I was having a conversation with a group of casual fans the other night and I was once again hit with the open question of, “How hard can it really be to fill out a perfect bracket?” due to the Billion Dollar Bracket Challenge that Warren Buffet and Quicken Loans has thrown out there. Well, for one thing, it’s never been done. So, I’m gonna’ go out on a limb and say based on that evidence, it’s pretty hard. But that didn’t convince these guys…I started with some simple math and they pooh-poohed it saying I didn’t need to worry about the high seeds….Okay, I agree with that. But there’s still a lot of variations that exist.For the sake of argument and because I love probability, let’s do some math and figure a couple of things out. First, if you filled the bracket out with every conceivable iteration that existed, you would need to complete a bracket that first considered every team winning the championship (yes, even the 16 seeds) and then progressing through each of the 63 (7) remaining teams to win the whole thing against that 1 Seed…. So, it’s a power calculation of 2 choices to the 64th, which equals:
18,446,744,073,709,600,000 (that’s uh...lets' see, million, billion, trillion, zillion...oh yeah, Quintillion!)
(for reference, the Universe is 13.7 Billion years old, or
5,184,518,400,000,000,000 Quintillion seconds…
So, even if you were filling the brackets out at a rate of 100,000,000 a second, you wouldn’t be able to even get half of the variations in from the time the brackets come out until they are due on Thursday at noon….
But that’s not reality. We can assume a couple of things:
No16 Seed has ever won a game. Now, you can assume that there is on a 2 to the 60th power of possibilities as you won’t have to complete a bracket for every 16 Seed winning the title Variation, which gives us:
1,152,921,504,606,850,000 Quintillion! That’s pretty Good! We knocked off over 17 Q brackets!
However, the news gets better! Based on the fact that we know from history that only 3 15 seeds have ever won a SINGLE GAME, we can reduce the number of brackets we need to fill out by another 3, meaning 2 to the 57th power:
144,115,188,075,856,000 – Hey! Getting manageable…Were out of the Quintillions!
Also, assume for a second that there have never been ANY 12 through 16 seeds in the Final Four! If we wanted to eliminate upsets early, we could then take another 20 decisions out of the matrix giving us 2 to the 37th power:
137,438,953,472 That’s only in the Billions! I think that’s almost doable!
But wait! What if we assume per the Bracket Science Championship Criteria that only 8 teams this season can actually win the whole thing? Now, we can limit the number of seeds we have to take all the way to the championship and only take them to their “Seed Limit” of where they would lose to a higher seed. This one is tricky as we have to do two calculations and add them together. So, we in effect need to take the 8 champions we pick per Bracket Science, or 2 to the 8th power and then add the remaining 29 seeds for the total potential scenarios against those 8 seeds winning, or 2 to the 29th giving us:
536,870,912 Million! That’s DOABLE!!!! For a Billion Dollars! Isn’t it? Come On!
Who’s with me???
Okay…By your silence I’m guessing that you’re still thinking it’s an impossible task. And I happen to agree with you. There’s only:
345,600 seconds between 6 PM Sunday and Noon Thursday.
Which means we would all still need to fill out 1,500 or so brackets per second….
Wow…No wonder everyone came out with a Billion Dollar Bracket idea….It looks impossible....because it is.
Anyway, have fun filling out your brackets and may the best (and LUCKIEST) man have a shot at winning the Billion…
Me, I just wanna’ win the office pool.