The following picture shows Paul at the release point, finishing off the maximal effort of throwing the ball. As you can see, the throwing arm is at full extension and is in line with the shoulders.
This arm position is what we call a “three-quarters slot” because it’s between sidearm (horizontal) and overhand (vertical).
It’s important to understand that the arm slot is determined almost exclusively by the alignment of the shoulders since the arm at release is normally in line with the shoulders. You can draw a line from the left shoulder through the right shoulder through the baseball at the tips of Paul’s fingers. In this picture you can see that Paul’s right throwing shoulder is several inches above his left non-throwing shoulder to create the “three-quarters” slot.
One advantage of a “three-quarters” arm slot is that it’s the best combination for accuracy (up and down as well as side to side). You can think about the strike zone being a box above the plate that is the width of the plate and height that is the approximate distance between the knees and mid-chest of the hitter. A “three-quarters” arm slot at release allows the hand to follow a path across the diagonal of the strike zone box. The diagonal is obviously larger than either the height or width of the box, and as a result, there are more potential release points with a “three-quarters slot” that can achieve a strike compared to throwing with a sidearm or overhand slot.
An overhand slot requires a much more dramatic spine angle with the head well off the target line. Tim Lincecum is an example of an MLB pitcher that throws nearly straight overhand. There aren’t a lot of other examples of pure overhand deliveries in the major leagues.
A sidearm slot has the accuracy disadvantage previously mentioned and additionally is characterized by a more horizontal ball flight after release. A 2-seam fastball, for example will tend to stay on the same horizontal plane unless the pitcher creates a lot of early pronation with his hand. Max Scherzer is an example of a pitcher that throws very close to sidearm.
Obviously, both Lincecum and Scherzer have had tremendous success in the major leagues, but major league pitchers tend to have unique physical gifts that more normal athletes do not exhibit. More average athletes need to optimize their techniques and mechanics as much as possible.
Another advantage of a “three-quarters” slot over sidearm is the fact that the height of the ball at release insures a downhill plane to the strike zone. This is important when combined with the better accuracy because hitters generally have more difficulty hitting a ball that’s moving toward the ground (changing elevation) than a ball that’s coming in level to the ground.
The “three-quarters” slot with the fingers on the inside of the ball will more naturally cause a two-seam fastball with movement that changes elevation even more than just the downhill plane offered by the arm slot.