## In Which an Infinite Number of Monkeys Brag About Picking Northern Iowa

By David Roher

There are over nine quintillion ways to fill out your bracket, and over four hundred trillion ways to predict the first two rounds alone. Based on the craziness of the first four days of the tournament, I bet you wish your bracket was one of the other nine quintillion. With the overall #1 seed, a #2 seed, and three #3 seeds gone, I was thinking that I could have done better by simply flipping a coin to decide each game.

To test the quality of a coin-flip bracket, I examined each of the 2^48 possible brackets of the first two rounds, awarding one point for a first-round pick and two points for a second-round pick. Going bracket by bracket would take quite a while (even for a computer), so I used a different method. If we only care about final point total, there are only three numbers to calculate:

• The first-round successes of teams picked to win in the first round, then lose in the second (0-16 possible points)
• The first-round successes of teams picked to win in the first and second round (0-16 possible points)
• The second-round successes of teams picked to win in the second round (0-2n possible points, where n is the number of teams who advanced in the above category)

There are roughly 4000 permutations there, making analysis more manageable. Through calculating the probability of each permutation, I was able to create the above histogram. The most frequent point total is 24, the result of roughly 21 trillion brackets. If you fill out a bracket with unweighted-coin flips, there’s a 7.5% chance you’ll get 24 points.

How does this compare to an average bracket? One that always advanced the higher seed would have netted 38 points thus far. A total of 38 or higher only occurs in roughly 2 trillion brackets (those totals are in green on the graph). This makes your chances of generating a coin-flip bracket as good or better than that of the top-seed method less than 1% of the time, even in a tourney as unpredictable as this one.

Congratulations: a monkey would probably not have picked a better bracket than yours. Give yourself a pat on the back with your opposable thumbs. But what if you picked all #1 and #2 seeds to advance to the Sweet 16 in every possible bracket, and flipped a coin to determine the other games?

In that case, 36 points is actually the most likely result, and 44% of possible brackets actually exceed that number. Using this method would have given you a 72% chance to be tying or beating Dick Vitale (34 points in his ESPN bracket) so far.

Here’s hoping that the next four rounds will be just as unpredictable.