Dynamic team attack and defense strength in international rugby union

Abstract

Abstract This article develops and compares dynamic Bayesian paired-score models for men’s international rugby union. The models decompose team quality into latent attack and defense strengths and embed these in a paired negative-binomial score model. We compare three alternative specifications for the evolution of latent strengths over time: a weekly random walk, a continuous-time random walk, and a two-speed event-gap process that combines background elapsed-time diffusion with additional active-appearance variation. The models are evaluated using out-of-sample forecasts for 2025 and benchmarked against both a simple exponential error-correction smoother and the official World Rugby rankings algorithm. All three Bayesian models outperform these simpler benchmarks, although there is little to separate the three on predictive accuracy alone. The continuous-time and two-speed specifications are especially attractive, however, because they retain similar predictive performance while better reflecting the irregular timing of international rugby. Then, examining the evolution of latent attack and defense strengths among tier-one rugby teams from 2020 to 2025, we discuss how the models reveal meaningful differences in teams’ attacking and defensive profiles, illustrating how this type of analysis can contribute to wider sports discourse and public discussion.