# The home run milestone nobody is talking about

1June 18, 2017 by jessepell

(Courtesy of Carlos Herrera/Icon Sportswire)

**Written by Jesse Pelletier**

On Friday, Jun. 16, 47 home runs were hit across Major League Baseball. And they were a great 47, including plenty of late-inning heroics, another Aaron Judge bomb and the longest homer by a pitcher in the Statcast era.

On such a good day of dingers, it makes sense that the Mayor of Ding Dong City himself, Travis Shaw, hit the longest one of the day. But among those 47 home runs was one more significant than any other, and it’s gone completely under the radar. Which one, you ask? I have no idea.

This anonymous home run marked a major milestone for Major League Baseball: one million feet of home runs hit this season.

One million feet. 189 miles. The distance from New York City to Philadelphia and back. However you quantify it, it’s mind-boggling. In honor of such a feat, let’s look back on this season’s dingers.

Some of the year’s home run headlines have been pretty wacky. At the end of Opening Day, Madison Bumgarner led the league in home runs. The best offensive performance of the season featured four homers from Scooter Gennett. The first player to get to double-digit homers hadn’t even played in the MLB since 2012. The guy leading the league today is a rookie leading the majors by a margin of four. And while not exactly “wacky,” Pujols joined the 600 home run club. Kind of a big deal.

When it comes to home runs, nothing has been more awesome than Aaron Judge. He leads the league with 23 long balls on the year while nobody else has cracked 20. He is also the proud owner of the longest homer of the year at 496 feet. Of course that’s impressive, but even more impressive to me is how much further it was than the next longest: Chad Pinder’s 483-foot bomb. The rest of this article will be devoted to that. Happy million, baseball!

(Courtesy of Kathy Willens/AP)

The difference in the two longest home runs is 13 feet. That may not seem like a lot, but the third longest home run and the 28^{th}-longest home run are separated by the same margin. Pretty impressive.

So, the science: air resistance increases quadratically with ball velocity. Basically what this means is that doubling exit velocity gets you less than double the distance. Kinetic energy is related to velocity squared, so to double your exit velocity you’d need four times as much energy. Long story short, quadruple the energy input and you don’t even get twice the distance output.

The launch angles of the two longest home runs were about equal; 26.4 and 26.0 degrees, respectively. The exit velocities were 119.6 and 115.6 miles per hour, respectively. Some math tells us that Judge’s ball had 7.0% more energy than Pinder’s off the bat. The result was a 2.7% increase in distance. That’s significantly less than the energy increase of 7.0%!

To show the effects of air resistance, I built a dumbed-down baseball simulator. Give it an exit velocity, launch angle and height off the ground at contact and it will trace the ball’s trajectory until it hits the ground. If you were wondering how much of a nerd I am, hopefully that answers your question.

Of course this is a very daunting task that would require a lot more work than I put in, but I included effects of gravity, air resistance and a very crude model of lift due to ball spin. The simulation doesn’t account for weather, but overall the sim seems fairly reliable. I tuned it so that the launch angle and exit velocity of Judge’s 496-footer indeed produced a 496-foot homer, and when I tested it with Pinder’s 483-foot metrics it spit out 479 feet. Given that it doesn’t include weather and the spin lift model isn’t great, I’d call that pretty damn good. Admittedly the sim doesn’t predict shorter homers quite as well, but it works well enough in the region of interest. More importantly, it proves the bigger picture I’m trying to paint.

Remember, the point of the sim was to show how much extra energy it takes to add distance to longer homers. Since the Judge-Pinder gap is a 2.7% distance increase, I used the sim to figure out exit velocities that yield a 2.7% increase, but instead from 350 feet to 359 feet. The sim tells me a 350 foot home run would have to be hit at 87.3 miles per hour and a 359 foot home run would have to be hit at 89.1 miles per hour. Those numbers don’t reflect the metrics of real-life homers of that distance quite as well, but even so, the sim says there’s a 4.2% increase in energy to add 2.7% distance. Perhaps the 4.2% has some error in it, but the fact that it’s significantly lower than 7% proves my point: the longer the home run, the harder it is to add distance.

So, yeah. Judge’s home run gap on Pinder? Impressive.

If you’d like to know more about how the simulator works, feel free to contact me!

Good article…liked the math spin on it! May want to consider making it a little less nerdy

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