Why flies go one way and grounders go the otherby Matt Lentzner
July 13, 2007
Did you ever wonder why groundballs are almost always hit to the pull side and why many more flies are hit to the opposite field than to the pull field? I did, because at first it didn’t seem to make sense. If a player pulls his hits, shouldn’t they all go to the pull field?
In his book, "The Physics of Baseball," Robert Adair theorizes on this subject. His explanation in a nutshell is that when hitters are out in front of a pitch they tend to hit it into the ground, and when they are behind a pitch they tend to hit it into the air. The fact that the bat does not move in the same plane as the ball caused this effect.
There may be some truth to this theory, but I think it is overwhelmed by the simple geometries involved when a cylindrical bat collides with a spherical ball. Just by looking at the results of this collision we will see how grounders will tend more to the pull field and flies to the opposite field. It doesn’t matter who’s swinging the bat or how good or bad the hitter's timing was.
To get to the nitty-gritty of this problem, we need to make some assumptions. While not 100% accurate, they get us close—physicists do this all the time to make their lives easier. We can do this because we are not trying to get an exact answer, but rather demonstrate the principle.
1. The bat is a perfect cylinder and the ball is a smooth, perfect sphere. This isn’t too far out. The business end of the bat is very close to a cylinder, and a ball without stitches would be very close to a sphere.
2. The ball does not contribute to the outcome. Because the bat is much more massive than the ball, it contributes about 80% of the effect. We’ll pretend that the last 20% doesn’t exist. We’ll be in the ballpark, so to speak.
3. The ball travels on a straight line from the center of the pitcher’s mound to the center of home plate and the bat strikes the ball perpendicular to this line of travel. Pitchers don’t normally pitch down the center line like this. They are usually a few feet to one side or the other depending on their handedness, but, as with the other assumptions, this one is “close enough”.
One thing we can’t ignore is that the bat is not level when it strikes the ball. This is a common simplification, but in our case it is something we need to be more accurate about if we want to get the right answer.
If you think about it, you will realize that the bat is almost never level during a swing—for it to be level the ball would have to be above letter high. That’s not a strike, and few batters will swing at a ball that high unless badly fooled. More typically, the ball is about thigh high. That puts the bat at an angle of roughly 45 degrees. So we have our third assumption:
4) The bat hits the ball at angle close to 45 degrees. Like so:
Figure 1: Here's a typical major league swing mere moments before contact. Notice that the angle of the bat is in the neighborhood of 45 degrees.
Now I’m not going to try to sell you on the idea that collisions in three dimensions are easy to visualize. They most certainly are not, but let’s look at some boundary conditions in a single plane that are easier to come to grips with.
First, we need to backtrack a little from the last assumption we made about the bat being at 45 degrees. We’ll get there a little later, but we need to start with some simpler cases first. Let’s take the case of the bat being parallel to the ground. We have already established that this is not a very good approximation of a real-life swing, but it’s a good starting place since a swing in one plane is easier to visualize. The thing to focus on is where, relative to the center line of the bat, the ball is struck. If we strike the ball dead center, it will start its flight level to the ground, and since our cylindrical bat is perpendicular to the path of the pitched ball, it is heading straight back at the pitcher’s mound. With me so far?
Now let’s imagine the bat hits a little below the center of the ball. In this case, the ball will be hit into the air. The lower the bat gets, the greater the vertical angle of the ball's path upward. The reverse is true, also. If our bat is too high, the ball will be sent toward the ground. This is an intuitive result.
Our second boundary case is when the bat is perpendicular to the ground. Imagine Alfonso Soriano hitting a ball off his shoelaces as only he is able (and willing) to do. Now, the effect of any deviations along the center line of the bat changes the direction of the hit ball instead of changing the trajectory. If we are off a bit to the left, the ball heads off to the right, and vice-versa. If you threw a ball at a round post you’d get a similar effect.
So we have established our two boundary states: Any deviation with a level bat changes the trajectory of the ball, while deviations with a vertical bat change the direction.
Let’s get back to our original model. We assumed a bat angled at 45 degrees, not coincidentally halfway between boundary one (level bat) and boundary two (vertical bat). What this means is that deviations from the center line of the bat have both a trajectory component and a directional component. Thus, a low swing tends to result in a flyball to the opposite field, while a ball hit with the bat being too high will tend to be a groundball to the pull side. Even though we assumed our bat was perpendicular to the flight of the pitched ball (that is, not pulling the ball), we can still account for groundballs to the pull side of the field. It’s all in the physics.
You can test this explanation with a simple experiment. Throw a ball at any cylindrical object, set at 45 degrees—an aerosol can and a ping-pong ball work nicely. Just hold the can at arm's length with one hand and toss the ball with the other. I guarantee that groundballs will go to one side and flyballs will go to the other. If you hit it dead-on, the ball should come straight back.
Now we know why right fielders have to be better fielders than left fielders: Because more batters hit from the right side than the left, right fielders are the ones who have to field many more poorly hit bloopers. Likewise, third basemen have to be on their toes to charge poorly hit grounders that come their way.
Now let’s take a look at why pull hitters are also flyball hitters.
Since pull hitters tend not to hit the ball straight back up the middle, we’re going to eliminate one of our assumptions. We no longer want to keep the bat perpendicular to the path of the pitched ball so we are discarding assumption three. Since we are looking at pulled balls, we want to know what happens when the bat moves further into the swing and is no longer striking perpendicular to the pitched ball.
Once again we will backpedal a bit to set up some boundary conditions—in fact, the same boundary conditions we already used. Once again, looking at the bat parallel to the ground, it is fairly easy to imagine that the further the batter gets into his swing, the more the ball is directed to the pull field. The ball will be deflected further and further toward the pull field the further along the arc of the swing the bat travels. As before, the level bat model is intuitive for most people.
Now let’s look at the boundary where the bat is perpendicular to the ground. As the bat moves further into the swing, the ball is projected at a higher and higher trajectory. Dave Kingman’s famous “pop-up that never came down” that was hit into the roof of the Metrodome was the result of a swing on a ball low and inside. The bat was very close to perpendicular. He was way out in front of the ball and hit it almost straight up. Most pop-ups are mishit, but this ball was tattooed—just not in the right direction. Of course, Mr. Kingman was not known for his disciplined hitting. That was another ball that most players don't offer at.
As before, the most realistic approximation is a 45-degree swing angle, and, as before, it combines the effects of both the boundary conditions. As a player turns on a ball, there is a directional component and a trajectory component to the result. The further into the swing the batter gets, the more a ball is pulled and the more it is lifted into the air.
If you pay close attention when watching a baseball game, you will see players hit over the ball, but the result will be a line drive instead of a grounder because they pulled it. What would have been a grounder when the bat was perpendicular to the flight of the baseball becomes a line drive when the ball is pulled. Likewise, hard line drives that are hit with the bat perpendicular to the path of the pitched baseball often become home runs when pulled.
If you grab your trusty aerosol can you can prove this through experimentation, although it’s a little trickier than the first test. You will need to hold the can at a 45 degree angle in two planes. Hold it at an angle the same way you did in the first experiment and then tilt the end the batter would be holding away from you. You will see now that almost all the ping-pong balls that strike the can will be flies and go to the pull side.
You may be thinking, “He just told me that players hit flies to the pull side when only a few paragraphs earlier he said they go to the opposite field.” Somewhat true, but here’s the distinction: Poorly hit flies go toward the opposite field while well hit flies go toward the pull field. This is another reason right fielders are much busier than left fielders. A large number of flies that left fielders see are traveling over their heads and into the bleachers. They see fewer balls and many of those that do head their way aren’t playable.