Event Date
Speaker: Guanyu Hu, Associate Professor, Department of Statistics and Probability at Michigan State University
Title: How Competitive Is Competition? A Bayesian View of Parity Over Time
Abstract: How competitive is a competition, really? In settings such as professional sports leagues, parity mechanisms are designed to keep competitors evenly matched, yet observed rankings often suggest substantial differences that may be driven as much by sampling variability as by true differences in ability. This raises several statistical questions: how can competitive balance be quantified in a principled way, how does it evolve over time, and what rank tier structure can be learned from the data?
In this talk, I will present a Bayesian framework that treats competitive balance as a model based quantity rather than a purely descriptive summary. The model represents latent competitor abilities within a time varying geometric constraint, whose scale provides an interpretable measure of parity. This geometric constraint also induces a data driven rank tier structure: under strong parity, the posterior distribution naturally compresses competitors into groups that are not credibly distinguishable, whereas weaker parity allows clearer and more meaningful separation. In this way, both competitive balance and rank tiers are learned jointly within a single probabilistic framework. To capture temporal dynamics, I introduce a hidden Markov mixture structure that allows competitive regimes and tier configurations to persist and change over time while avoiding the excessive fragmentation that often arises in existing dynamic clustering models.
I illustrate the approach with applications to professional sports leagues, showing how it can be used to study the rise and fall of parity, the persistence of competitive tiers, and the uncertainty inherent in ranking based comparisons. More broadly, the framework provides a probabilistic perspective on when rankings are statistically informative and when apparent differences should be attributed mainly to noise.
Bio: Guanyu Hu is an Associate Professor at Michigan State University whose research focuses on Bayesian nonparametric methods and sports analytics. He has served as Chair of the ASA Statistics in Sports Section, Program Chair of the ISBA East Asia Chapter and as an Associate Editor for The Annals of Applied Statistics, Biometrics, and the Journal of Quantitative Analysis in Sports. He is also a member of the organizing committee for the American Soccer Insights Summit. His work develops flexible Bayesian methodology for modeling sports performance, competition, and decision-making.
Faculty website (external link)