I dunno...I've shot baseball with a few different lenses, and depending on WHERE you shoot from, different lenses will be better, or easier to use. If you can shoot from the home team's dugout, a long lens is a PITA to use, and a zoom like a 70-200 f/2.8 is pretty handy, whereas a 300/2.8 is too long, and the 200/2 is also too long.
There are different kinds of baseball images: shots that are "vanity shots" that show individual players sort of isolated from the action; newspaper shots that show action with some context (maybe even, gasp, two or even three players in one frame!), and other types of photos also.
I've used 70-200, 100-300 Sigma f/4 HSM-APO, 300/2.8 AF-S,200/2, 400/3.5 manual focus with pre-set focusing distance, 80-400 f/4.5~5.6and APS-C, APS-C with both the standard 1.5x crop and also a high-speed 8.2 frames per second 2.0 x crop, and Full frame.
I think in terms of overall "BEST" image, the 300/2.8 is the best focuser for speed, sureness, AND its big, wide aperture (the physical SIZE of the hole in absolute terms, not relatrve, not the f-value) allows you to shoot from behind the backstop or through side-fences, and TOTALLY defocus the chain-link; the 300mm focal length lens is NOT too good for really close-in shots, like say 1st base action from the home team dugout; it is actually wayyyy too long a lens on 1.6x.
The 300/2.8 has MUCH better optics than these low-cost 150-600 zooms AND allows MUCH faster shutter speeds, for very deep,deep crop-ins on outfield shots, or from 3rd base dugout shooting across the infield to first base and to second base slides. The big lenses lend credibility to you: it's a weird psychological effect, but very,very real.
For stationing yourself at third base area in the stands, the longer zoom lenses, with 100mm short end, come into play: the Sigma 100-300 f/4 HSM would be the best easily-hand-held lens for covering close and moderately-far action. The APS-C cameras really change the way lenses behave.
Canon 's 70-200/2.8 MK-II has ASTOUNDING optics...I would not overlook it. People forget about cropping-in at the computer a lot these days. Only you can know how you shoot a game, and under what kind of lights/no-lights, and from where, and what you can sell.