Yesterday I was talking with my friends and we started talking about pitching, as I used to be a pitcher myself prior to this year. We ended up discussing how the way softball pitchers throw does much less damage to your arm than the way a baseball pitcher throws. Because of this, softball pitchers are able to throw every game, while baseball pitchers throw once every 5 days or so, and I definitely understand how much a shoulder can hurt in the days following a pitching outing. It really made me wonder why throwing the ball overhand is so much worse for the body than underhand, so I wanted to look at the physics behind it. What I found actually shows that softball pitchers are at similar risk to shoulder injuries as baseball pitchers, but that is a product of overuse. The pitching motion is definitely safer and more natural for a human body to perform than that of a baseball pitcher.
Softball pitchers are required to throw underhanded in fast-pitch games, so it is important that they do the windmill type motion with their arms in order to apply as much force to the ball as possible before releasing it. The whole time the ball is going around the "windmill", it is gaining acceleration, thus causing a faster pitch to come out of the pitchers hand. Pitchers also tend to rock slightly and lunge forward during their throwing motion, thus applying greater momentum towards the pitch. Applying all of these forward motions gives the greatest force to the ball in the "positive x-direction" and allows the ball to reach a peak velocity upon release.
So much of physics analysis on baseball pitches involves what happens to the ball as it flies through the air. It's a true spectacle to see curveballs and sliders that baffle hitters to no end. But what I'm more interested in here is the motion of the pitcher. As a baseball pitcher throws, they generally have a sort of rock in their motion, similar to a softball pitcher but usually slower. After taking a short step back, pitchers lift their legs up high and then stride towards home. This high leg kick provides a potential energy to the throw, which gets converted to kinetic energy during the stride. During the stride, pitchers begin to bring all of their momentum forward as they come closer to releasing the ball. During the stride, many pitchers use the rubber mound to push off of with their back foot, similar to how a swimmer kicks off the wall in order to shoot forward with greater speed. This push off allows the pitcher to have even greater momentum moving forward as they throw the ball. Then, once they complete the stride, pitchers release the ball towards home plate. Young pitchers are told not to go through a motion with the same force as if you were throwing if you aren't releasing the ball, as this means that their is no force acting back on you as you release, thus causing greater stress on the shoulder. If you even replace the ball with a towel, you get that force acting back on you that allows your shoulder to proceed being healthy. This "equal and opposite" force is what Newton described in his 3rd law.
So, upon analysis, although they look completely different, baseball and softball motions have certain similarities. They both apply as much momentum forward as possible, and release either directly above or below the shoulder. Stress on the shoulder in unavoidable in both situations, however softball pitchers are able to be used in much greater amounts. The thing I miss least about baseball, although I loved pitching, is the pain in your shoulder the days after pitching.