The advantage of lefties in one-on-one sports

Left-handers comprise approximately 15% of professional tennis players, but only 11% of the general population. In boxing, baseball, fencing, table-tennis and specialist batting positions in cricket the contrast is even starker, with 30% or more of top players often being left-handed. In this paper we propose a model for identifying the advantage of being left-handed in one-on-one interactive sports (as well as the inherent skill of each player). We construct a Bayesian latent ability model in the spirit of the classic Glicko model but with the additional complication of having a latent factor, i.e. the advantage of left-handedness, that we need to estimate. Inference is further complicated by the truncated nature of data-sets that arise from only having data of the top players. We show how to infer the advantage of left-handedness when only the proportion of top left-handed players is available. We use this result to develop a simple dynamic model for inferring how the advantage of left-handedness varies through time. We also extend the model to cases where we have ranking or match-play data. We test these models on 2014 match-play data from top male professional tennis players, and the dynamic model on data from 1985 to 2016