It is switch around he bats left and throws right. LouisEly It is not that people don't bat right and throw left, they're players that do. I believe that Cody Ross does ,but it is the position that Shaw plays. To play Second base you have to throw right handed. Same with catcher, shortstop, and thirdbase it would be a disadvantage to be left handed at those positions. Plus since there are more right handed pitchers then left most batters would want to take advantage of their ability to hit left if they can.