I came across this post by trainer Kelly Baggett on the Cressey Performance blog about gaining athletic quickness. Baggett brings up some good points about the importance of decreasing muscle tension in order to increase quickness.
As I tell my youth players, relaxed muscles are quicker than tense muscles. Unfortunately this idea is usually the opposite of many players' natural instinct.
When faced with an incoming pitch, the batter often reacts by "muscling up" to try to hit the ball hard. They clutch the bat tight, twist away from the pitcher and reach back for more power. But they won't find any more power back there. Since they have so much tension, the fast-twitch muscles of the front arm cannot fire quick enough. They lengthen their swing path, and sometimes completely bar the lead arm, creating a stiff, sweeping motion to the ball. The result is a late swing and a jam shot off the handle of the bat.
When a pitcher wants to blow a fastball by a batter,
he often goes through a similar process. He "reaches back" for more power, actually shoving the ball behind his body with a stiff arm and sometimes locked elbow. His throwing arm becomes a catapult, thus robbing him of the necessary velocity to be effective.
If the batter would relax his arms, he could increase his bat speed. He could jerk the front elbow forward, get his hips and hands through the hitting zone quickly, and his barrel to the ball. If the pitcher would raise his arms gently as he glides down the hill, he could whip the ball to its proper release point more quickly and add a few mph's on his fastball.
You can have great looking mechanics, but without relaxation and quickness, you cannot perform your best.