Deterministic Evolution of Strength in Multiple Comparisons Models: Who is the Greatest Golfer?

We present a statistical methodology for fitting time-varying rankings, by estimating the strength parameters of the Plackett-Luce multiple comparisons model at regularly spaced times for each ranked item. We use the little-known method of barycentric rational interpolation to interpolate between the strength parameters so that a competitor's strength can be evaluated at any time. We chose the time-varying strengths to evolve deterministically rather than stochastically, a preference that we reason often has merit. There are many statistical and computational problems to overcome on fitting anything beyond toy' data sets. The methodological innovations here include a method for maximizing a likelihood function for many parameters, approximations for modelling tied data and an approach to the elimination of secular drift of the estimated strengths'. The methodology has obvious applications to fields such as marketing, although we demonstrate our approach by analysing a large data set of golf tournament results, in search of an answer to the question who is the greatest golfer of all time?'