Recent advances in the Bradley--Terry Model: theory, algorithms, and applications

This article surveys recent advances in the Bradley-Terry (BT) model and its extensions. We focus on statistical and computational aspects, with particular emphasis on the regime in which both the number of objects and the volume of comparisons tend to infinity-a setting relevant to large-scale applications. The main topics include asymptotic theory for statistical estimation and inference, together with the corresponding computational algorithms. We also review applications of these models in sports analytics, social choice, psychometrics, and machine learning. Finally, we discuss several key challenges and outline directions for future research.