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-Run Data, Aaron Judge vs. the League
Home Runs Average Dist. (ft) Average EV (mph) Average LA (°)
Judge (21) 410 111 27
MLB (2275) 401±28 104±4 28±5
Data as of this past Wednesday.
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!

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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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So in other words he isn’t living up to his potential. Clearly another overhyped Yankee prospect.