Many studies, including some dealing with shot selection in basketball and play selection in football, demonstrate that the generalized matching equation provides a good description of the allocation of time and effort to alternative responses as a function of the consequences of those alternatives. We examined whether it did so with respect to left- and right-handed at bats (alternative responses) and left- and right-handed total bases earned, runs batted in, and home runs (three consequences) for the outstanding baseball switch-hitters Mickey Mantle, Eddie Murray, and Pete Rose. With all hitters, undermatching, suggesting insensitivity to the consequences of behavior (reinforcement), was evident and there was substantial bias towards left-handed at bats. These players apparently chose handedness based on the rule “bat opposite the pitcher,” not on differential consequences obtained in major league games. The present findings are significant in representing a counter-instance of demonstrations of a matching relationship in sports in particular and in human behavior in general and in calling attention to the need for further study of the variables that affect choice.