Mechanical work is defined as the energy transferred into a system through a force, such as when a pitcher applies force to a baseball to accelerate it towards home plate.
How can a pitcher throw harder? Simply put, do more work on the baseball to transfer a greater energy into it before it’s released. (We will ignore rotational and potential energy for the purpose of focusing solely on pitch velocity.)
The kinetic energy of the baseball and its linear velocity are related by the well-known equation for kinetic energy: E = ½mv2. Since the mass of the baseball is constant, the only variable we can manipulate to affect velocity is energy, and therefore, more energy in = more velocity out. The obvious next question is “How do we transfer more energy into the baseball?” This is the multi-million dollar question that is not so easy to answer. But the kinetic energy equation gives us an interesting insight into why it is so hard to throw at elite velocities (90 mph+).
The fact that the “v” is squared in the kinetic energy equation makes all the difference. If the equation had been E = ½mv then the relation ship between energy put into the system and the velocity out would have been linear. However since the velocity is squared, it takes increasingly more energy input to get each additional mile/hour of pitch velocity (Figure 1).
So what does this figure mean in regard to pitching at a high velocity? For a pitcher to throw 80 mph (35.7 m/s), the ball needs to have 92.7 joules of kinetic energy at release. For a 90 mph pitch (40.2 m/s), the ball’s energy needs to be 117.4 joules. This is 26.6% increase in energy input for only a 12.5% increase in velocity. To get from a 90 mph pitch to a 100 mph pitch, requires an addition 23.4% energy input for 11.1% more velocity.
The diminishing returns of velocity with regards to energy input into the baseball is a big reason why there are plenty of high school pitchers who throw 80 mph but only a small percentage of athletes will ever touch 90. It just takes so much more energy to do it and the harder a pitcher throws, the more each addition mph costs. The tremendous difficulty to produce this magnitude of energy is a main reason that high velocity pitchers are one of the most sought after commodities in professional sports.