In a simple model for sports, the probability A beats B is a specified function of their difference in strength. One might think this would be a staple topic in Applied Probability textbooks (like the Galton–Watson branching process model, for instance) but it is curiously absent. Our first purpose is to point out that the model suggests a wide range of questions, suitable for “undergraduate research” via simulation but also challenging as professional research. Our second, more specific, purpose concerns Elo-type rating algorithms for tracking changing strengths. There has been little foundational research on their accuracy, despite a much-copied “30 matches suffice” claim, which our simulation study casts doubt upon.
"Elo Ratings and the Sports Model: A Neglected Topic in Applied Probability?." Statist. Sci. 32 (4) 616 - 629, November 2017. https://doi.org/10.1214/17-STS628