Andrew Fritz ’26 has played soccer his whole life. So when it came time to write a senior thesis, he wanted the math to meet the beautiful game. The result is “Quantifying Individual Player Performance in Association Football (Soccer),” a model that assigns value to every on-ball action a player takes and uses that data to compare players across positions, leagues, and eras.
The idea grew out of a junior seminar paper on Markov chains, a method for modeling processes where each event depends only on the one before it. Fritz, an applied math major with a minor in economics, found research applying that framework to soccer and followed the thread. His model, built on a metric called expected threat, calculates how each action — passing, dribbling, or shooting — shifts the probability that a team will score. Using data covering every match across Europe’s top five domestic leagues, the 2018 World Cup, and the 2016 European Championships, Fritz developed a framework that accounts for factors like set-piece quality, foul severity, and the strength of the opposition.
His advisor, Professor of Mathematics and Statistics Robert Manning, gave Fritz ample room to explore while keeping the project coherent. “He gave me a lot of freedom to work through different ideas on my own, but was excellent at helping me connect different aspects of the work together concisely,” Fritz says. Manning also helped him navigate the challenge of sustaining a long research project for the first time.
The model draws on skills Fritz developed across numerous courses, including “Mathematical Modeling, Microeconomics, and Foundations of Data Science” at the University of Pennsylvania, made possible through the Quaker Consortium. He says that building most of the model’s components himself taught him to think about systems holistically. “Working alongside the data was frustrating at times,” he admits, “but I was able to create a model that effectively measured players’ actions and can be used to compare players who play similar positions.”
His biggest finding? By his model’s measure, superstars and endless debate topics Messi and Ronaldo are equally good, though Messi plays a more involved role in the buildup of play. Fritz is quick to note the project was always meant to be fun. “Rob and I knew this was a fun application of what I’d learned to a topic I enjoy,” he says, adding that professional clubs operate with far more advanced versions of similar tools.
Still, the skills he grew at Haverford will translate into his post-College life. This fall, Fritz will join Bates White, an economic consulting firm in Washington, D.C., where he will help build economic models that inform legal proceedings, work he sees as a natural extension of what he practiced in his thesis. He also plans to apply to graduate school after a few years in the field.