How to Win at Math(ematical Modeling)

Three Duke Rugby players who are math majors tackled a challenge inspired by professional soccer

Three students posing and smiling for the camera

This is a summary of a story written by Cara August on Trinity College of Arts & Sciences.

Daniel Cheng, Malachy O’Donnabhain and Zain Radwan met through Duke Rugby. They’re also math majors. And now they earned top honors in the international Mathematical Contest in Modeling for their project that tackled a challenge inspired by professional soccer: how to build a team that can remain competitive, financially sustainable and avoid the steep costs of relegation – demotion to a lower league.

“It was exactly the type of problem that fit our interests,” Cheng said, a double major in math and economics. “It involved operations research, economics and statistical modeling all at once.”

First, they spent a lot of time upfront just breaking the problem down. Once they agreed on a structure, they divided up the work.

Their model combined economics, operations research and statistical analysis to evaluate player performance, injury risk, ticket pricing and revenue optimization. A key metric they designed was called PP90 (Performance Per 90 Minutes), designed to compare the value of players across different positions while accounting for playing time and injury risk.

In addition to earning the contest’s Outstanding Winner designation against more than 32,000 teams from 28 countries, they received awards for creativity and technical excellence and a $9,000 prize.

Beyond the awards, the students say the experience reinforced a simple lesson about college life. “There are so many opportunities here,” O’Donnabhain said. “If you just try things and put yourself out there, you never know what might happen.”

To learn more about their model, go to Trinity College of Arts & Sciences.