Sunday, March 26, 2006

March Madness :: Final 4 Probabilities!

I was looking on ESPN.com to see if anyone picked George Mason in the Final Four... and lo and behold, there was a guy who not only has them in the Final Four, but has correctly picked GMU, Florida, LSU, and UCLA!

It's pretty amazing. It seems freakish at first glance. It's one thing to pick an 11 upset in the first round, or the 2nd round. To have that upset all the way through to the final four, along with nailing the other 3 teams correctly (who are 2,3, and 4 seeds)... defies the odds. This should be worth more than $10k in my humble opinion. ESPN and Pontiac are getting a deal on this marketing!

There are very close to 2,681,679 brackets that were filled out on ESPN.com (each person is allowed to fill out up to 5 brackets per signup, so it's not necessarily 2.6 million people). The reason I know this is because according to their leaderboard, I am in the 94.7 percentile with a single Final Four team selected (UCLA), and my rank is a distant 142129. ...=142129 / 5.3% = 2,681,679. (surely this 94.7% will plummet in the next couple of days as I have ZERO possible points remaining with UConn being knocked out!)

The number of possible outcomes to the tournament is 2^64... which ends up being: 18,446,744,073,709,551,616 to 1 that you get all 63 games picked correctly. But that is to get every single game correct, those aren't the odds to get the final 4 teams. To just get the Final Four teams, (I'm not 100% sure my math that follows is accurate, but I believe it is: please correct me and provide justification if I am wrong) you have to get 16 coin flips correct in succession (4 teams through 4 rounds -- which would be 50%^16 = 0.001526%. But that assumes you know the four teams from the beginning, it doesn't include the selection of the 4 teams, which would be 4/64 * (50%^16) = 0.000095367%. This makes 1 in 1,048,576. So it makes sense that they have at least 1 person with these final 4 teams. ...my logic might be incorrect though, but that's how I see it, with the teams as ping pong balls. I'd like to get the answer from a probability guru.

Anyway, March Madness... great times!

Here is the guy who correctly picked these 4 teams:
Here is my defeated bracket :(

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