The pitch is on the way, you've coiled and taken your stride and now you're ready to swing. The first thing to realize is that your swing should not be driven by your arms, but by your legs and hips. We'll take a look at each area of your body and follow it through the swing.
As your weight moves forward from your back leg, your back foot will pivot towards the pitcher and your knee will turn in. The front foot will not pivot and you will want to keep that leg stiff. It's not necessary to keep it completely straight, but you don't want to flex it as you transfer your weight. (This can cause your head to drop as your tracking the ball.)
While you pivot on your back foot, you also will open up your hips. The degree to which you open your hips depends on the location of the pitch. On inside pitches, you need to completely open the hips to get your hands through right next to your body. On outside pitches, you have to keep your hips more closed to get your hands out and drive the ball the other direction. An important point on feel for the player: It should feel as if the back hip is driving the hips open, not the front hip pulling the hips open. It may seem like a subtle difference, but a player that is pulling open will often start by pulling his front shoulder open. This can cause all types of problems.
Your legs and hips are going to drive your swing and provide power. Work hard on both of these and you will see a difference in the batting cage and on the field.
When you begin your swing, you want your hands to be at the top of the strike zone. Any lower and you will be swinging up at a high strike. This most likely will result in a fly ball or pop-up.
To have a quick bat, you must start your swing by bringing your hands through close to your body. On inside pitches, your hands stay closer to your body longer than on outside pitches. Remember to extent the bat towards the ball just before contact. If you extend the bat too soon, you will slow down your swing. As you make contact with the ball, your bottom hand (closest to the knob) should be palm down and your upper hand should be palm up. This means that you haven't yet rolled your wrists over. Rolling your wrists happens naturally after hitting the ball. Concentrate on driving through the baseball. Sometimes players are in such a hurry to start running that they actually start slowing down their swing before contact. Hit the ball hard first, then run. As your hands continue forward and your wrists roll over, it's natural to let you top hand come off the bat. This allows you to continue with a good follow through on your swing.
It's essential that you track the ball from the start of the pitch to the bat. Often hitters want to see where they hit the ball before contact. Concentrate on watching the ball all the way through contact and look at the contact spot for a split second after you hit the ball. This ensures that you have tracked the ball the entire way.
Another way to think about tracking the ball is shoulder to shoulder. Start your chin near your front shoulder; after you swing, your chin should end up on your back shoulder. If it doesn't, then you're leaving your head out in front of the plate and not watching the ball all the way in.