Belly Button Height:
Photo 1: Belly button height
with glove facing down
Improved breaking pitches. For the same reasons described above. If a pitcher is late getting to his release point on a fastball when his arm speed is fastest, he probably is going to be very late getting there on his breaking pitches and change-up. The result is flat or hanging off-speed pitches up in the zone. Shortening the arm path gets more of those pitches to the proper release point which gets them down in the strike zone with better action (break, movement, etc) on the ball.
Photo 2. Fingers facing the
sky, ball facing the chest, and
usually an exposed wrist.
Clears the path. Some pitchers come set with the glove in front of their chest with the glove fingers facing up towards the sky and the ball facing their body (Photo 2). This can create a problem related to the one explained above. Part of the glove (the heel) is under the ball and prevents the ball/hand from freely exiting the glove. This can create enough of a delay in the arm circle to not get to the release point in time. In Photo 1, Mariner's pitcher Felix Hernandez has nothing under the ball making it easy for his hand to exit the glove and begin his arm path/circle. That is because his glove is facing down.
Hides the wrist. I admit it. I was a cheater. Well, sort of. When I batted, I looked for anything a pitcher did to tip off his pitches. This became much easier to do when I could see the pitcher's throwing wrist when he came to the set position after getting the sign. When the pitcher comes set with the glove facing his chest (Photo 2), it exposes his wrist as he is gripping the ball. Variations in wrist position that can be seen by the batter often tip off when a certain pitch is coming. Holding the glove facing down when you come set not only allows for the ball to exit more freely, it hides the wrist from the batter as well.