Should You Bet the House on Pereira? by Carlos Hernandez Tavares ’25

Pairwise comparisons are ubiquitous in our everyday life. When we pick our favorite ice cream, it’s much easier to choose between two flavors than to choose between 32. When we debate who is the greatest tennis player of all time, we rarely have the privilege of having a head to head matchup between every single possible contender. Luckily, mathematicians Ralph Bradley and Milton Terry (building upon previous work) constructed the Bradley–Terry model for pairwise comparisons, which allows us to—even in cases where not all objects have had head to head matchups—create probabilistic rankings for a set of pairwise comparisons.

In this colloquium, we will explore Thomas Jech’s derivation of the Bradley Terry model published in his paper “The Ranking of Incomplete Tournaments: A Mathematician’s Guide to Popular Sports.” We will trace Jech’s proof before applying the Bradley–Terry model to predict the winner of UFC 313’s main event: Pereira v. Ankalaev.