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

There can be a surprising amount of physical variation from baseball to baseball. (via slgckgc)

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.

Postseason Home Runs by Year
Year Home Runs Games HR/G
2017 104 38 2.74
2018 71 33 2.15
2019 95 37 2.57

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.

World Series Home Runs by Year
Year Home Runs Games HR/G
2017 25 7 3.57
2018 14 5 2.80
2019 22 7 3.14

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.

David Kagan is a physics professor at CSU Chico, and the self-proclaimed "Einstein of the National Pastime." Visit his website, Major League Physics, and follow him on Twitter @DrBaseballPhD.
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Bobby Ayala
2 years ago

I think the term “juiced ball” does not specifically refer to the exit velocity off the bat, it refers to a difference in ball resulting in increased distance, which includes reduced drag as well as exit velocity. Perhaps I missed the boat but I’ve never heard it so specifically pinpointed to only refer to an exit velocity difference.

2 years ago
Reply to  Bobby Ayala

Took the words right out of my mouth. As is often the case with technical discussions, there is a narrow, specific definition of the term used by experts, that can be contrasted with a more general definition used by the public. I appreciate David’s explaining the difference, but to most of the public–which won’t read articles like this–any change to the physical properties of the ball that increases the distance it an travel given the same performance of the hitter is considered juicing.

2 years ago

While it is fine to point out the differences between drag from the air and bat-to-ball collision, when the general twitter clone references the “juiced ball”, they are talking about the ball going further than before. When trying to describe the cause, what you are saying makes sense.

However, there is a significant percentage of fans that have finally had enough with watching guys that never hit more than 7-10 HR’s in a season, hit rockets off the end of their bats two inches off the ground that go 360 feet to the opposite field.

Korea has already successfully “de-juiced” their ball. So MLB saying they are perplexed by the behavior of their balls is condescending to anyone who follows the sport worldwide. MLB can control this stuff in a lab if Korea can.

Why can’t the commissioner explain what is different about the factories/balls used by MLB and the balls used by Korea that makes one league able to fix this issue in a single season, and the other league cannot even figure out what the cause is, let alone change it? I would be interested to know the gritty details and data so that everyone can say: “See, the commissioner was right all along and this is why the average fan doesn’t understand the data.”

I don’t think the method that is used to fix the problem is as important as getting the game back to a point where the HR is not the main form of offense for most of the league; especially when the data shows that this issue has been addressed already in a successful manner. You can’t get the owners to stop moving in the fences multiple times either as they have done in so many modern stadiums, fixing the ball is the most efficient way to keep the game from becoming like softball in an under-sized field.

2 years ago

If the drag reduction is coming from something done to the surface of the ball during production, I would still call it a juiced ball. In this sense, there might be core-juiced ball which is likely to change COR, and surface-juiced ball which is likely to change drag.

2 years ago

maybe that’s the scientific definition but literally nobody uses it that way

Green Mountain Boy
2 years ago

Okay, so we have solid information on how the ball has (or hasn’t) changed over the recent past. However, I can think of at least two other factors which haven’t been looked into deeply (to the best of my knowledge) that also affect the distance the ball will travel.

As anyone who has taken a basic physics class knows, F=ma. Force equals mass times acceleration. Since the mass of the ball is for all intents and purposes the same from one ball to another and leaving drag coefficient out of this discussion, the factor we should be looking at is a. Acceleration. So what is accelerating? One or both of the pitch thrown and the bat. The bat is easy to comprehend. Simply put, if the bat’s acceleration has increased, the ball will go farther when it’s hit. A whippier bat will do it, and so will a harder wood. Spring effect.. Think of it as less of the pitch’s energy absorbed by contact with a harder surfaced bat. So where does that energy go? It’s imparted to the ball, making it go farther.

The other factor could be the pitch itself. If it’s coming in faster on average than it has historically, it will be going out faster as well. Have average pitch speeds increased? If so, by how much?

Bobby Ayala
2 years ago

The biggest factors also tend to be ignored in these explorations: differences in the pitchers and hitters today. More pitchers throw harder and take chances to get Ks. More hitters sell out for max power and HRs. Both are using science in new ways to push toward extremes we’ve never seen before on a mass scale. These are not as quantifiable as trackable data like exit velocity, etc, but I believe they are having a greater impact to average distance than changes to the balls.

2 years ago

All of this is already taken into account. The data show that balls having the same exit velocity (which necessarily includes all effects of pitch speed, bat speed and ball/bat collision) are traveling farther now. So — insofar as locally- or time-varying gravity are excluded by various independent tests — it has to be the ball/air interaction, as stated in the original post.

When I read the official MLB report, I didn’t see much detail about spin during post-impact flight, so I remain curious whether the exit spin has changed recently in the era of spin-rate swing-plane consciousness.

Joe Joemember
2 years ago
Reply to  mgwalker

MLB Report, while correct the biggest change in distance is due to drag changes, undersold the effects of other factors. The change in homers was nearly what would be expected based on the change in drag alone. This is not the same as saying other factors aren’t important…it means the other factors canceled out during the years of the study. K rates were going up with or without LA craze. Batters are hitting ball with optimal homer LA, EV about 13% more per batted ball than they did in 2015 (i.e., we’d expect a 13% increase in homers to LA craze if pitchers weren’t piling up the Ks and drag on ball didn’t change).

2 years ago
Reply to  Joe Joe

Sorry, I was responding to the F=ma post. But I guess the fact remains that there is solid evidence for decreased drag, and of the known factors leading to the HR increase, this is the one that remains unexplained.

2 years ago

As others have pointed out, I think you’re misunderstanding how we used the term “juiced ball” (and “de-juiced ball” for the playoffs, though there’s some question on that). I have had many conversations with other fans about the “juiced ball” and we’re talking about drag and seam-height. We have read the studies and almost all of it is about drag these days – we get that. Considering no one is pouring literal Minute Maid inside the balls, I think we all take the word “juiced” to mean “the ball goes farther” rather than any particular reason for it.

2 years ago

Why would they measure COR at a relative velocity of only 60 mph? Why not something closer to the practical relative velocity of 200 mph? Maybe the average COR would be the same, but maybe not. Also, maybe the COR variability would be different.

2 years ago

I’m wondering if anyone has taken into account the effects of climate change?

2 years ago

From MLB report section 2.9:

“…showing that the differences in home run rate persist even at fixed values of
the temperature. A similar result is found by examining home run rates in
closed stadiums, where the temperature is constant.”

2 years ago

People use juiced to refer to balls that travel farther for whatever reason.

2 years ago

You might consider the spinning top as a model, with regular features asymmetrically displayed on the surface (as are threads) or surface roughing. If you capture precession behavior and spin velocity it provides a nice analog to drag on a baseball in flight.