Mathematical Modeling Seminar: Who is the GOAT? Sports Rankings and Random Walks on the Symmetric Group

Mathematical Modeling Seminar
Who is the GOAT? Sports Rankings and Random Walks on the Symmetric Group

Dr. Juan Carlos Martinez Mori
Schmidt Science Fellow and a President’s Postdoctoral Fellow
Georgia Institute of Technology

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Abstract:
Given a collection of historical sports rankings, can one determine which athlete is the Greatest Of All Time, i.e., the GOAT? In this work, we introduce a data-driven random walk on the symmetric group to obtain a stationary distribution over athlete rankings, spanning different time periods in sports history. We combine this distribution with a notion of stochastic dominance to obtain a partial order over the athletes. Implementing our methods by using publicly available data from the Association of Tennis Professionals (ATP) and the Women’s Tennis Association (WTA), we determine the GOATs in the respective categories. This is joint work with Gian-Gabriel Garcia.

Speaker Bio:
Dr. Martínez Mori is a Schmidt Science Fellow and a President's Postdoctoral Fellow with the H. Milton Stewart School of Industrial and Systems Engineering at the Georgia Institute of Technology. He earned his PhD in Applied Mathematics from the Center for Applied Mathematics at Cornell University (2023). Prior to that, he earned his BSc in Civil Engineering and minor in Computer Science from the University of Illinois at Urbana-Champaign (2017). Prior to joining Georgia Tech, he was a Postdoctoral Fellow at SLMath (formerly MSRI). He has also participated in semester-long research visits at ICERM and IPAM, research internships in industry, and REU mentoring at MSRI and ICERM. He was born and raised in Guayaquil, Ecuador. He is broadly interested in discrete mathematics. His current research spans mathematical programming and game theory, enumerative and algebraic combinatorics, applications around equity in public decision-making for the built environment, and most recently sports analytics.

Intended Audience:
All are Welcome!