MLB player Paul Goldschmidt throws right.
MLB player Paul Maholm throws left.
MLB player Paul Clemens throws right.
MLB player Paul Konerko throws right.
MLB player Adam LaRoche bats left.
Left.
This riddle refers to a boomerang. When you throw a boomerang to the right, it travels in an arc and returns to your left side, allowing you to see it again. However, if you throw it to the left, it continues on its path and does not return, so you won't see it again.
For right handed people they do catch with their left and throw with their right. For left handed people, they catch with their right and throw with their left. Both players have to potential to bat from either side of the plate.
Paul DiGiovanni writes with his left hand, but plays guitar right-handed.
Michael Vick throws a football with his left hand, but he writes with his right hand.
MLB player Will Smith throws left.
MLB player Will Venable throws left.
NHL player Paul Bissonnette shoots left.