>>> Why steroid do not really help. The home run comes from the pitcher, not the batter if we consider momentum. The batter ideally reverses both the momentum vectior and the angular momentum. <<<
Below are a couple videos from "Sports Science" discussing results from bat/ball collision tests. The first addresses what effect the "Grip" has on the ball's exit speed. The second addresses your statement that "home run comes from the pitcher, not the batter." The reader can decide if they agree with you or test results ran by a number of Bat Manufactures.
The "Grip" vs Ball's Exit Speed
Pitch Speed vs Ball flight