Swing training is specific. Train your swing by swinging - going through full range of motion with various weighted bats. The weighted bats stay in a specific range to keep you moving near or above game speeds. Heavier bats help your muscles get stronger and improve efficiency, and lighter bats help train your muscles at faster speeds.
I use the SPRT5A bat speed and reaction trainer from SETPRO. This equipment provides feedback on each swing which helps the player monitor intent and progress. Reaction training addresses each player's specific need to not only create bat speed, but to create the most amount of bat speed in a specific amount of time and/or target that bat speed to a given point in time (timing). Here is where players develop bat speed AND swing quickness.
Very simply, if you want to swing faster, you have to train to swing faster. If you want to have a quick swing, you have to train your swing to be quick. Over/under training with feedback is the quickest and most effective way to accomplish those goals!
This is more towards the hitting (skill) side than training (ability), but must also be taken into consideration.
I enjoy watching MLB players prepare for game time, namely during batting practice. See for yourself how they approach hitting:
