Oooh, oooh, Mr. Kot-TAIR!

I know the answer to this one. It turns out that, from a physics point of view, one needs to consider both the speed of the ball (and the bat), and the MASS of the ball (and the bat). If the batter were swinging with a toothpick-like bat, very thin, which had the same mass as the ball, you'd be right: the faster the ball comes in, the harder it would be for the batter to send it out of the park. But since the bat has a much larger mass than the ball, and a speed which is (at the point of contact) almost as fast as the ball, then the bat has a much larger momentum. You can see how fast the bat moves if you check out the "Meeting the bat" section of my little document here:

http://spiff.rit.edu/richmond/baseball/precept/precept.html
and, in particular, this little video clip:

http://spiff.rit.edu/richmond/baseball/precept/cabrera_swing.mp4
Now, in cases in which two objects meet head-on, travelling in opposite directions, and one (the bat) has a much larger mass than the other (the ball), the conservation of momentum allows one to derive a simple result: the massive object keeps moving in its original direction, slowed down just a bit ... but the less-massive object (the ball) basically turns around and leaves the collision with more than its original speed.

For example, for some typical speeds of bat and ball, take a look at the result:

If you'd like, I can go through the math ... but I'd suggest you just read the document. Feel free to ask me questions via PM or here, if you like.