Exit Velocity vs. Pitch Speed

This week we find ourselves in the middle of the Major League Baseball (MLB) Post Season. In the flurry of excitement we hear commentators spouting off different stats. Since everyone "digs the long ball" you better believe you are hearing exit velocity and pitch speed stats.

The exit velocity is the speed of the ball coming off the bat and - quite obviously - the pitch speed is the speed of the incoming throw from the pitcher. These stats are important elements of predicting the characteristic of the hit ball, particularly the ball's distance travelled. However, there has been much debate on the importance of pitch speed on the ultimate exit velocity. Some argue the faster the ball comes in the faster the ball will go out. However, this is not the case. To understand the impact of pitch velocity we need to look at the momentum of the ball.

In this system we consider the forces acting on the ball. Consider the set-up below:

The impulse (I) is the average force (Fav) delivered to the ball over time (delta t). This is also considered the change in momentum (delta p). The change in momentum can also be expressed as the initial momentum subtracted from the resulting final momentum. When we combine these two equations with the formula for momentum (mass multiplied by velocity) we see a relationship between the force delivered by the batter (Fav) and the speed of the pitch (vpitch). Since we are primarily interested in how these pieces interact to influence the exit velocity, let's isolate the exit velocity:

You may be thinking to yourself, "Whoa, the pitch velocity is added to the force applied by the batter. So faster pitches should lead to faster exit velocities." However, I would remind you to remember our coordinate system. If our pitch velocity is 90mph, we would write vpitch = - 90mph since it is traveling in the negative x direction. Therefore, pitch velocity decreases the ultimate exit velocity.

To give you an example, let's assume two pitches are thrown and the batter applies the same force to each pitch. How would the exit velocity differ? (We will assume the Fav term will equal 200mph for the ease of the example.)

This phenomenon can be observed in the MLB stats. Visit Statcast to see that some of this season's hardest hit balls were on relatively slow pitches. Another theory MLB player's have is that since the ball is traveling slower the batter has a better chance at hitting the ball square. There is some truth to this in the likelihood of turning a pitch into a "dinger." However, the physics shows us that if both balls are hit in the same manner that the ball hit off the slower pitch will go faster.

​Enjoy the rest of the Post Season with this tidbit of information. Ask your friends watching the game what they think would result in a harder hit ball, then impress them with your insight.

Go Cubs! :P