@Lane A. As a former baseball player myself (pac-10, well 12 now), I know the commitment it takes to be successful there... You'll do well in real estate as you'll just transfer the work ethic over. I never made millions in the pros but have made a few million in business / investing and I think it's the result of transferring hours in the batting cage over to the next "obsession".
The awesome part about your job is you get to be in a bunch of different cities throughout the spring and summer on the club's dime. I'd pull out the schedule and do a little research on those areas and then when you get a little off time while your there, go check things out and do some networking with property management, other investors, etc... (just don't lose focus on playing ball, you only get one youth to spend on that my old catcher's knees ache just writing that)
You've got the perfect situation.. play ball spring and summer, and buy houses in the fall and winter. I think you're going to need to get good at managing property managers though as I don't think anybody should do everything solo, especially if they have to be on the road a lot.