The Physics of the Home Run Boom

Increased exit velocity could partially explain the home run boom, and no one had a higher exit velo in 2017 than Aaron Judge. (via Keith Allison)

Whoa! Don’t think for even one short nanosecond this article will definitively explain the cause of the current increase in home runs in MLB. Instead, think of it as more of a summary of our current understanding from the point of view of the underlying physics.

From a scientific point of view, there are only two interactions that result in a home run. The first is the ball-bat collision, and the second is the flight of the ball. The ball-bat collision depends upon the properties of the bat and the ball, while the flight of the ball depends upon the properties of the ball and the air through which it travels.

The single most important physical idea that emerges from the physics of the ball-bat collision is that during the fraction of a millisecond of contact between the bat and the ball, there is nothing the batter can do to affect the outcome of the collision.

This is not to say the batter doesn’t affect the collision. After all, teams hire coaches, trainers, sabermetricians, and even psychologists to improve players’ ability to swat the sphere. These effects are all limited to the time before the ball and bat actually collide. As proof, I offer the “No Hands Homer” hit by Todd Frazier. The batter didn’t even need to be touching the bat during the collision, and yet he hit a bomb.

The underlying physics is based upon the fact that it takes around 300 milliseconds for a batter to get the bat from the ready position up to speed in the hitting zone. After the bat gets there, it only takes around two-thirds of a single millisecond to complete the collision. The collision time is so short–and such a small fraction of the time needed to get the bat up to speed–that the batter can’t change anything meaningful about the collision during that short time.

Given the batter can’t affect the collision once it begins, the results of the collision can depend only upon the properties of the bat at the beginning of the collision and not on the properties of the batter himself. Of course, the batter has a lot to say about what the properties of the bat will be just as the collision begins, but once there is ball-bat contact, the batter is irrelevant, although Frazier did get credit for the dinger!

The important properties of the bat just before collision can be put into two categories, ones the batter can change during the swing and ones associated with the specific bat involved. Here is a list of the properties the batter can change during the 300 milliseconds before the collision.

  • The velocity of the bat at the contact point with the ball (in all three dimensions)
  • The orientation of the bat (level, barrel below the hands, bat behind the hands, etc.)
  • The location along the bat where the ball collides
  • The distance off the center line where the ball collides

The relevant properties of the bat are:

  • The weight of the bat
  • The length of the bat
  • The shape of the bat (diameter, center of mass, and rotational inertia)
  • The bat’s ability to absorb energy during the collision (vibrational modes)

The properties of the ball also affect the collision. These include:

  • The velocity of the ball at contact
  • The weight of the ball
  • The diameter of the ball
  • The ball’s ability to absorb energy during the collision (coefficient of restitution)

The physics that describes the flight of the ball after the collision depends upon the properties of the ball and the air through which the ball travels. The weight and diameter are not only relevant to the collision but are also relevant to the physics of the flight. In addition, the following properties of the ball and the air make a difference:

  • The speed of the ball just after collision (exit velocity)
  • The direction of the ball just after collision (launch and spray angles)
  • The spin on the ball just after collision
  • The surface properties of the ball (roughness and seam height–drag and lift coefficients)
  • The atmospheric conditions (temperature, pressure, humidity, wind speed and direction)
  • The elevation of the ballpark

If it is so easy to delineate the physical properties, why can’t physics just simply explain the home run explosion? Many of these items simply are not measured, even in the Statcast Era, particularly the first four items regarding the motion of the bat. Also, the bat’s shape and ability to absorb energy are not known for every MLB-approved bat.

Another issue that complicates the physics is that theories that describe the collision and the flight include many approximations and parameters that are not well known. For example, surface roughness and seam height. We have no complete model that describes the effect of the seams on the flight of the ball. Instead, we have some empirical data that give approximate values for the lift and drag coefficients instead.

That said, every theory that purports to explain the home run boom must pass muster with the laws of physics and connect to at least one of the parameters enumerated above. Let’s examine a few of the more prominent theories.

Juiced ball players: Whether the juicing is due to PEDs or more time in the gym, the velocity of the bat is the primary parameter that would be affected. Stronger players can swing the bat harder. While we have no direct measurements of bat speed, we can infer bat speed changes from exit velocity changes using a physical model of the collision. This is not as simple as it sounds because the collision model uses hte first dozen items listed above, and variations in any one of them could muddle any conclusion about bat speed.

A Hardball Times Update
Goodbye for now.

Juice baseballs: This is all about the ball’s ability to absorb energy. This is often called the “coefficient of restitution” or COR. There is very limited publicly available information about COR and whether it has changed over the last few years. MLB claims to have done testing and assures us there is nothing out of the ordinary. Mitchel Lichtman commissioned his own study showing a noticeable increase in COR. Rob Arthur and Tim Dix analyzed the internal structure of baseballs and found changes in balls from 2016 and ’17 compared to 2014 and ’15.

Barreled balls: Often referred to as the “Fly Ball Revolution,” Statcast analysis has shown that fly balls are more effective at increasing offense than ground balls. As a result, many hitters now are deliberately trying to hit the ball with large launch angles. This requires hitting “under the ball” and/or a more upward swing, which is associated with the velocity and orientation of the bat. Many suspect this to be part of the explanation because it also could explain the increase in strikeouts.

Increased Exit Speed: There is evidence that the exit speed has increased recently, although the cause of this increase is uncertain.

Increased Pitch Speed: This also could have a part in explaining the growth of strikeouts. But the increase in pitch speeds over the last few years is not large enough to make it a significant part of the explanation of the home run boom.

Warmer Weather/Climate Change: It’s possible variations in the density of air associated with atmospheric conditions could have an impact. However, the effect of climate change is simply too small to explain the longball increase.

Changes to the Ball: Here we are referring to the aerodynamic properties of the ball. There is some evidence the aerodynamics have changed slightly. In addition, the increase in pitchers suffering from blisters might be indicative of changes in seam height of the ball.

Hopefully, MLB is investigating the situation. And we expect baseball will do what needs to be done to ensure the integrity of the game. After all, large sums of money are involved. However, we are less certain they will share what they learn and whether their explanation(s) will be consistent with the physics of home runs.

References and Resources

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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5 years ago

Great article. Isolating some of these variables will be easier than others. I wonder if MLB really wants to know or more importantly if they want others to know the physics of the tweaks they make to the game?

Marc Schneider
5 years ago
Reply to  martyvan90

I think all the leagues (MLB, NFL, NBA, maybe NHL) realize that offense is more attractive to fans than defense. Pretty much every rule or technical change in the last fifty years has been in the direction of increasing offense. If MLB is, for example, tinkering with the balls to increase offense, I don’t see why this is any different than the NFL changing rules to make passing easier. I don’t have a problem with it but at least let the pitchers know what they are dealing with.

5 years ago
Reply to  martyvan90

I think PEDs are the only issue the league would want to hide.

Tweaking the balls or bats wouldn’t be profitable to keep secret. Clubs and the league don’t keep it a secret when some team brings the walls in a bit, or lowers them. MLB didn’t keep it a secret when they lowered the mound. Even if keeping these things a ‘secret’ is technically impossible, it’s not like MLB even lowers the volume or otherwise minimizes these types of news items- they are dealt with pretty plainly. When Coors or Arizona change the humidifier used for baseballs, it’s not kept a secret. Turf adjustments, changes to acoustics, changes to lighting, changes to field maintenance, etc,. are all pretty public and openly disclosed in today’s game, with far less of the ‘muddy base path’ secret groundskeeping and the like from the early days.

PEDs, of course, are totally different. All pro sports leagues have strong incentives to have their players using. Treated players have more dynamic strength, can accomplish more amazing feats- and perhaps most important, stay great for nearly twice the length of a non-treated player: recovering from injuries that would otherwise end careers. Such longevity is crucial for marketing, for record chases, for q-scores, for father-to-son generational fanhood, etc. Most sports fans take it for granted that the NFL and other leagues allow rampant PED use without a serious thought towards enforcement. Only really in MLB, and sometimes (bizarrely) the olympics (and soccer fwiw) does the sport pretend to have prevented/cured/overcome PED use (despite almost no serious evidence).

There may be multiple causes to the recent HR binge, but ruling out PEDs (as the media has largely done save for very few excellent pieces like this imo) is almost counter-factual.

5 years ago

You didn’t mention changes to the bats. While this is more heavily policed in the game than changes to the ball, I had heard more players were using maple bats instead of ash. It’s also possible more players are using longer or heavier bats, with more barrel area (not sure of the rules on this) to ensure harder, truer contact. Has there been any testing of bat type – make, size, weight – that would lend assistance to explaining the homer run explosion?

5 years ago
Reply to  DD

I think this is the most under-researched possibility. I know this is just anecdote, but I don’t see nearly as many broken bats as i once did- I wonder if bat construction is getting better.

5 years ago

By way of a control, is a similar phenomenon ongoing in Japan? If the HR surge is related to batting approach, you’d expect it to be reflected there to some extent.

Which train of though leads to the one variable everyone’s missed – juiced rubbing mud anyone?

5 years ago

Thank you for your great knowledge in Baseball, it is terrific writing.

5 years ago

Statcast analysis has shown that fly balls are more effective at increasing offense than ground balls – I can’t suspend reality long enough to entertain this idea. Without Statcast players were unaware of this? I think players are adopting the higher launch angles in response to the juiced ball… not just discovering that you have to hit a ball high enough to hit it over the fence but not so high as to not sail over the fence. I think that kind of thinking is why sabermetrics and traditionalists butt heads – its insulting to everyone who already understands the basics of hitting. That is the reason why people with sufficient experience and knowledge of the game get a bit miffed at times at the launch angle discussion.

5 years ago

Outstanding article.

The PED issue is a hard one to even discuss at times, but I’m impressed that the author’s comprehensive approach touched on the issue and treated it as it is: a potential explanation.

I do wonder whether a player on typical ‘balco style baseball PED treatment’ would tend, compared to his non-treated self, to have a greater exit velocity, better ‘hard hit’ rates, and therefore have the incentives (sufficient impact) and the ability (greater wrist/arm/body strength) to increase launch angle.

I believe the answer is yes (greater EV), yes (more hard hit), and likely yes (more incentive/ability to increase launch angle), but would love to see the matter tested properly.

That’s not to say that all launch angle guys must be PED users- but rather, it that perhaps all the caught PED users from the past would today be seen as ‘launch angle revolution’ guys, or would perhaps have that (supposedly) alternative explanation.

Notably, it’s not only launch angles and HRs that are up, but velocity of all types (even adjusted for usage changes) and EVs- all consistent with the symptoms of typical baseball PED use.