Published by the Students of Johns Hopkins since 1896
September 23, 2020

How math can help to create winning brackets

By VIVIAN LI | February 13, 2020

One in 9.2 quintillion (that’s 92 followed by 18 zeros) — those are the odds of one generating a perfect bracket for the National Collegiate Athletic Association Men’s Division-I Basketball Tournament, or what is more commonly known as “March Madness.” On Feb. 6, the Hopkins Undergraduate Society for Applied Math (HUSAM) invited Professor Tim Chartier from Davidson College to give a talk on how ranking methods and algorithms could better your chances of making a winning bracket.

Once or twice a year, HUSAM invites speakers to talk about popular or intriguing applications of mathematics.

“Professor Chartier was suggested to us by Dr. Wierman, a professor in Applied Math and Statistics,” Steven Witkin, a senior in Applied Math and Statistics (AMS), and president of HUSAM, explained in an interview with The News-Letter.

“We emailed him and luckily we were able to set up a talk in February, just when March Madness is starting to become relevant.”

In his talk, Professor Chartier told the audience that he first became involved in the field of bracketology in 2008, when he was developing ranking methods for search engines.

“Data science will create something, but you have to figure out if it means anything,” Chartier said.

To figure out if his data meant something, Chartier and his colleagues created March Madness brackets to test their ranking methods. Their algorithm slated the better ranked team to win each pairing. 

Chartier’s team ended up submitting eight brackets to ESPN, out of which their best prediction landed in the 97th percentile amongst four million submissions. In the following years, Chartier extended this project to his students, and eventually the public to participate, which made the project more robust. Robust, but not perfect.

“The truth is, no one could have a perfect bracket,” Chartier explained.  

The computing power and storage space that it takes to run through all 9.2 quintillion possibilities that arises from the games is simply unimaginable. And this is exactly where mathematics comes in to help you narrow down the choices. 

According to statistics on bracket submissions of past March Madness tournaments, on average, people were able to predict 70 percent of the games correctly. So if your model is able to be just one percent better, your choices would be limited significantly.

However, it is easier said than done. During the talk, Chartier invited the audience to participate in a simple activity — they were to come up with a ranking for the teams based on the outcomes of the matches Chartier showed them. Initially predictions were comparable, but dispute quickly arose as the number of teams increased, and the wins and losses became more complicated.

“One of the most important parts about bracketology is actually realizing that people who do not follow the sport may beat you,” Chartier said.

According to him, non-fans can often do better because they do not try to make the math fit their perception. Indeed, making brackets demands an equal share of skill and luck. Therefore it is perfectly normal when a mathematical model goes wrong. 

“You can always override the mathematics. That’s not a bad thing — people who do applied math are always used to the randomness in things,” he said.

Towards the end of the talk, Chartier invited the audience to try generating their own brackets using the website that uses his ranking methods. It was unlike other sports websites that simply give you a ranking; here you could generate your own by tweaking how you weigh each element. 

For example, you can choose to weigh games played over the course of the tournament uniformly, linearly or on a logarithmic scale. You can decide whether to take the scores into account. You can take home advantage into account. 

The possibilities go on. Although the audience was only dipping its toes in the algorithm, they could already get a clear sense of the myriad of factors a ranking method could take into account.

Chartier’s talk, which provided insight into the applications of math at a novel angle, turned out to entertain Applied Math and non-AMS majors alike.

“I found it surprising how different the rankings generated by his methods can be combined to form the national rankings that are used by ESPN and CBS,” Witkin said. 

Whether you would like to gain an edge on your brackets this year, or just want to play around with the math, you should definitely go explore the website: www.marchmathness.davidson.edu

For coding enthusiasts, the website also includes source codes for Chartier’s rankings in Python, Java and Mathlab. For hardcore math-lovers, the linear algebra behind the ranking is explained in Chartier’s paper, “Bracketology: How can math help?”

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