On the (Page) Ranking of Professional Tennis Players

We explore the relationship between official rankings of professional tennis players and rankings computed using a variant of the PageRank algorithm as proposed by Radicchi in 2011. We show Radicchi’s equations follow a natural interpretation of the PageRank algorithm and present up-to-date comparisons of official rankings with PageRankbased rankings for both the Association of Tennis Professionals (ATP) and Women’s Tennis Association (WTA) tours. For top-ranked players these two rankings are broadly in line; however, there is wide variation in the tail which leads us to question the degree to which the official ranking mechanism reflects true player ability. For a 390-day sample of recent tennis matches, PageRank-based rankings are found to be better predictors of match outcome than the official rankings.