It’s Physics: Juiced Balls Don’t Explain the Home Run Explosion

Well, the 2019 World Series was another postseason dinger festival. And why not? The last few years have seen an unprecedented number of home runs. The table below is a summary of combined postseason homers. You can see this year was just a bit shy of the insanity of 2017, with 2018’s rate noticeably lower.

If you just look at the World Series, the same pattern emerges. This year, Washington and Houston were only three blasts behind the record-setting 2017 matchup between the Astros and the Dodgers, who together clubbed 25 round-trippers.

There are many possible reasons for the recent uptick in home runs, both postseason and otherwise, beginning around mid-season 2015: some we can rule out, and one that is very likely but as yet not fully explained.

Last month’s episode of physics and baseball, The Challenge of Explaining the Home Run Explosion, focused on the reason why the cause of the home run explosion since 2015 has yet to be found. Well, it turns out that’s not exactly true: It is very likely the reason is a reduction in the drag on a baseball in flight. What we don’t know is the exact cause of the drag reduction.  

As explained previously, the problem with finding the cause is because the ball-to-ball variation in drag is much larger than the change in the average drag needed to explain the increase in home runs.

The majority of comments on the article referred to a “juiced ball.” So there are either a lot of conspiracy theorists out there to whom data is irrelevant or there is some confusion as to the distinction between a juiced ball and a ball with a smaller drag coefficient. Let’s see if we can clarify the difference using some basic physics.

There are two distinct interactions that determine the distance a baseball will travel. The first is the collision with the bat, which determines exit velocity of the ball, the launch angle, and the spray angle, as well as the spin on the ball. The second interaction is between the air and the ball during the flight.

The drag coefficient is only relevant to the flight of the ball and has nothing to do with the ball-bat collision. The term “juiced ball” doesn’t refer to properties associated with the flight of the ball but instead is associated with the collision. Drag is associated with the flight of the ball, while a juiced ball is related to the ball-bat collision.

A juiced ball will come off the bat with a greater exit velocity than a non-juiced ball. So the question is: How do we know a ball is, in fact, juiced? The standard methodology is to fire a 60-mph ball at a wall of northern white ash (a common wood used for bats) and measure the speed of the rebounding ball. The rules require the rebound to be 32.76 ± 1.92 mph.

The standard way to report this value is as a fraction of the initial speed. This fraction is called the “coefficient of restitution,” or COR. The COR, then, must be 0.546 ± 0.032. We now know the scientific definition of a juiced ball. It is a ball with an elevated COR.

The UMass Lowell Baseball Research Center (UML) performs these COR measurements on six dozen baseballs every year for Major League Baseball. Below is a graph from the Report of the Committee Studying Home Run Rates in Major League Baseball from 2017 showing COR values by year from 2003 to 2017. Hopefully, we’ll soon have the data for the last two years if MLB makes the 2019 follow-up report public.

The data above has so many interesting features. First, note the rules require the average COR to be 0.546, which is just barely at the bottom of the graph. In some sense, then, the ball has been juiced over the whole time period covered by the graph. However, the ball has been less juiced recently than in the past.

Near the 2006 on the horizontal axis you will see a blue arrow labeled “6 ft.”  The length of this arrow indicates the change in COR needed to increase the flight of a well-hit ball by six feet. Compared to the proper COR of 0.546, the ball should travel around 12 to 14 feet farther from 2003 to about 2010, and around seven to eight feet farther during the home run explosion starting in 2016. Thus, the recent ball should be traveling a shorter distance, not a longer one, because the COR has dropped in the last few years.

The error bars on each data point indicate that in any individual year, the range of the ball-to-ball variation in COR is less than 0.01, which is much smaller than the 0.032 allowed by rule. That is to say, the manufacturing tolerances in any given year are much smaller than the variations allowed by MLB.  

These actual ball-to-ball variations are a bit smaller than the blue arrow, so they can cause about a four- to five-foot variation in the distance a given ball might travel. It is kind of amazing to realize any given ball in play can have a five-foot difference in the distance it will travel due to random variation in COR. That gives a whole new meaning to the expression “he got a good ball to hit.” This issue has been understood since at least Kirk Gibson’s home run in 1988.

Last month we learned we need to explain a 40% increase in home runs in 2016 through 2019, compared to 2014, requiring a 15.4-foot increase in distance. Indeed, the COR has increased from its value of 0.554 in 2013 and 2014 up to 0.557 in 2016 and 2017. However, this accounts for only a two-foot increase in distance – nothing close to the 15.4 feet we need to explain.

Also, last month we understood the ball-to-ball variation in drag was much larger than the change in the average drag that could explain the 15.4-feet increase needed to account for the home run explosion. Therefore, it is very hard to identify the source of the reduction in drag. For COR, the ball-to-ball variation only explains a change of four to five feet, while the change in average COR only explains two feet. Thus, it is certain juiced balls are not the cause of the increase in home runs. 

I can hear the conspiracy theorists now: “You just showed us MLB data, and you know they are a bunch of…”  But at least the difference between the drag on a ball and a juiced ball is clearer, and those who are inclined to learn might have a better understanding as to why juiced balls don’t explain the huge increase in round-trippers.