Pitches and Stuff: The Curveball

Does a fastball really rise? How does the pitcher’s grip lead to movement? What separates a slider from a slurve? Baseball is packed with buzzwords that experts use 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?

Why does a curveball curve? There are two great families of pitches: fastballs and curveballs. The basic curveball serves as our introduction to the latter group. As we examine this pitch, we will compare it to the basic fastball. For a more technical description, consider reading the effect of air on baseball pitches.

Curves have Topspin

One big difference between a basic fastball and a basic curveball is the direction of its spin: fastballs have backspin while curves feature topspin. All pitches are affected in the same way by the forces of gravity and air resistance, but their spin rate and direction control the Magnus force, and thus how the pitch breaks.

In order to isolate the effect of spin, compare these three pitches that all start with the same speed (90-mph) and direction, all influenced equally by gravity and air resistance. The first pitch has no spin at all and, therefore, no Magnus force. So, it ends up in the middle of the strike zone. The second is a basic fastball, with 2200 RPM of pure backspin. Backspin produces a force lifting the ball vertically, and it crosses the plate nearly two feet higher, at a height near the batter’s shoulders. The pitch with 2200 RPM of topspin, on the other hand, is pushed down by Magnus force of the same magnitude but in the opposite direction ‒ it ends up bouncing off the plate.

Curveball IMG 1

The graphic above is a bit misleading: it implies that one can throw a ball spinning forwards at the same rate that a fastball spins backwards. In real life, for reasons we will examine in a moment, humans cannot give a pitch with topspin the same speed and rate of spin as a typical fastball. The basic curveball travels (80-mph rather than 90-mph) and spins more slowly (1300 RPM rather than 2200 RPM) than its fastball cousin.

To make a fair comparison, this next graphic shows the trajectories of a basic fastball and a basic curveball, each thrown to end up right in the middle of the strike zone:

Curveball IMG 2

In order for the curveball to reach the plate at the same height as the fastball, the pitcher must release the pitch in a slight upward direction above the horizontal. The ball thus “rises” to an apex before tumbling down into the strike zone. The fastball, on the other hand, follows a nearly straight line on its way to the plate as the lift of the Magnus force counteracts the pull of gravity.

Another difference between these two pitches is their speed. Count the circled symbols along each trajectory; they occur every 0.1 seconds. You’ll see that the fastball reaches the batter about 0.44 seconds after leaving the pitcher’s hand, while the curveball takes about 0.50 seconds. This difference of 0.06 seconds corresponds to a gap of about six feet in their position. If a batter times his swing for the fastball, the bat will be “way out in front” of the curve.

Real World Examples

Let’s look at a pair of actual pitches to see how well this simplified view applies to the real world. We’ll pick a fastball (blue color) by hard-throwing reliever Aroldis Chapman of the Cincinnati Reds, and a curveball (red color) by Clay Buchholz of the Boston Red Sox. The bottom left panel shows the same side view as the graphs of the simulated pitches. The path each ball would take if one ignored its spin is shown as a solid line. A new symbol is drawn every 0.01 second, with a darker symbol every 0.1 second.

Curveball IMG 3

The fastball does indeed fall more slowly than a pitch without rotation, due to the upward force produced by its backspin, while the curveball drops more rapidly. Buchholz’s curve, like the model, reaches a slight peak about 20 feet from the mound before dropping into the strike zone. Chapman’s fastball, because of its terrific speed ‒ far above the 90-mph of our basic fastball ‒ reaches the plate about 15 feet in front of the curve. If Chapman could launch the same sort of curve as Buchholz, batters would have no chance. Fortunately for hitters, his pitches rarely travel at less than 85-mph.

Generating Topspin

Why does basic curveball move and spin more slowly than the basic fastball? The answer is simple: the natural motions of a human arm, hand, and fingers when throwing a ball overhand combine and result in backspin. A player who just “does what comes naturally” can sling a decent fastball.

Recall for a moment the mechanics of throwing a fastball. The pitcher allows the ball to rest in the crook of his index and middle fingers. As he brings him arm up and over his head, the ball is pushed forward by those fingers, directly toward the plate, and eventually rolls forward off the tips of the fingers. The arm and fingers accelerate the ball toward the batter.

Curveball IMG 4

To throw a curveball, the pitcher grips the ball from the side and top instead of from behind and below. The arm still brings the ball forward, just as in throwing a fastball, but the hand and fingers play a different part. The hand is rotated roughly 90 degrees relative to its position in a fastball grip, touching the ball from the third-base side (for a right-handed pitcher) or the first-base side (for a southpaw), rather than from behind. As a result, not as much speed gets imparted to the ball.

This somewhat awkward hand position places the middle and index fingers on top of the ball as the arm approaches the release point, so they roll over the front of the ball and give it topspin. Like the hand, the fingers cannot provide an extra push forward to the ball. So as it flies out of the hand, the ball is moving considerably slower than a fastball. In effect, the pitcher is generating topspin by releasing the ball in an inefficient manner, trading speed and power for control over the direction of spin.

Curveball IMG 5

The Speed/Spin Diagram

An experienced observer can tell a fastball from a curveball simply by watching the flight of the ball, either in person or on a television screen. In recent years, technology has provided us with tools to make pitch identification easy for everyone. The PITCHf/x system is described in an article by Mike Fast and others, which are collected here by Alan Nathan. Below is a brief overview.

Major League Baseball installed special high-speed cameras at two locations in each stadium which record the position of each pitch roughly 20 times during its journey to the plate. By fitting a model of the baseball’s three-dimensional trajectory ‒ one which incorporates the effects of gravity, air resistance, and Magnus force ‒ to these measurements, the ball’s initial speed, direction, spin rate, and spin orientation can be derived. These fitted parameters are used to make the graphic overlays seen on some TV broadcasts and real-time apps. They are also made available to the public at the excellent Brooks Baseball Pitchf/x website.

Let’s use the Pitchf/x tool to analyze the performance of lefthander Barry Zito of the San Francisco Giants in a game against the Dodgers on March 31, 2008. By default, the tool will create a series of graphs illustrating the properties of Zito’s pitches. One of them shows the speed of each pitch (in mph) against its spin orientation (in degrees away from pure topspin). We have added a few additional notations to the original graph in our modified version shown below. Please note that these graphs are from the catcher’s point of view.

Curveball IMG 6

Most pitches fall within a few small regions in this diagram. The most common appear near the top; they share a relatively high speed and a spin axis oriented at about 180 degrees. In this diagram, a value of 0 degrees or 360 degrees denotes pure topspin, while 180 degrees indicates pure backspin. A combination of “fast” and “backspin” means that these pitches are fastballs.

In the lower–right–hand corner of the graph is another clump of symbols. These pitches are much slower, averaging about 70-mph, and their spin axis is close to 360 degrees, indicating they have nearly pure topspin. “Slow” and “topspin” is the recipe for curveballs.

There is one more large cluster of symbols in the lower-middle region of the graph. They represent pitches which were relatively slow, yet possessed backspin. We have not met a pitch with that particular combination yet, but do not worry – we will!

Remember that the pitcher’s job ends when the ball leaves his hands; after that, all that matters is the spin of the ball. If you understand the interaction of the ball with the air, it may help you to recognize when a pitcher is on top of his game or having a bad day.


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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.

8 COMMENTS

  1. Very informative. Looking forward to the next piece. Love having all this stuff clearly summarized.

    As someone with no physics background whatsoever, I do have a question on Chapman (or anyone) theoretically throwing a curve at a high velocity. A hypothetical high-90s curveball would be airborne for a far shorter time than a traditional curve topping out around 80, and thus would have less time in the air to actually curve before reaching the plate. At the same time, the higher velocity would seemingly subject the ball to greater forces as it traveled toward the plate. Would these forces offset the fact that the ball had less time to move? Or would a curveball thrown with regular curveball spin but at a higher velocity see less movement than one thrown at a lower velocity?

    • Good question! As you mention, there are competing effects. Let’s consider an “ordinary” curveball, pure topspin at 1300 RPM and moving at 80 mph, and a “super” curveball, pure topspin again at 1300 RPM but zooming toward the plate at 95 mph.

      The size of the Magnus force depends on the speed to the second power, so that would suggest that the “super” curve will have a larger breaking force by a factor of about (95/80)^2 = 1.4. On the other hand, the Magnus force also depends (to the first power) on the ratio of the rotational speed to the translational speed; that ratio goes into what’s called the “lift coefficient”. The smaller that ratio, the SMALLER the Magnus force. Since the “super” fastball has the same spin rate, but moves faster, it will have a smaller lift coefficient, by a factor of (80/95) = 0.84. These two factors act in opposite directions, so that the net effect is a slightly larger Magnus force.

      And, of course, as you point out, the faster pitch will reach the plate more quickly, giving the slightly larger Magnus force less time to act.

      The net result is that the two pitches have almost identical breaks. I find that the “ordinary” curve breaks down by 7.1 inches, while the “super” curve breaks down by 7.0 inches. That’s pretty much no difference at all, as far as the break goes.

      On the other hand, the “super” curve gives the batter less time to react. So, on the balance, I’d say that if a pitcher COULD throw the “super” curve, it woud be a very effective pitch!

  2. Regarding the spin on a curveball, I recently wrote about that for Baseball Prospectus, http://www.baseballprospectus.com/article.php?articleid=25915. In that article (“All Spin Is Not Alike”), I discuss how to use measurement using Trackman to distinguish total spin from “useful spin”. The latter is spin that results in movement, the same spin that Mike is discussing here. The total spin includes that plus any “gyrospin” component, the latter not contributing to any movement. For the small set of data I analyzed, I found that the total spin on a curveball is typically about the same as for a fastball, 2200-2500 rpm. However, whereas all of the fastball spin is useful spin, only a fraction of curveball spin (1000-1200 rpm) is useful. So, I agree with Mike’s remark about the spin on a curveball being less than that on a fastball, but only if he means “useful spin”.

  3. What is the minimum speed a pitched baseball must reach for it to curve (travel a path altered by the ball’s rotation). Also, the minimum speed a pitched baseball must reach for it to wobble from being thrown with no rotation (knuckleball)?

    • Hmmmm. That’s an interesting question. In theory, a ball of ANY speed will curve, as long as it has some spin. Now, the Magnus force does depend in part on the speed of the ball through the air — so the faster you throw it, the larger the force. On the other hand, the faster you throw it, the more quickly it arrives at the plate, and so the shorter the period that Magnus force has to alter the position of the ball. To some extent, the two factors (a larger force vs. a shorter period in the air) cancel each other, meaning that the amount of drop of a curveball, relative to a non-spinning ball, when it finally reaches the batter will be (very very) roughly the same, regardless of its speed.

      As for your second question, I’m afraid that I don’t understand the physics of the knuckleball well enough to answer it. I need to study and learn more.

  4. Here’s a question I’ve had for a long time: what is the physical meaning (if any) of the term “hanging breaking ball”. You hear it all the time, but it’s never been clear to me what exactly is going on. Does if fail to spin, or spin in the wrong orientation, or what?

  5. I’ve watched many games and seen many pitches described as “hanging,” just as you have. As far as I can tell, the common feature of these mistakes is that they are located high in the strike zone when they reach the plate; as a secondary feature, they don’t show a lot of motion or break. This unfortunate combination makes them easy for batters to punish, of course.

    I can’t say for sure what causes a pitch to “hang”, since there are two somewhat distinct possible causes. One is that the ball doesn’t spin as rapidly as usual. Since the Magnus Force depends linearly on the rate of spin, a ball which slips a bit from the pitcher’s fingers and spins at half the normal rate will break by half the usual amount. The other possibility is that some error in the grip or release leaves the spin axis of the ball pointing in the wrong direction. As you will see in a (near) future installment of this series, the largest breaks occur when the spin axis is perpendicular to the velocity of the ball; in other words, if the spin axis points basically along the third-to-first line, or titled vertically relative to it. If the ball’s spin axis happens to point nearly straight toward the batter, then the size of the Magnus Force will drop precipitously, yielding a trajectory which has little or no break.

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