Mathematics and Statistics Colloquium
Rating and ranking based on pairwise comparisons has a long history and a wide range of application areas. In this talk we will present a method that goes back to Zermelo but has been rediscovered and renamed several times since. His original application was to chess tournaments, but the method has been applied in many areas including taste tests, rhetorical power analysis, and gamete competition models.
Using modern technology, it is relatively easy to apply the same method to much larger data sets, such as the complete list of all NCAA Division I basketball games. The central ideas behind Zermelo's method are accessible to calculus students and provide an introduction to both maximum likelihood and EM algorithms.