Pitches and Stuff: The Gyroball

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Why does a curveball curve? How does a pitcher throw a changeup with the same arm speed as a fastball? Baseball is filled with buzzwords that are often used imprecisely. In this series of articles, Mike Richmond explores the baseball’s motion as it travels through the air: How does it behave, and what can a pitcher do to control it? This article looks at the gyroball to see if it actually exists and, if it does, how it is thrown.

Why does a curveball curve? What’s the difference between a cutter and a slider? The art of pitching is filled with arcane terms, and even when two players are talking about the same thing, they often use different words. In this series of articles, we’re going to look carefully at the motion of a baseball through the air: how does it behave and what can a pitcher do to control it?

Today, we look at the gyroball. This mythical — or is it near-mythical? — pitch has captured the imagination of a generation of baseball fans, through its depiction in manga, anime, and even the western press, but just what is it? In my view, the gyroball is a close cousin of the common slider, as I will explain below. Though it is a real pitch, and can be thrown without recourse to superhuman twisting motions or long years of Zen meditation, it doesn’t appear very often in competition, simply because it doesn’t do much to fool batters.

The Magnus Force on a spinning ball

A ball thrown with no spin will travel along a simple path: nearly a perfect parabola, with just a small correction due to the slowing influence of air resistance. All the “interesting” aspects of pitches — the rise of a fastball, the dip of a curve, the sweeping arc of a slider — are due to the interaction of the spinning ball with the air around it. The details of this “Magnus Force” may be a bit complicated, but they boil down to one particular factor: the angle between the spin axis of the ball and the velocity of the ball.

The velocity of the ball has an obvious direction: from the pitcher’s mound toward home plate. But what is the direction of the spin axis of the ball? Below is a batter’s view of a fastball, coming straight at him with a strong backspin. It’s clear that the spin axis is horizontal … but which way does it point? Toward first base, or toward third?

To help us answer this question, we need Casper the Friendly Ghost, or perhaps Adam Smith, to lend us a virtual right hand that we can position next to the ball, in mid-air. Let’s ask the hand to curl its fingers into a loose fist and stick out its thumb. Do the fingers curl in the same direction that the ball spins?

Nope, this isn’t correct. The fingers are curling toward the batter, down over the top, but the ball is spinning toward the batter, up from the bottom. We need to ask the hand to stand on its head:

That’s it! Now that the fingers curl in the same direction that the ball spins, we can use the thumb to determine the direction of the ball’s axis of rotation. In this case, it points to third base.

Okay, now that we know the directions of the velocity and the spin axis, let’s examine the Magnus Force on a fastball which is heading toward the plate. It will make things easier if we switch to a bird’s-eye view of the situation:

What’s the angle between the spin axis and the velocity? A nice, simple, right angle; in other words, θ = 90 degrees.

The Magnus Force depends on this angle (and some other factors, too, but we can ignore them for now). It turns out that the size of the force includes a term of sin(θ). As you may recall from your math classes, the sine function is largest when its angle is 90 degrees. That means that a ball with pure backspin, moving towards the plate, will experience the largest possible Magnus Force, and thus have the largest possible break. Since the basic fastball grip and release tends to produce this sort of spin, a simple fastball has a lot of break; most of it is upward.

How to throw a gyroball

But we aren’t interested in the fastball; we want to figure out how to throw a gyroball. We’ll use the slider as a starting point. To throw a slider, a pitcher grips the ball between his thumb and index finger and allows the ball to roll out between them as he releases it. Like a fastball, this pitch will have a large amount of backspin.


As the pitcher allows the ball to roll up and out between the thumb and index finger, he may twist his wrist, curling his index finger around the outer side of the ball. The motion is not unlike the classic “royal wave:”

This twist and extra contact with the index finger can increase the spin of the ball — which is good: the faster the spin, the bigger the break. It may also give the pitcher better control of the ball’s trajectory — which is also good. But it may twist the spin axis of the ball, too, pushing it away from third base and towards the batter. And that is NOT good.

The angle between the spin axis and the velocity has shrunk: Iin the picture above, it is only θ = 50 degrees. The sin(θ) term shrinks, too, so that the Magnus Force on this pitch will be only about 75% as large as that on a ball with pure backspin.

If a pitcher twists the spin axis even farther, so that it points almost directly at the batter, he will decrease the Magnus Force — and the break — even more. In the example below, the Magnus Force is only about one-sixth as large as that on the pure backspin.

Now, what would happen if a pitcher threw the ball so that the spin axis pointed forward — directly in line with the velocity? The batter would see a little motionless spot coming right at him, at the center of the spinning surface; something like the ball in this video of a very young Daisuke Matsuzaka.

In this idealized case, the angle θ between the spin axis and the velocity would be zero degrees … and since the sine of zero degrees is zero, there would be no Magnus Force. The ball would have NO BREAK. In the standard vertical-versus-horizontal-break diagram, this pitch would fall in the exact middle, marked by the big black circle.

This modified slider with no horizontal break and no vertical break could be called a gyroball. Many people have written about it, and even more have talked about it; some of the stories make it sound amazing and completely unhittable. But look where it falls in the graph above: not far from the cloud of symbols marking the slider. If batters can hit a slider, they can certainly hit a gyroball.

In fact, very few MLB players throw pitches which fall in this central region of the “vertical-vs-horizontal-break” diagram. I suspect that the main reason is speed. In order to twist the spin axis into the forward position, one’s fingers must grip it mainly on the sides, rather than from behind, as a quarterback does when he throws a nice, tight spiral. That lack of a big push from behind will yield a relatively slow-moving pitch.

So, is the gyroball a real pitch? I believe that it is: A pitch which travels straight in the direction of its spin axis (or, if you prefer, a ball the spin axis of which points directly forward). Is it hard to throw? Harder than a fastball, for sure, but easy enough after some practice. Is it an EFFECTIVE pitch? Evidently not — and so it seems likely to remain tucked away in the shadows of baseball lore, emerging every now and then to befuddle fans and players alike.


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Michael grew up on the South Shore of Massachusetts, but rebelled against his parents by rooting for the Orioles (eventually, he came to his senses). After receiving his Ph.D. in Astronomy from UC Berkeley, he spent five years as a post-doc at Princeton working on the Sloan Digital Sky Survey. He now lives in Rochester, NY, studying supernovae and listening to baseball games far too often.

6 COMMENTS

  1. The one thing the spin does do is prevent the pitch from losing as much velocity as other pitches, so it CAN throw off a batter’s timing to some extent. That’s not necessarily worthless. However, the effect may not be significant enough to make a big difference.

    • Brandon,

      You write that the spin of a gyroball may prevent the pitch from losing velocity as quickly as other pitches. I’m not exactly sure what you mean by this. If you mean “a ball spinning around an axis pointing forward has a lower drag force than a ball spinning around an axis perpendicular to the velocity,” then that would be very interesting. I haven’t read of such an effect, but I’d love to learn about it. If you could provide a reference or two, I’d appreciate it very much.

  2. But you could argue on first principles that it makes sense: air resistance goes as the square of the relative velocity, therefore you would have a minimum of drag if the rotation of the ball was perpendicular to the direction of motion. Probably a minor effect, though… but aerodynamics can be tricky.

  3. Note that the linked article describes an experiment which shows that, contrary to some theoretical model, the coefficient of drag of a rifle-spin ball (gyroball) is not significantly different from that of a standard backspin fastball. Thus, the linked article does not support your interesting hypothesis, as far as I can tell.

    Thank you very much for providing that reference!

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