Analysis of GNAC Volleyball using the Bradley-Terry Model

Abstract

Ranking is the process by which a set of objects is assigned a linear ordering based on some property that they possess. Not surprisingly, there are many different methods of ranking used in a wide array of diverse applications; ranking plays a vital role in sports analysis, preference testing, search engine optimization, psychological research, and many other areas. One of the more popular ranking models is Bradley-Terry, which is a type of aggregation ranking that has been used mostly within the realm of sports. Bradley-Terry uses the outcome of individual matchups (paired-comparisons) to create rankings using maximum-likelihood estimation.

This project aims to briefly examine the motivation for modeling sporting events, review the history of ranking and aggregation-ranking, communicate the mathematical theory behind the Bradley-Terry model, and apply the model to a novel volleyball dataset.