What A Rare Baseball Collision Tells Us About The Physics Of The Game

14:10 minutes

Recently during a pre-game warmup, Phillies right fielder Bryce Harper was doing some batting practice when he hit a line drive to right field, and it collided with another ball in midair.

It was an extremely rare event we’ll probably never see again. But if someone were to try and duplicate the collision, would physics work in their favor? 

Ira is joined by Rhatt Allain, assistant professor of physics at Southeastern Louisiana University and writer for Wired’s Dot Physics blog, for a quick back of the envelope discussion. Plus, baseball players and fans are learning more about the physics of the game—exit velocity and launch angle are now statistics that people can calculate and tally. Dr. Alan Nathan, professor emeritus of physics at University of Illinois and professional baseball consultant, talks about how physics is changing how America’s pastime is played. 

a simplified map of a baseball field showing the path of the two balls, where they collided, and basic physics formulas describing the paths
Rhett Allain’s illustration and analysis of the two colliding balls. For more detail on his analysis, check out his blog post. Credit: Rhett Allain

Further Reading

Segment Guests

Rhett Allain

Rhett Allain is the author of Geek Physics and an associate physics professor at Southeastern Louisiana University. He also writes WIRED’s Dot Physics blog.

Alan Nathan

Alan Nathan is an emeritus professor of Physics at the University of Illinois in Champaign, Illinois.

Segment Transcript

IRA FLATOW: This is Science Friday. I’m Ira Flatow. As a long-time baseball fan and overall baseball geek, I think that if you watch enough baseball, you think that you’ve seen just about everything there is to see, and then something really new and surprising happens. Here’s what I mean. Recently, during a pregame warm up, Phillies right fielder Bryce Harper was doing some batting practice. He hit a line drive to right field, and it collided with another ball in midair.

ANNOUNCER: Bryce Harper lines one to right center field, but it hits a ball that was coming in from the outfield, and the ball spins. That is amazing.

IRA FLATOW: It was amazing, an extremely rare event you’ll probably never see again. You’d have to get the physics just right for it to happen. But if you were to try and do it again, how would that work? Joining me now is someone who enjoys thinking about these questions almost as much as I do, but he is a lot smarter and has the physics to answer them. Rhett Allain, professor of physics at Southeastern Louisiana University and writer for Wired’s Dot Physics blog. Rhett, welcome back to Science Friday.

RHATT ALLAIN: Well, thank you for having me.

IRA FLATOW: OK Rhett, so how did those balls collide? What are the odds? How do you figure that out?

RHATT ALLAIN: It’s pretty much impossible to figure out the odds because there’s so many– they’re unconnected events that just happened to happen. You can look at Bryce Harper hitting the ball and you can look at the throw from the outfield, and those aren’t related at all, so one could start at some time and the other could start at some other independent time.

And so if you say I’m going to start these at the same time, then you can start playing around with the numbers and doing some calculations to see what the likelihood of those two hitting are. And let’s just say that just looking at the hit alone and the angles that you hit at the ball, it’s pretty unlikely that that would happen.

IRA FLATOW: But you did go ahead and model the motion.

RHATT ALLAIN: Of course, I want–

IRA FLATOW: –that, yeah, have all that, tell us what you came up with.

RHATT ALLAIN: So what I like to do is to find events in real life. It’s a physics problem. And the great thing about a baseball is that if you throw it at not too great of a speed, then it’s your classic projectile motion problem in physics, where you only have one force acting on it and that’s the downward gravitational force.

It’s a solvable problem, but you can take it a lot further. You could add in air resistance to the ball and make it more realistic. And that’s what we like to do in physics is to make something as simple as possible, we start off that way, and then add more complicated things as they go on. So what I did was just model a whole bunch of different baseballs on a computer and see how many of them would hit an incoming ball that was tossed from the outfield.

IRA FLATOW: And how many balls did you actually have to get in this so-called Monte Carlo calculation?

RHATT ALLAIN: So I did a Monte Carlo calculation, which is named after the Monte Carlo Casino in Monaco, and the idea is we’ll just start with a bunch of random different numbers to generate a bunch of different cases. So what I did was start with 5,000 hit baseballs, and then the tossed baseball from the outfield is always the same.

And I would vary the two angles that that ball would leave the bat at. I didn’t change the speed, I didn’t change the time, I didn’t change the location, and I did 5,000– well, I didn’t do it, I made a computer do it. I did 5,000 hits.

And this is actually a really nice thing to do because programming languages are so easy compared to the way they were in the past that this is something a student could do. If you can get it to work once, you can get it to work 5,000 times, there’s no difference.

And so of those 5,000 times, just a few of them hit, and I looked at which starting angles from that hit resulted in a collision in the air, and it was within plus or minus 0.1 degree that it had to leave from that bat in order to hit the ball in the air.

IRA FLATOW: So you actually came up with an answer to the question.

RHATT ALLAIN: The answer was that 0.1 degree variation. If it was more than 0.1 degree off from the baseball bat, it would miss the ball in the air. But that doesn’t include the timing, changing in the timing of the hit, or the initial speed of the hit. I kept those always the same. So it shows you how difficult it is just by changing those two variables, the elevation angle and the side-to-side angle of that ball leaving the bat. If you’re off by more than 0.1 degree, it’s going to miss.

IRA FLATOW: So given that probability, I’ll probably never see that happen again.

RHATT ALLAIN: And then on top of that, you think of all the things that have to happen. You have to have a camera there. How many cameras are even recording the swings before the game? They probably don’t even do that. Or it could be looking in the wrong direction.


RHATT ALLAIN: Yeah, you’re not going to see it again.

IRA FLATOW: Right, I love talking baseball and physics. Thank you for taking time to be with us today.

RHATT ALLAIN: Thank you.

IRA FLATOW: Rhett Allain, associate professor of physics at Southeastern Louisiana University and a popular Dot Physics blogger at Wired science blogs. There is so much else having to do with the physics of baseball that I just got to keep talking about it, so I’m going to bring on another guest, Dr. Alan Nathan, professor of physics emeritus at University of Illinois, and someone who has worked with the MLB to answer questions about the game from a physics perspective. Dr. Nathan, welcome to Science Friday.

ALAN NATHAN: Great to be here.

IRA FLATOW: Baseball fans, and I’m sure you must be one of them, they’ll tell you that baseball is nothing if it’s not about statistics. And one of the latest statistics about the spin of the baseball, which we’ve never used to keep track of it before, why are we keeping track of the spin of the baseball now?

ALAN NATHAN: Because we can. It’s a simple answer. So basically, one of the goals of the pitcher is to confuse the batter. So if the pitch were going perfectly straight or if it were just under the influence of gravity, for a major-league hitter that would be very, very easy.

But the fact that the ball is spinning makes it move in different directions, depending on the axis of rotation of that spin. That determines the direction that the ball will move. And the rate at which it’s spinning, RPM, revolutions per minute, determines how much movement there actually is. And these are very important features of a pitched baseball that pitchers, batters, and baseball fans all consider rather important.

IRA FLATOW: And we have this other new statistic that’s kind of nutty also, which is exit velocity and launch angle of the ball leaving the bat.

ALAN NATHAN: Right. So yeah, the exit velocity, the speed with which the ball leaves the bat, launch angle is the vertical elevation angle, the angle above the horizontal. And I would say five years ago that wasn’t part of the– it was part of the physicist’s lexicon, but not part of the baseball fan’s lexicon, but now it is.

People know that, for example, if you want to hit a home run, that exit velocity better be in the neighborhood of about 100 miles an hour or greater and the launch angle better be in the range maybe 20 to 35 degrees. Below 20 there aren’t too many home runs, above 35 not so many.

As I said, physicists have known this for a long time. Fans now are much more appreciating what those terms mean. When you say exit velocity, they know what a good exit velocity is, what a good launch angle is.

IRA FLATOW: And so are the ball players. You hear them talking about all this stuff all the time.

ALAN NATHAN: Absolutely. People even talk about the launch angle revolution. So if you hit the ball hard, over 100 miles an hour, but at a low launch angle, you may get a hit, but you’re not going to get a home run. To get a home run you have to really elevate that batted ball. And batters in the past several years have been doing exactly that. They’ve been altering their swings in such a way as to increase that launch angle, in effect going for the long ball as opposed to just the base hit.

IRA FLATOW: How big a factor is the wind? Because you watch these games and you see, the wind is blowing out in Wrigley Field, there are going to be a lot of homers. It’s blowing in in Fenway, no one’s going to hit it out today. It seems like the wind really is a big factor.

ALAN NATHAN: The wind is a big factor. It has a tremendous effect on how much that ball carries through the air. And even something like a 5 mile per hour wind could have a huge effect.

IRA FLATOW: Is that right? Just 5 miles per hour?

ALAN NATHAN: Just 5 miles an hour. On a ball that’s otherwise optimally hit, a ball that might travel close to 400 feet, if the wind is blowing out at about 5 miles an hour, it travels about 15 feet more. And if it’s blowing in, about 15 feet less. And that’s only 5 miles an hour. So the wind plays a huge, huge role.

IRA FLATOW: Do you have any opinion on moving the mound? They’re testing this out in the minor leagues, moving the mound back about a foot or so. Will that have a lot of effect on the physics? Will the physics change?

ALAN NATHAN: Yeah, so adjustments have to be made. So the principal adjustment is since the ball travels over a longer time, then gravity will exert its effect over a longer period of time, so the ball will drop more than it otherwise would. And the pitcher is going to have to compensate for that. Batters have the advantage that since the ball is in the air longer, that gives them more time to observe the pitch and make a decision about whether to swing or not, how to swing, et cetera, et cetera.

IRA FLATOW: Has MLB talked to you at all about this possibility?

ALAN NATHAN: Yeah, so I was part of this committee a couple of years ago looking into the reasons for the big increase in home runs. And we’ve kicked around, in a sort of informal way, ways that the game could be changed to create more fan interest in the game.

There are a lot of people these days, and I count myself among them, who worry that the game seems to be dominated by two things, home runs and strikeouts. And when the ball is not actually put in play so a fielder actually has a chance to do something, it becomes less interesting to a lot of people. So looking for ways to increase the number of balls in play, decrease strikeouts, actually try to decrease home runs.

IRA FLATOW: This is Science Friday from WNYC Studios. We’re talking baseball. I almost started singing the song, we’re talking baseball this hour with my guest, Dr. Alan Nathan, professor emeritus of physics, University of Illinois, a freelance consultant for professional baseball. There were fewer home runs this year than– well, certainly not last year, no one’s counting last year, but the year before. Do we know why that was?

ALAN NATHAN: This is something near and dear to my heart. In the half hour or so prior to coming on with you, I was actually analyzing the latest data about that. One thing is for sure true, home runs per ball in play has dropped this year relative to what it was two years ago. Two years ago it reached an all-time high, the most home runs in any season of baseball. This year is going to be down significantly.

One of the reasons, and probably the primary reason why it’s down, is that the air drag on the ball is greater than it was two years ago. And this is sort of a property of the baseball, it has the technical name drag coefficient. It’s something you can actually measure. And suffice to say the greater this drag coefficient, the more the ball slows down in the air, the less the drag coefficient, the less it slows down.

So it affects the air resistance on the ball and has a tremendous effect on how far that ball will carry. So when that property of the baseball, for whatever reason, changes, it actually can affect the number of home runs in a very dramatic way.

IRA FLATOW: So no one thinks that maybe they changed something on the inside, they deadened the ball from the core, the winding, or something like that?

ALAN NATHAN: They did, in fact, and they told everyone that they did. But the change that was made to the ball doesn’t affect the carry of the ball, the air resistance. It does affect the dynamics of the ball-bat collision. In effect, as you say, they deadened the ball a little bit, so it’s less bouncy and it’s likely to come off the bat a little bit slower than it otherwise would have.

I have not seen, in the data that I’ve looked at so far this year, any strong evidence that that’s the case. So if you look at exit velocities, if the ball were significantly deadened, you might expect to see a reduction in exit velocities, and at the moment I would say it’s hard to say that you see it. It’s also hard to say that you don’t see it. It’s a complicated statistical problem to be able to examine that.

IRA FLATOW: I could go on talking baseball all day long about different things, I just have run out of time. I just leave you with one request. If you talk to MLB, please tell them not to get rid of the pickoff throw to first. That is crucial for keeping the game the way it is.

ALAN NATHAN: I completely agree. I’ll make sure they know about that.

IRA FLATOW: OK, all right. OK, give them a little talk for me. Thank you very much for taking time to be with us today. Dr. Alan Nathan, professor emeritus of physics, University of Illinois, freelance consultant for professional baseball.

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