The Physics of Aaron Judge
In the earliest days of spring training, Jeff Sullivan was moved by a mammoth home run to pen (type?) a piece on how difficult it is to exaggerate Aaron Judge’s power. Here’s the video of his inspiration:
Well, as the solstice approaches, the season nears its halfway point and Aaron Judge has continued to distinguish himself in his first full year in the Bigs. He currently dominates the Statcast Leaderboard, leading the majors in maximum exit velocity, average fly-ball/line-drive exit velocity, and barrel percentage. He’s second in average exit velocity.
The table below compares Statcast data for Judge’s home runs against MLB averages for 2017 as of last week.
| Home Runs | Average Dist. (ft) | Average EV (mph) | Average LA (°) |
|---|---|---|---|
| Judge (21) | 410 | 111 | 27 |
| MLB (2275) | 401±28 | 104±4 | 28±5 |
Numbers denoted with “±” sign denote standard deviations.
Certainly, AJ’s number suffer from S3 Flu (Small Sample Size). Nonetheless, at this point, they show a player who can hit homers a bit longer than average with launch angles consistent with MLB overall. The impressive number is the exit velocity. On average, he ignites the ball with a speed almost two standard deviations above MLB average – yikes!
On Sunday June 11, he hit what is likely to be the longest bomb of the season. It cleared the left-field bleachers in Yankee Stadium and was recorded by Statcast at 495 feet. Here’s the video:
So, what’s the physics behind these impressive stats? Jeff Sullivan describes Judge’s swings as “quick.” He states, “They’re quick because of the bat speed. The bat speed is where the strength comes from.” While this has some logic in the parlance of baseball, it’s not precisely how a physicist would think of it. Rather, it’s Judge’s strength that allows him to produce sufficient force to accelerate the bat to high speed quickly.
Sullivan makes a comment more relevant to the science of the matter later in the article, “There’s an ease with which Aaron Judge clobbers the baseball. It’s not actually easy, but Judge’s giant body allows him to swing a heavy bat super-fast, and that’s how you get light-tower power.”
How one goes about converting long limbs and strong musculature into bat speed is a topic for hitting instructors; however, a physicist can say something modestly relevant like, Newton’s Laws of Motion tell us that, in order to accelerate an object like a bat more quickly, a larger force is required. So, strength and bat speed are related, but you knew that already.
You also don’t need to be a “rocket scientist” to understand that the ball will leave the bat at a higher speed if the bat is moving faster. Just compare the result of the zero-speed swing of a bunt to the tornado of one of Judge’s rips. This is the essence of “Garvey’s Law.”
A more detailed look at the physics involves a bit of math which I will spare you. The key point is that the exit velocity is, in the simplest approximations, linearly proportional to the bat speed. So, looking at the numbers in the table, we can see that his bat speed is about 7.5% higher than the MLB average. At least for his homers.
It would be great if Statcast could provide direct information on bat speed to test this theory. For now, we’ll have to settle for exit velocity and assume I have reported the physics correctly.
There are two pieces of physics related to home runs: both (a) the just-discussed ball-bat collision and (b) the flight of the ball. I have described the basic physics of the flight of a baseball several times previously in THT, most recently here.
Here’s the Cliff Notes version. The three forces on the ball are gravity, drag, and lift (Magnus Force). The batter can do nothing about gravity – Earth just sucks. The batter can do almost nothing about drag because the faster the ball is moving, the larger the drag. The batter has the most control over the lift because the lift depends upon the backspin on the ball.
A homer is a result of the interplay between these three forces. The batter must hit the ball with a high enough launch angle so the ball stays in the air long enough to travel past the fence; however, the launch angle can’t be so high that the drag force slows the ball so much the result is just a “loud out.”
In addition, the batter must ensure the bat hits the ball below its center so that the backspin helps keep the ball in the air long enough to get out, but no so much that again it is just a high fly ball to the outfield. It’s a tricky business.
Looking at the data in the table again, you can see Judge launches the ball at about the same angle as the rest of MLB, but with about 7.5% more exit velocity. Yet he only gets an additional 9 feet of distance on the ball. This seems too small: what gives?
Of course, the S3 Flu might explain it, but what fun is that? So, let’s investigate instead by using Alan Nathan’s new Trajectory Calculator. Entering the exit speed and launch angle for MLB’s 2017 homers and then adjusting the backspin to give the average MLB 2017 distance gives a backspin of 1480 rpm for the average MLB 2017 homers.
Using Judge’s exit speed and launch angle along with the 1480 rpm backspin results in an average distance of 438 feet. Adjusting the backspin to get the actual 410-foot distance actually averages 548 rpm of backspin.
Applying this technique to AJ’s 495-foot blast results in a substantially higher backspin than this average value and, to be honest, a bit of a boost by the wind. So, all and all, it appears that Aaron Judge could substantially increase his home-run distances with more backspin. Perhaps, I do have something to discuss with a hitting instructor after all!
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.
So in other words he isn’t living up to his potential. Clearly another overhyped Yankee prospect.
I love the tracer effect on that home run. Good post.
How much actual control does a batter have over the backspin? It feels like something really difficult to consciously change in an actual game environment without hurting their swing.
I think they have control over it, but it isn’t something that can be flipped like a switch. Through training, batters who hit the ball with more backspin have conditioned themselves to aim just a little bit more under the ball compared to batters who hit the ball with less spin.
Doesn’t the mass of the bat need to combine with the bat speed to give you the energy transfer to the ball? I can swing a broom handle pretty quickly, but that doesn’t do anything to a baseball.
Yes the mass of the bat makes a difference, but Judge uses a 33 ounce bat, which I think is pretty standard.
Judge has long arms and so large leverage, which will enable him to reach a higher bat speed with the same rotational velocity from the various parts of his body. He also obviously has the strength to make use of that increased leverage.
Great post and topic. Last year, I looked into the spin issue and the biggest takeaway was that the best (most consistent hitters) are hitting the ball flatter (in terms of spin) than average. Some of the flattest hitters were Joey Votto, Freddie Freeman,JD Martinez, Kris Bryant.
Since most the above hitters have “natural power” as does Judge, it makes sense that these type hitters don’t need to pay the very high price (through less consistent results) for added distance. For some less powerful hitters, the bargain may make a little more sense but for most the cost>benefit.
http://www.fangraphs.com/community/the-home-run-conundrum-is-it-a-matter-of-how-you-spin-it/
Agreed. I wouldn’t want Judge to try to alter his swing to create more backspin and end up popping up more. As is, he hits lots of line drives and doesn’t pop up often, thus leading to high BABIP. He hits enough homeruns as is and doesn’t need to hit them further.
Thanks for articulating this, it’s nice to see you and Dr Nathan in here commenting on this. From watching Judge on a near daily basis this year, this makes perfect sense. He simply seems to hit laser line drives that easily clear the fence, where an average hitter striking the ball the same way would hit the wall on a bounce, or at best hit the wall. Specifically his power to right-center, where he seems to be able to routinely hit it 420-430 ft with one even at 450 ft:
http://i.imgur.com/u0u6G1l.png
I think it might be interesting to see Judge’s homers laid out on a graph with all other homers (from RHH) this year looking at spray (x) and launch (y) angle (perhaps with exit velo as a 3rd variable denoted by dot size). There might be some that can come close or even at times match his pull side power, but my guess is that his consistent power to right center is what really sets him apart. And this seems to be a result of waiting as long as possible to swing, which lets him maximize his contact rate, and carry a higher batting average than your typical power hitter.
I love this. Let’s get more economists, physicists, psychologists, etc in here writing for Fangraphs. I will read all of it.
Anybody know what length of bat Judge is swinging?
You know that big tree in your neighbor’s yard? I bet it’s like that, because Aaron Judge is something like 18 feet tall and two tons.
To generate more backspin, he would need to hit the ball more obliquely (with more offset). That would slow down the exit speed. So basically it is impossible to generate more backspin and keep the EV constant without increasing bat speed. This is why distance is always limited to a fairly narrow range even though the range of EV might suggest much more of a range in distance.
If Statcast is capable of capturing bat speed, would it be measured in angular velocity? Pure velocity at the point of contact? Something else?
I always wondered how scouts judge bat speed. Its impossible to accurately measure it with the naked eye or any tool a scout could bring to the park. So are they looking for how well a hitter can make contact with high velocity pitches? Or how the ball jumps off the bat? Can they really differentiate bat speed based on just a swing, without taking any other factors into account?
I find this subject pretty interesting and would love to read more about it
From visual judgment it also looks like he isn’t hitting the ball with backspin, but I don’t think he should start doing so. Home run distance doesn’t matter, he just has to get the ball over the fence. He has been hitting the ball plenty hard enough to do that without backspin.
I wonder how many balls he has hit this year that would have benefited from more backspin, i.e., they weren’t home runs but would have been with more backspin. From watching the games, I am guessing there are just a small number. However, part of the efficiency of his offensive game is his ability to avoid hitting under the ball. If he were to attempt to hit the ball with more backspin to get more carry on his fly balls, I think he would most likely hit under a lot more balls and his BABIP, batting average, and wOBA would all suffer.
This topic seems to come up fairly often these days, but I would throw up the correlation/causation caution flag before attempting to play the what if game with launch distance.
The energy balance of the batted ball event tells you that any effort spent by the batter to alter the rotational velocity of the baseball will be a net negative to translational exit velocity. The actual +/- to batted ball distance depends on too many factors to capture in this type of “back of the envelope” analysis, but in general, lift due to backspin is going to have a higher order effect than launch velocity and angle.
That said, the body kinematics of swinging a bat is going to play a huge role in limiting what a batter can physically control, and determining the “optimized” swing for a given batter. Some players will converge on proven home run swings which naturally results in more backspin, considering the various factors like power/balance transfer from the lower body, swing path, wrist “rollover”, etc. I don’t think there is any data or analysis to back up the notion that consciously optimizing for extra backspin (at the inevitable expense of launch velocity and angle) will have a net positive impact on home run distance.
The effect of backspin on the flight of the baseball was discussed here: http://www.hardballtimes.com/going-deep-on-goin-deep/. Because the air drag increases with spin, there are diminishing returns to putting more backspin on the ball. I am currently working on firming up that result with additional analysis.
Thanks for the link, Dr. Nathan. These discussions have prompted me to dust off my old fluid mechanics textbook to revisit some of these concepts, and as I attempt to cobble together some crude spreadsheet models of baseball flight dynamics, I’m struck by the completely dynamic and non-linear nature of modelling this problem.
For instance, in terms of aerodynamic forces, the baseball doesn’t only cares about airspeed, not ground speed. So as a baseball is launched into an upwards trajectory, the lift vector is angled up and back so that its horizontal component is effectively slowing the ball down (decreasing its horizontal component). Meanwhile, drag is pointed down and back, so it is detrimental to flight both horizontally and vertically.
On the flip side, once the ball crests its maximum altitude, lift is now helping to push the ball up and forward, while there is a drag component working to slow the fall, in effect helping the ball travel farther.
However, the rotational velocity of the ball is constantly decelerating due to drag, and the trajectory angle of the ball is constantly decreasing, so the detrimental component of lift is maximized, and the complimentary effect of drag happens when it at a minimum.
2nd law of thermodynamics at work.
Another aspect in hitting the ball hard that I never see mentioned is rigidity through contact. When the ball hits the bat, the bat is forced backwards. The batter’s ability to resist this force is what allows the kinetic energy of the bat to be transferred to the ball.
Imagine a bat tied to a rope and swung at a ball. The flexibility of the rope prevents the bat from effectively transferring it’s energy to the ball. This is likely where the term “string wrists” came from when talking about power hitters.
The collision is actually too brief for this to come into play. Strange as it may seem, if the batter let go at the moment of contact, it wouldn’t affect the flight of the ball.
Look at a bat/ball collision in super slo-mo, and you’ll see a bending wave travels down the bat. If the wrists are perfectly rigid, the wave will reflect and travel back up and bring the bat back forward. But by the time it takes for the wave to travel, the ball is long gone from the bat.
E.g. Todd Frazier’s no handed home run!
https://www.youtube.com/watch?v=fczUzv0kcNw
This particular topic is a favorite of mine and one that I have written and talked about extensively. See http://baseball.physics.illinois.edu/grip.html
Hey everybody! Read Dr Nathan’s article, it’s fantastic, and the data is definitive.