While we're on the subject of baseball (and that is not a subject you'll very often find me talking about--no offense, Red Sox), I have to mention this XKCD page: Relativistic Baseball.
Have you considered what the effects might be if a pitcher could throw a baseball toward the plate at just under the speed of light? No? Why ever not? Well, the creator of XKCD has, and you owe it to yourself to read his eye-opening and funny analysis. Suffice to say, the effects on the surrounding habitable zone are not pretty. There is surely an SF story in this somewhere.