Julray, you actually are NOT saying 'see the ball, hit the ball' you are saying 'see a spot on the ball, hit a spot on the ball' -- again, I think the algorithm responsible for superior hand-eye coordination is much more complicated than that.
TDS, you tell a kid that is swinging under a pitched ball to....do what exactly? Try to see and hit the top of the ball? And by doing that they'll move their contact point up and hit the center of the ball? When they are having trouble hitting the ball at all in the first place? Not sure this is how hand-eye coordination works or should be trained for.
What I am saying is "see ball, hit smaller ball in the center". Not sure what those training balls are called, but they are the size of a golf ball. If I can train my eye to hit those from a machine or front toss, then why not pick a spot that big in the central location of a softball and attempt to hit that? It could be the way I explained it, but you guys are referring to the spot on the ball way literal. Can we see the entire outline of a ball when it's pitched to us? Yes we can, so why not swing for the "golf ball" in the middle.
I don't understand how barrel path improves our vision or focus as some people are saying here, I can understand how it helps us hit what we see.
What do you tell a kid who regularly pops up and hits grounders? Try to hit the center of the ball. What's the difference in trying to tell a kid to hit the top of the ball vs hitting the center?