In baseball, a pitcher is often assumed to have an advantage over a batter based on his handedness (i.e. left-handed vs right-handed). I think it is that right-handed pitchers have an advantage of left-handed batters, and vice-versa.
Why is this advantage? If it is related to the break of the curve, is this advantage only relevant for pitchers that use a curveball, or does it also apply to pitchers that primarily use a fastball/change-up?
There are several things, including a major one that you mentioned before which is the break of the curveball/slider.
Generally speaking, hitters can handle pitches on the inside portion of the plate better than the outside. Also, hitters can track and see a ball that is moving towards them better than away. So for a lefty on lefty (or righty on righty) a 4 seam fastball tends to move slightly away (advantage pitcher) and both curveballs and sliders will break much further away (advantage pitcher).
You'll notice that many of today's best left handed pitchers have developed excellent Change Ups (Johan Santana, Cole Hamels, and popularized by Tom Glavine). Since there are far more right handed batters than left, they needed a pitch that would break away instead of towards the right handed hitters.
For pitchers who use primarily a fastball change-up it still makes a difference but it is not as exaggerated. The 4 seem fastball should still be a tougher pitch for the left on left matchup.
The last thing is: everyone, both left and right handed hitters, see far fewer left handed pitchers throughout their careers. Just being unfamiliar and unique is an advantage to the lefty pitcher.
It makes a huge difference if the pitcher's delivery isn't completely overhand.
When a left-handed batter faces a left-handed pitcher throwing sidearm (or vice versa) it's downright intimidating. It's much more difficult to track the ball out of the pitcher's hand, because the ball basically starts behind the hitter. This also makes it feel like the ball is sneaking up on the batter (as if he has less time to respond) since he picks it up later with his eyes.
When a left-handed sidearm pitcher is throwing a sharp breaking ball to a left-handed batter... forget about it. That's when you see lefties who hold opposing batters to batting averages under .200.
It helps to think about it from the hitters perspective. A right handed hitter would prefer the ball to be coming from an angle that is closer to first base (a lefty pitcher). This allows more room to "pull" the ball.
A right handed pitcher would be releasing the ball closer to third base. This forces the right handed hitter to "push" the ball - or hit it the other way which is more difficult.
Sidearm pitchers and pitches that move horizontally increase this angle advantage even more.
Most batters have trouble hitting "inside." (That is between themselves and the plate, meaning from the left side of the plate for a right-handed batter, and the right side for a left-hander.)
Most pitchers prefer to pitch "inside." In theory, right handed pitchers have trouble pitching to left handed batters (and vice-versa), because the right-handed pitcher's "inside" is the left-handed batter's "outside." Left handed pitchers get to pitch "inside" to left handed batters.
One exception to this rule is Jose Bautista, of the Toronto Blue Jays, whose forte is hitting inside (and is weaker outside). Left handed pitchers do better against him because their inside is his outside.
