 
I was part of a study a few years ago at the University of Arizona to
see whether cross dominant individuals (those with a particular handedness
but who had dominance in the opposite eye) were better hitters than
those with same side dominance of hand and eye.  I was picked from
my softball class because I was cross dominant (right hand, left eye)
which put me in a small minority (and the grad student was trying to get
an equal number of cross dominant and same side dominant people).  To
control the study, she used a pitching machine - fast pitch.  Since
I was used to slow pitch, I didn't come close (actually I think
I foul tipped a few) to hitting the ball.  If there were a lot of people
like me in her study (i.e., those who can't hit fast pitch, or are
not used to hitting off a machine),  I would seriously question the
results of that study!!  I think there have been some studies of major
league players (across a fairly large cross section of players) to test
whether eye dominance being the same or opposite side was "better" -
but I don't know the results.  (The woman who ran the study I was in
said that there was a higher incidence of crossdominance in major
leaguers than across the general population - but I'm not sure
whether I'd believe her.)