I decided to spend part of my Easter reading The Sports Gene by David Epstein. It has a lot of information relevant to baseball. Part of his argument is to debunk the idea that great baseball, tennis, etc., players have unusually great reflexes or genetic gifts giving them faster reaction times than average. He cites a great deal of studies showing that even high level pro baseball players do not score higher than average on reaction time or reflex tests, for example, pressing a button in response to a light coming on. This seems counter-intuitive, but it seems the science is fairly settled on it.
Epstein tells an anecdote about the female softball pitcher Jennie Finch who made a show of going around blowing away MLB stars with her 68MPH underhand pitch. She destroyed Albert Pujols and Mike Piazza. Barry Bonds refused to swing until Finch started telling him which pitches were coming, and even then couldn't register a hit off of her. Alex Rodriguez refused to face her, saying "No one's going to make a fool out of me."
Of course, female players hit her pitches. Epstein's point is that what makes a great hitter isn't primarily, or even at all, great reflexes or reaction times. It's at least in part experience. The male players had no experience against a pitcher like Finch, so they couldn't succeed. To some fairly sizable extent, then, becoming great at something like hitting a baseball (or a softball) comes down to a massive collection of reps facing game-like situations.