, please, Warren.

Sidebar: this is why it’s so hard to ever go undefeated in sports. Imagine the shortest season — college football, twelve games — and a team that’s a huge favorite in all of them. If that team is given 90% odds of winning every single game, its odds of going are undefeated are still only 0.9012 = 28%.  What I’m trying to say here is it’s okay, Nick Saban.  Even your dark magic is no match for the power of exponents.



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