Thursday, March 08, 2007

I'll Take Two Powerball Tickets and A Yoo-Hoo

Several days ago I began pondering the likelihood of a perfect bracket. I thought to myself of all the years people have been filling out brackets and all the people who actually fill out a bracket, someone has to have penciled in the perfect bracket. Why hadn’t this ever made ESPN? Why hadn’t someone gotten their 15 minutes of fame, a mention at the ESPY’s, and a 10-year anniversary special on ESPN Classic for filling out the perfect bracket? Something had to be done. I contacted AwesomeUSA’s research and marketing staff to get some financial backing. They gave me 10 dollars and a Hardee’s Thickburger combo meal and told me I wasn’t welcome in their offices anymore. With that, I pocketed the ten dollars and found a scientist masturbating in some bushes near my car. He accepted the Thickburger combo meal and in three days had returned this stunning report. Here it is, courtesy of Codename Curveball. We thank him for the hours he brushed off work and complied this data. For your pleasure:

So you think you are going to have a perfect bracket this year? Someone has to have done it before, right? Well, my friends, in this situation I have to turn to my other friends, numbers. Hereís a simple exercise to show how difficult it is to pick a perfect bracket.

Assume that you have a 50% chance of picking the winner in each game. Likely, you always have a better chance than this, but for simplicityís sake, we will assume this initially. Since each game is independent, the probabilities multiply and you are essentially asking, ìIf I threw a coin 63 times (corresponding to the number of games), how many times would you guess it correctly?î The answer to that is:

100%*0.5^63 = 0.0000000000000000108 % chance

You have a 0.000000648% chance of winning the powerball if you play one ticket. I like them odds. Basically, you have a better chance of buying two tickets and winning the lottery twice than you do of winning the bracket. Alas, this situation is sort of a worse case scenario, and you can do better. The best case scenario is when the team with the higher seed always wins the game. In that case, letís call the odds like this:

1 versus 16 seed: 1 seed has a 16/17 or 94% chance of winning

2 versus 15 seed: 2 seed has a 15/17 or 88% chance of winning
and so on, remembering that there are 4 of these games, so the chances of all the 1 seeds moving on is 100%*0.94^4 = 78%, etc.

By that reasoning, you have a 0.003% chance of picking all of the first round games correctly. That is 1/32,656.

In the second round::

1 versus 8 seed: 1 seed has an 8/9 or 88% chance of winning

2 versus 7 seed: 2 seed has a 6/8 or 75% chance of winning
and so on…

The final numbers look like this:

First round correctly: 0.003%.

First two rounds correctly: 0.000004%.

First three rounds correctly: 0.0000002%.

First four rounds correctly: 0.00000004%.

All of it correctly: 0.0000000005%.

That is 1/19,704,059,564.

You're 134 times more likely to win Powerball.

Good luck.

-But let's be honest: If the perfect bracket does ever happen, it will be some girl who filled out the bracket because she likes the sport with the orange ball and dunk shots.


Blogger Runs With One Horse said...

Am I the only one that likes the game for the orange balls and dunk shots? What else am I missing?

March 8, 2007 at 7:58 PM  
Blogger Codename Curveball said...

I like the squeaky shoes.

March 8, 2007 at 8:34 PM  
Blogger the butler said...

The long, flowing garments.

March 9, 2007 at 11:23 AM  
Blogger Natty Bumpo said...

The only thing that would have made me enjoy this post more is a vampire reference. Well done, Curveball.

March 9, 2007 at 3:12 PM  
Blogger Natty Bumpo said...

The poisonous thickburger, literally the oldest trick in the book.

March 9, 2007 at 3:16 PM  
Blogger SonDog said...

What are the odds if my wife fills out a bracket by picking her favorite mascosts? I love it when women say that when they're "filling out" a bracket. I also love the look on their face when I mock them with fake laughter. At any rate, based on my personal experience, I say the your odds with picking mascots are better than trying to use "sports knowledge reasoning."

March 10, 2007 at 10:58 AM  

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