One of the coolest things about baseball in the internet era is that there are as many stories as you have time to read. Last week, for example, Giancarlo Stanton hit a home run at Fenway Park, and a fan threw the ball back onto the field. That’s not unique, but the fact that the throw hit Stanton on one hop certainly was. That story was all the rage for a few days, and you can certainly see why. It seems really hard to throw a ball that far! In video form, it looked roughly like this:
One of the worst parts about baseball in the internet era is that stories don’t hang around for long. This story was incredible! It’s basically the plot of Rookie of the Year, a fact that everyone certainly brought up when it happened. That was kind of it, though. After the initial clips and laughter, the hive mind of baseball moved on to the next funny video and that was that. Now that it’s the offseason for the Cardinals, though, baseball is going to move a lot more slowly in these parts. I had a take I wanted to investigate. Who do you think throws harder- anonymous Red Sox fan, or Marcell Ozuna?
It’s worth acknowledging that this wouldn’t have been a question before this year. On the Marlins, Marcell Ozuna had an absolute Large Hadron Collider of an arm. Since he arrived on the Cardinals, a shoulder injury has sapped Ozuna’s arm strength. It hasn’t sapped it a little, either- he finished last among all qualified outfielders on the average speed of competitive throws this year. Statcast’s measures of outfield arm strength aren’t publicly searchable, but digging through articles about Ozuna got me a few answers. In this article about Ozuna’s shoulder injury, Jennifer Langosch drops a few throwing strength tidbits. In 2015, Ozuna averaged 92.1mph on the top 10% of his throws (see here for an explanation of why the top 10% is the metric Statcast uses). The shoulder injury has been worsening since then, however. He averaged 89mph in 2016 (still good!), 81.5mph in 2017 (bad!), and 77.9mph this year (seemingly impossibly bad!). He’s literally last among outfielders with at least 75 throws this season.
That’s alarming, but it’s not really the purpose of this article. Instead, it just gives us a baseline for the kind of mustard Ozuna is putting on the ball. Now it’s time for a dorky divergence. Take another look at the Stanton home run throwback. Use this article for a few vantage points. Nothing about the guy’s form says so, but he must have put some real force on that one just to get it from the wall to second base. The problem is, Statcast isn’t tracking fan throws on throwbacks, so I had to do a little math on my own.
First things first: I had to figure out how far the ball traveled before hitting Stanton. Some of the replays of the throw showed a wide angle, so I was able to estimate roughly how far along the Green Monster the fan was when he threw the ball. Using published distances for Fenway, I estimate that the wall is about 330 feet from home plate where the fan threw the ball back. Additionally, he’s standing about five feet behind the front of the wall when he releases, so his throw comes from about 335 feet from home plate. You might be asking why I care about the distance from home plate. He threw towards second base, after all. Well, it’s about to get a little math-y in here. We have the distance from home plate to the fan. We know that the distance from home to second is roughly 127 feet (thanks to the Pythagorean Theorem, a rare time the *actual* Pythagorean Theorem is used in a baseball article). Connecting second base and the fan’s release point leaves a triangle that looks like this:
I also estimate that the angle between the two lines we know is about 30 degrees. The fan was roughly a third of the way across the Monster, and the full angle from foul line to center is 45 degrees, so that’s where 30 comes from. Then, things head into full-on trigonometry. Using the law of cosines, those two lengths and one angle are enough to provide us with the third length- 234 feet. The ball bounced about five feet before getting to Stanton, so let’s call it 229 feet of length from the fan to where the ball bounced. I’ll stipulate that these are definitely just estimates- I don’t have the precise angle from which the ball was thrown, and I know that the ball didn’t go exactly to second base. Still, though, it’s pretty close, certainly close enough for a kooky article trying to guess how hard the ball was thrown.
Okay, so at this point we have the distance the ball traveled. The Green Monster is 37.2 feet tall, and let’s say the fan threw the ball from another 6 feet higher (his hand level at release). Now we have a release height, and a final distance. Next, things go full-on Zapruder. By watching the above clip over and over (and over) with a stopwatch, I worked out that the throw took roughly 3.8 seconds from release to bounce. That’s another variable solved. The last thing we need is the fan’s release angle, and I won’t lie- this is getting somewhat close to guesswork. Ten more views later, I’m going to call it a 45 degree launch angle. Is that definitive? Most definitely not. It’s my best estimate from the video we have, but I’m open to suggestions if anyone thinks it was a little different.
With all the variables accounted for, the next thing to do was figure out how to calculate a baseball’s speed based on all the other stuff I had. My first stop was googling ‘baseball trajectory equation.’ A quick tip- don’t do that. I’m no math simpleton, but there’s simply too much. You want an equation for the drag the air exerts on the ball? The interaction of the Magnus Force with the initial spin of the ball to produce lift? They’re all out there, and they have Greek letters in them like you wouldn’t believe. Luckily, my second stop was a lot more fruitful. Professor Alan Nathan, the most famous physicist in baseball, runs an incredible website called The Physics of Baseball. While I couldn’t call Dr. Nathan and ask him to solve my problem for me, his website includes a handy Trajectory Calculator.
This paragraph break is for dramatic effect- the fan’s throw came out of his hand at around 85mph. That’s not a cannon or anything- it’s below the major league average- but it’s still 7mph faster on average than Ozuna’s throws have been this year. Ozuna’s hardest throw as of August was 83mph, so the fan even beats that. There’s definitely plenty of margin of error in my calculation. Drop the release angle to 40 degrees and the fan’s throw would only need to be released at 75mph, marginally slower than Ozuna’s average throw. There’s no way of checking the accuracy of my measurements- they could add or subtract several miles per hour from my estimate of the throw’s release speed. Let’s not get caught up in the semantics, though. Some dude was watching the Red Sox play the Yankees when he happened to catch a home run ball. With no warmup, he threw it back onto the field. That throw was, in a manner of speaking, major league caliber. It wasn’t GOOD major league caliber, necessarily. Still, though, Marcell Ozuna was worth 2.7 WAR this year. He was an All-Star in 2017. He’s a phenomenal athlete, even if his shoulder is a bit banged up. It’s pretty incredible that a Red Sox fan a couple beers deep can equal him in a throwing contest.