A Ranking Model Motivated by Nonnegative Matrix Factorization with Applications to Tennis Tournaments

TL;DR

This paper introduces a new ranking model for tennis players that combines nonnegative matrix factorization with the Bradley-Terry-Luce model, revealing latent factors like court surface influence and identifying top players objectively.

Contribution

The paper develops a novel ranking framework integrating NMF with probabilistic modeling, providing an efficient algorithm and uncovering latent variables affecting player performance.

Findings

Court surface significantly impacts male player performance.

The model objectively identifies top players across different surfaces.

Latent variables influencing performance are effectively uncovered.

Abstract

We propose a novel ranking model that combines the Bradley-Terry-Luce probability model with a nonnegative matrix factorization framework to model and uncover the presence of latent variables that influence the performance of top tennis players. We derive an efficient, provably convergent, and numerically stable majorization-minimization-based algorithm to maximize the likelihood of datasets under the proposed statistical model. The model is tested on datasets involving the outcomes of matches between 20 top male and female tennis players over 14 major tournaments for men (including the Grand Slams and the ATP Masters 1000) and 16 major tournaments for women over the past 10 years. Our model automatically infers that the surface of the court (e.g., clay or hard court) is a key determinant of the performances of male players, but less so for females. Top players on various surfaces over this longitudinal period are also identified in an objective manner.