## Exploring the Variation in the Drag Coefficient of the Baseball

Editor’s Note: This research was completed while Charles Young was still a student at University of Illinois, Urbana-Champaign.

It’s hard to imagine that an obscure property of the baseball known as the “drag coefficient,” a quantity well known to physicists but hardly to baseball people, would become part of the baseball vernacular. But it has, thanks in no small part to the rapid increase in home runs in major league baseball over the past several years and the conclusion of many people that that increase is due to changes in this otherwise elusive drag coefficient (CD). In fact, the committee of scientists and engineers commissioned by MLB to determine the causes for the recent surge in home runs found that the principal reason was a reduction in drag coefficients between 2015 and 2017. In a follow-up report, the committee found that the decrease in home runs in 2018 and the increase in 2019 were due, in part, to changes to CD.

One remarkable finding was that a change in the average CD value of a baseball by as little as 0.01 (about 3%) would change the distance of a fly ball on a typical home run trajectory by four to five feet, leading to an increase in home run probability of about 10-12%. Equally interesting was the finding that the ball-to-ball variation in CD within a given season was large compared to the small shift in mean value needed to explain the home run surge.

While the primary focus of recent research has been on the evolution of mean values of drag coefficients, we are aware of no serious studies of how the ball-to-ball variation in CD has evolved over the years, the focus of the present article. We start with a simple discussion of drag and what it depends on in Section II. Next, in Section III, we discuss several caveats related to the method used to determine CD values from publicly available pitch-tracking data. Then in Section IV, we get to the heart of the analysis before getting to the principal results in Section V. A summary is given at the end.

### II. What is the Drag Coefficient?

When a baseball travels through the air, it collides with air molecules, in effect pushing them out of the way. With each collision, the ball loses a tiny bit of speed, though not nearly enough to result in any measurable difference to the speed of ball. But there are many such collisions, with the net effect being that the baseball slows down significantly. For example, a pitched baseball loses about 9-10% of its speed over the roughly 55-foot distance between release and home plate, so that a ball released at, say, 95 mph is only moving at 86 mph as it crosses home plate. The effect on a fly ball is even greater, since the path length is longer and the ball experiences many more collisions with air molecules, resulting in a huge loss of distance. In fact, a typical 400-foot fly ball in the presence of air would travel over 700 foot in a vacuum if otherwise hit identically. That’s a huge effect. The larger the drag force, the more the ball slows down and the less it carries. Conversely, the smaller the drag force, the more it carries. Read the rest of this entry »