An Analysis of Drag Coefficients Through the Years
The benefit of internship and job application season are the multitude of mini projects given as part of the process. I especially enjoyed completing this analysis of MLB’s seemingly always changing baseball. The prompt stated that many people believe the reason for the increase in home runs is due to a change in the drag coefficient of the ball. A lower drag coefficient would allow each ball to travel through the air further, leading to more home runs.
To determine this empirically, I had to find some way of measuring this change throughout the years. My initial idea, comparing the distance balls were hit with similar launch angle and velocity, posed small sample size issues as I was only given a dataset containing 1,000 hits each year from 2015 to 2019. I then thought about comparing the average distance a ball traveled throughout the years, but I was too concerned about compounding variables such as changing hitting and pitching strategies.
I ultimately thought about an at-bat, in the physical sense, as projectile motion. Looking at the motion of the ball between pitcher and hitter allowed me to isolate the affects of either player. In the dataset I was given the velocity of the pitch as it left the mound and at the plate. Using the standard distance from mound to plate, and simple kinematic equations, I could calculate the acceleration of the ball for each at bat. If the drag coefficient of the ball changed at some point over these four years, the acceleration would change. A lower drag coefficient would cause the ball to slow down less, or have a smaller negative acceleration.
My repository with my RScript can be found here. This file contains all the calculations of acceleration as well as the averages and statistical tests to determine differences (all done with a significance level of .05).
I completed a hypothesis test comparing the variances of the acceleration in each year before completing the comparison of the means. At a significance level of .05, there was a difference between the average acceleration in 2015 and all years except 2016. Specifically between 2015 and 2019, there is less than 2.2e-16 probability (or 2.2e14% chance) that the averages between the two years are equal. In 2019 the average acceleration was a smaller negative value than in 2015 which means the ball was not slowing down as much. This indicates that it is possible there was a change in drag coefficient over these years. More specifically, each year saw an increase in average acceleration (smaller negative value), except for the year 2018, which decreased slightly from 2017.
Image 1 helps visualize the averages (the darkest line) for each year. While they do not appear to change much, this is on a factor of 10⁴ to fit in outliers. There is still a notable difference between 2015 and 2019, among others, at alpha of .05. Had it not been for the decrease in acceleration in 2018, I would have said that 2017 was the year the ball changed — possibly by a decrease in the drag coefficient. 2015 and 2016 are considered to have the same mean, and 2015 and 2016 are different from 2017. However, 2017 is different from 2018 while 2018 is the same as 2016. 2019 has a smaller negative acceleration than all years except for 2017. It is possible the ball was changed in 2017, changed back in 2018, and back again in 2019. I’m not sure what caused the dip in 2018, but from this, I would say the ball was altered in 2017 and possibly by affecting the drag coefficient as the balls began to slow down less between the mound and the plate.
I made a few assumptions with this method that could be sources of error. First, the kinematic equation I used assumes a one-dimensional projectile path which is not the case. Without more in-depth data about the path of the ball between the mound and the plate, I couldn’t complete a two or even three-dimensional analysis. I also considered the effect of differing release speed and its possible effects on acceleration. I thought a consistent increase in release speed over the years might contribute to an increase in acceleration. However, according to NASA’s “The Drag Equation,”[1] drag is directly proportional to velocity. Therefore, had there been a universal increase in release speed, it would not be a cause for the increase in acceleration seen, further contributing to my belief that the drag coefficient has changed. Finally, external factors like altitude, indoor or outdoor facilities, temperature, pressure, humidity, and wind speed and direction were considered constant in this analysis.
I completed my analysis back in January, and at the time, I truly did not know when and/or how the ball changed. I stumbled upon this article when researching a practice Diamond Dollars Case Comp a month later. The author states, “I first wrote about the role of decreasing drag in boosting home runs in 2017, and MLB’s commission of scientists and statisticians later confirmed that the more aerodynamic baseballs in use that year were largely to blame for the spike in home runs.”
I have to admit I was ecstatic when I realized this little project I completed actually came back with the correct year. At the time I completed it, I did not consider that the ball could have changed multiple times. I naively believed once MLB changed the ball, they would keep it that way… but that is a discussion for another time.
