I've been playing (and playing around with) sports simulations since I was knee-high to a grasshopper. I actually created my own stat-based baseball game (laying out teams on COBOL programming sheets that my Dad brought home from work) before I even saw my first commercial game - Statis-Pro Baseball in the late 1970s. (This wonderful piece brings back a lot of great memories from those days.) From there, it was on to the APBA Master Game and my first league play in college, and I've played pretty much every baseball game that's been on the market over the past forty or fifty years.
I currently play Season Ticket Baseball more or less exclusively - it's got a blend of playability and detail that I've not found anywhere else, to go along with excellent realism and aesthetics - but I maintain soft spots (and admiration) for Inside Pitch, Box Seat and Replay. There are many other fine simulations available these days as well - this is truly a Golden Age for tabletop baseball!
[Image Credit: The banner image for the front page of this blog is from an historical photograph of Opening Day, 1908 at Hilltop Park in New York which was colorized by Baseball In Color.]