A dynamic paired comparisons model: Who is the greatest tennis player?

We present a methodology for fitting time-varying paired comparisons models in which the parameters are allowed to vary deterministically, as opposed to stochastically, with time. Our dynamic paired comparisons model is based on a new closed-form for Stern's continuum of paired comparisons models which include the Bradley-Terry model and the Thurstone-Mosteller model. The dynamic element of our model is facilitated by utilising barycentric rational interpolants BRIs. An incidental result of our work is to show that BRIs often provide a better fit to data than the obvious alternative of spline interpolation. We use our model to shed light on the debate of who is the greatest tennis player of the Open Era of men's professional tennis since 1968. Constructing a single rankings list from our model is not trivial as there are many alternative metrics that could be used to identify which player was the best ever. We present three alternative rankings lists derived from our model. In general our rankings lists largely agree with the rankings list based on number of Grand Slam titles won, which, to some extent, validates our choice of metrics. So who is the greatest tennis player of the Open Era? Roger Federer seems like the most likely candidate, with Bjorn Borg and Jimmy Connors close behind.