Bracket Perfection

“While there is no simple path to success, it sure doesn’t get much easier than filling out a bracket online.” These boarder-line philosophical words were uttered by the great billionaire Warren Buffet. As all Americans have heard, unless you live under a rock, Buffet has offered one billion dollars to whoever makes a perfect bracket for NCAA March Madness tournament. It has surprisingly gotten quite the hype and causing people who would never fill a bracket out giving it a shot.

I myself have participated in March Madness for the last 3 years now and being the mathematician I am I have already done the research for the perfect bracket. It seems every year there are outrageous rewards from people to whoever fills the perfect bracket. Unfortunately without much digging one will find that no one has EVER filled out a perfect bracket. The odds are 1 over 2 to the 63rd power (that’s 1 in 9 quintillion).  With odds like that I would be willing to offer my first born child to whoever gets the perfect bracket. With that being said that does not mean I have not tried to create the perfect bracket… and I think I succeeded.

I used a little history to help make this bracket. For instance, a number one seed has never been beat by a number 16 seed. So, all four of the first seed teams will win round one. That makes picking 4 out of the 63 games easy. That means only 59 more games to pick. Now things get a little tricky; only once in history has a team seeded higher than 11 made it to the elite eight. I think this makes it safe to say that the seeds 12-16 won’t make it to the elite eight; meaning they will lose somewhere before then. This also means in the elite eight seeds 1-11 could be in it. For each region 2 out of the 11 teams will be in the elite eight. There are 230 teams that have been in the elite eight in the last 29 years.

Seed # % to Elite Eight
 1 34.783%
2 23.487%
3 13.043%
4 7.826%
5 3.478%
6 5.652%
7 3.043%
8 3.043%
9 .869%
10 3.043%
11 1.304%

We see that seeds 1 and 2 have the largest probability to getting to the Elite Eight. To be honest though there will never be a time in March madness where all the teams in the elite eight are all 1 and 2 seed teams. This means we have to step away from the math and guess. In each region you need to pick a 1 or 2 seed team for the elite eight. Typically if they are in the big 10 conference you should put them through…well unless it’s Michigan (they typically choke). As for the other team for each region I usually skip around by picking at random.

After you establish your elite eight you must make educated guesses for the games that were in the sweet sixteen and second round. You must expect upsets so don’t pick the lower seed. For the elite eight I have two 1st seeds, two 2nd seeds, 3rd seed, 4th seed, 10th seed, and 8th seed.  The odds of these seeds going to the final four are

Seed # % to final four
1 41.228%
2 21.93%
3 12.281%
4 11.404%
8 3.509%
10 0

Again you’re not going to get all 1 and 2 seeds in the final so you won’t pick all 1’s and 2’s. We can clearly see the 10th seed is out of the picture. I think it would be safe to both 1 seeds, one of the 2 seeds, and the 4th seed. For the final game you want to a number one seed and then random so we will go with 2. For the final you need to flip a coin, a head is seed 1 and a tails is seed 2. In this instance we go 2. So my bracket looks like this

Image

Now for each region you can you could do the same steps. For instance, this could have been Michigan winning it all. Essentially you must be the best guesser in the world for all the possible options.

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One thought on “Bracket Perfection”

  1. So how many different brackets meet your criterion? Just 4 by rotation? Also curious that no 12s show up.

    Good explanation of your thinking.
    Consolidation: be interesting to relate this to your actual bracket. Which did well… coincidence?
    other C’s +

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