Estimating the salaries of professional athletes has received a substantial amount of attention both in the press and in academic journals. A statistical technique that can be used to obtain an estimate of a player's salary with a given set of performance characteristics is the classical least squares regression analysis. This technique does not work well, however, if the data upon which the model is based contain outliers or are not normally distributed. In this paper we focus our attention on the salaries of American League baseball players in 2007 and demonstrate the usefulness of an alternative estimation approach that of quantile regression analysis. Our results indicate that ordinary least squares regression overestimates the salaries of poor players, and underestimates the salaries of star players. This, we believe, is a compelling reason to apply quantile regression in the prediction of baseball player salaries.