Fame and fortune in elite tennis

Abstract

Previous research bas suggested that prize money serves as an incentive for player performance, whereas rankings are considered more useful for administrative purposes such as tournament selection, seeding, handicapping and for predicting match outcomes. However, for top players it may be that it is their ranking which serves as their incentive to perform, because extraneous income and reputation is tied to rankings rather than to prize money per se. There is of course a relationship between rankings and prize money, but the intricacies of the ATP ranking system means that this relationship is perhaps not as predictable as one might expect. This paper investigates the relationship between rankings and prize money and performance using data for the top 108 ATP singles players in 2011. Performance is measured in tenns of the proportion of matches won and the number of matches played in the years 2004 to 2010. Generalized linear models and more accurate multi-level models, with binomial and Poisson response distributions, are used for this purpose. Differing results for these two models indicate that it is essential to take account of the repeated measures nature of the data as is done in the multi-level analysis. However, marked differences in the results obtained for the two performance measures suggest that more work is needed in order to reach a deeper understanding of the factors motivating elite tennis players