The Likelihood Of A Perfect March Madness Bracket

March Madness is finally here, the field of 68 has been revealed, and the betting odds have been published. Across the country, fans will participate in the time-honored tradition of bracketology, trying to predict the winners of the men’s and women’s NCAA basketball tournaments. Some will meticulously analyze every possible upset, hunting for this year’s Cinderella story, while others might make their picks based on something as simple as the team’s mascot. While there are countless ways to fill out a bracket, one thing is almost certain this March: not a single one of the tens of millions of brackets will be perfect.

Computing Likelihood Of A Perfect March Madness Bracket

Calculating the likelihood of a perfect bracket is an exercise in applied probability. Each game in March Madness is an independent event meaning the outcome of one game does not affect the outcome of the others. For every matchup, there will always be one winner and one loser. Therefore, the likelihood of predicting a perfect bracket is equivalent to the likelihood of correctly predicting the outcome of 63 independent matchups. In this case the 63 matchups are the 32 first round games, 16 second round games, 8 Sweet Sixteen games, 4 Elite Eight games, 2 Final Four games, and 1 Championship game in March Madness.

To determine the likelihood of a perfect bracket, we compute the product of the likelihoods of correctly picking each of the 63 games. In mathematical terms, the likelihood of an event occurring is denoted P(event occurs). Therefore, we can represent the likelihood of a perfect bracket as the following:

March Madness Coin Flip Model

The simplest way to estimate the probability of a perfect bracket is to assume each pick is made completely at random. This would be the equivalent of selecting March Madness picks based on the flip of a fair coin. In other words, there is no available information about either team in any of the games. It would be the equivalent of correctly guessing the outcome of a fair coin flip 63 times in a row.

Correctly guessing the outcome of a single coin flip has a likelihood of 50% or 0.50. Therefore, the likelihood of guessing 63 coin flips in a row is 0.50 multiplied by itself 63 times. While this model is basic, it represents the extreme case of random guessing, giving us the lowest possible chance of a perfect bracket. The likelihood of predicting a perfect bracket with random guessing is 0.00000000000000000010842. This is the equivalent of 1 perfect bracket in 9.223 quintillion submissions.

March Madness Chalk Model

Fortunately, the NCAA Tournament Selection Committee provides some guidance on the likelihood of the outcome of individual games in the form of team seeding. In each of the four regions of the tournament, teams are seeded No. 1 through No. 16 where No. 1 is considered the best team and No. 16 is considered the worst team. While March Madness is known for its surprises, the higher-seeded team typically has the edge. This leads to a popular strategy known as “chalk,” where people predict that the lower-seeded (better) team will win every game.

Using historical data on matchups between different seeds, we can calculate the likelihood that a March Madness bracket will be perfect based on all chalk predictions. In other words, it is the likelihood that no upsets will occur. With this strategy, correctly predicting the winner becomes more likely than random guessing. For example, No. 1 seeds are 154-2 all time against No. 16 seeds. This is the equivalent of flipping a coin which lands on heads 98.7% of the time. The most difficult first round matchup to predict is the No. 8 seed versus the No. 9 seed which goes in favor of the No. 8 seed just 50.6% of the time.

When using seeding information alone, the likelihood of a perfect bracket increases dramatically. To correctly predict the outcome of 63 games is the product of many likelihoods which are greater than 50%. The likelihood of a perfect bracket when using the chalk method is 0.0000000000145129. This is the equivalent of 1 perfect bracket in 68.904 billion submissions. While this is still a shockingly small number, the likelihood of a perfect bracket using the chalk method is over 100 million times greater than that of making completely random picks.

The Elusive Nature of the Perfect March Madness Bracket

While seeding can be a simple and effective tool to improve your chances at a perfect bracket, do not be surprised if your bracket gets busted early. In fact, it is highly likely that a perfect bracket will remain elusive in our lifetime. To put it in perspective, compared to predicting a perfect bracket, you are over 200 times more likely to win the Powerball, 15 thousand times more likely to die by shark bite, and 4 million times more likely to be struck by lightning.

Luckily, part of the fun and excitement of March Madness is the uncertainty that underpins every game and the upsets that we witness without fail every year. So, this year, go forth and trust your gut. Odds are, you will be wrong.