The answer is because left handed batters hit worse off left handed pitchers.
There are two reasons for this. The first reason is spin. A left handed pitcher will more easily be able to put spin on a ball that causes the pitch to move from the right side to the left side of the plate (from the catcher's view). This spin moves away from a left handed hitter and toward a right handed hitter. It is believed, with lots of data to support it, that a ball spinning away from a hitter is harder to hit than one spinning closer to the hitter. That's one reason a left handed batter is worse at hitting a left handed pitcher.
The other reason is sight and release points. The same principle of spin applies that a pitch moving away from the batter is harder to hit than one moving closer to a batter. Because of the pitcher's release point, a left handed pitcher will release the ball somewhere to the right of the mound (from the catcher's view) when the ball is thrown. If we assume the ball has no spin and is pitched to the center of home plate, it will have moved from the right of the mound to the center of the plate. This movement from a left handed pitcher is going away from a left handed hitter and going closer to a right handed hitter.
There is not much difference between how well right handed batters fare against right handed pitchers and left handed pitchers because right handed pitchers are so common that right handed batters don't have the same level of disadvantage as left handed batters do against left handed pitchers. But the reason why right handed batters are better than left handed batters against left handed pitchers is mostly explained with spin and release points.
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If a southpaw is pitching the ball will curve slightly more because everyone has a muscle that is stronger in their left arm than right. The ball won't curve on it's own, it is probably a curve, slider, or spitball (illegal).
Lefty's (also called southpaws) are very valuable in because there simply different. Batters struggle to hit them, because they are used to righty's. Also left handed pitchers have a natural curve, so even their fastball moves.
They don't only pitch to left-handed batters; they pitch to both right and left-handed batters, the same way a right-handed pitcher pitches to both.
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It depends if the pitcher is left or right handed, a lefty will face first, while a righty will face third.
No WAY Right Handed pitchers break their arms during pitching too
Baseball is uniquely American. Its a sport of numbers and statistics. The strike out is one such statistic that many a fan counts. For any pitcher a strike out is a difficult task especially against todays amazing batters. To find a pitcher throwing 13 strike outs in 2009 isn't an easy task but it is possible. Many a true fan has counted each strike out. Pitch by pitch is recorded and posted. The almanac is one of these places where the records go, as well as, team sites and fan built pages. With a little effort any question can be answered.