  Dynamic paired comparison models, such as Elo and Glicko, are frequently used
for sports prediction and ranking players or teams. We present an alternative
dynamic paired comparison model which uses a Gaussian Process (GP) as a prior
for the time dynamics rather than the Markovian dynamics usually assumed. In
addition, we show that the GP model can easily incorporate covariates. We
derive an efficient approximate Bayesian inference procedure based on the
Laplace Approximation and sparse linear algebra. We select hyperparameters by
maximising their marginal likelihood using Bayesian Optimisation, comparing the
results against random search. Finally, we fit and evaluate the model on the
2018 season of ATP tennis matches, where it performs competitively,
outperforming Elo and Glicko on log loss, particularly when surface covariates
are included.
