  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.
