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Inspired by applications in sports where the skill of players or teamscompeting against each other varies over time, we propose a probabilistic modelof pairwise-comparison outcomes that can capture a wide range of time dynamics.We achieve this by replacing the static parameters of a class of popularpairwise-comparison models by continuous-time Gaussian processes; thecovariance function of these processes enables expressive dynamics. We developan efficient inference algorithm that computes an approximate Bayesianposterior distribution. Despite the flexbility of our model, our inferencealgorithm requires only a few linear-time iterations over the data and can takeadvantage of modern multiprocessor computer architectures. We apply our modelto several historical databases of sports outcomes and find that our approachoutperforms competing approaches in terms of predictive performance, scales tomillions of observations, and generates compelling visualizations that help inunderstanding and interpreting the data.

Pairwise Comparisons with Flexible Time-Dynamics