Wait a minute guys. You're starting to get this backwards. If we are going from the baseball theory, which I have heard before, a right handed batter who is left-eye dominant has the advantage. This is because the closest eye to the ball (the left eye in this case) is able to better focus in on the ball. This is not necessarily because it is closer by a couple of inches, but because it is in more of an open position relative to the ball. Its periferal abilities of a ball coming in from the left far exceed the periferal abilities of a right eye with a ball coming in from the left. Does that make sense?
Also, I learned that I was somewhat of an abnormality, being right handed and left eye dominant, when I first learned to shoot a rifle as a kid. Almost all people who are right handed will shoot right handed (which means you look down the sites with your dominant right eye). I however had trouble with that and constantly tried to position my left eye over the sites while shooting right handed (a very clumsy position). I finally gave up and started shooting left handed. What I mean by this little story is - I think most right handers are right eye dominant.