Pitches and Stuff: The Fastball

The fastball is the most prevalent pitch in MLB. Thrown at speeds of up to 102-mph, the ball travels sixty feet, six inches through the air and, depending on the grip and release, can act very differently. In this first installment of his series of articles on MLB pitches, Michael Richmond helps us understand the physics of fastballs.

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?

Let’s start with the simplest and most common pitch of all, the basic fastball. It’s the first pitch a kid learns when he enters Little League, in part because it rolls so naturally off the fingers, and in part because it places little stress on the shoulder and elbow. Because it is so simple, we’ll use it throughout this series as a standard against which other pitches will be compared.

Before we can discuss the fastball, we need to set up some ground rules and spend some time on the forces acting on a ball as it heads toward home plate.

Setting The Stage

The actors in our little drama will occupy a region of space which is just about the width of a theater’s stage – around 60 feet. In real life, pitchers of different sizes and shapes will release the ball from slightly different locations, and batters will stand a bit closer or farther from the mound, but for our purposes, it will be handy to have a standard starting and ending point for the baseball’s journey.

There are a number of additional assumptions which will go into our calculations, but it would be tedious to list them all. If you are interested in a more technical breakdown you can find it here.

The Simple Forces Acting On The Ball

A pitcher can exert all sorts of crazy forces on the ball with his hand, but when he releases it only two influences remain.

  • gravity pulls the ball toward the ground
  • air resistance slows it down*

* Yes, air can have another effect on a spinning ball, but we’ll talk about that in a moment.

How important are these two influences? One way to find out is to compare the trajectory of a ball thrown in a vacuum to one thrown through the air. Let’s start each ball at exactly the same speed – 90-mph – and in the same direction.  You can see in the diagram that each pitch travels on a different path to its destination.

Drag impacts the ball’s motion in two ways: The ball takes longer to reach the plate (note the location of each pitch after 0.40 seconds), and it drops toward the ground more rapidly than the ball in the vacuum.

It’s easy to overlook this effect when you’re playing catch in the backyard, but it has a strong influence. For a typical fastball, the drag force is a bit greater than the gravitational force; it can really change the speed of a pitch. For example, if a ball leaves the pitcher’s hand moving at 90-mph, it will be moving at about 80-mph when it crosses the plate! Whenever we mention the speed of a pitch in this series, we mean the speed of the pitch as it leaves the pitcher’s hand.

The Complex Forces Acting On The Ball

When a ball is thrown through the air, we can imagine the ball moving through a stationary atmosphere, or we can consider a strong wind flowing past a motionless ball; the results will be the same. Let’s adopt the second model for the moment. It’s clear that the wind will push the ball backwards – we call that “air resistance.” But, if the ball happens to be spinning as the air blows past it, a different type of force arises.

Picture a horizontal wind flowing past a ball fixed in place, but rotating with backspin.

The top of the ball will be moving in the same direction as the wind, so the air will have to catch up to it. The bottom of the ball is rotating against the wind. Some rather complicated fluid dynamics between a thin layer of air rotating with the ball and the passing wind cause stronger turbulence over the top of the ball. The net result is that the ball pulls air down and so, in an equal and opposite reaction, the air pushes the ball up.

Physicists call this the Magnus force. Its size depends on a combination of the speed of airflow past the ball and the rotation of the ball.  For velocities around 90-mph and spin rates around 2200 RPM – a basic fastball – the Magnus force is roughly half the size of the gravitational and drag forces.

The Trajectory Of A Basic Fastball

In order to throw a fastball, the pitcher employs a natural-feeling grip: He holds the ball with his thumb on one side, index and middle finger over the top, and ring and little fingers on the other side. He cocks his arm as he rocks back on the rubber before bringing the ball over his head while sitting on top of his fingers. As he extends his arm forward the ball rolls off his index and middle fingers picking up a strong backspin.

The defining features of a fastball are its high speed and its pure backspin. This backspin will lead to a Magnus force which pushes the ball upward, not enough to counter gravity completely, but enough to alter its flight.

If we include all three effects – gravity, drag, and Magnus force – we can make a realistic model of a basic fastball. If we compare it to a pitch with the same initial velocity, but no spin (and hence no Magnus force), we see that the pitch with backspin ends up crossing the plate about two feet higher.

How long does it take this pitch to reach the plate? You could count the dots in the graph above to find out: Each small dot is one hundredth of a second, and a big dot appears every tenth. So this ordinary fastball takes a bit more than 0.4 seconds to cover the distance to the batter.

To get a feeling for that interval, try the following experiment. Say the name of the sixteenth president of the United States; you know, the guy with the stovepipe hat: Abraham Lincoln.

As noted in the graph, if the ball leaves the pitcher’s hand as you start speaking, it will zip past the plate before your mouth forms the “m” in “Abraham.”

Not All Fastballs Are Created Equal

Now, the examples so far have assumed some “typical” values for the speed and spin rate of the ball. In real life, pitchers can give their “basic fastball” a wide range of properties. For example, some throw it much faster than 90-mph. Aroldis Chapman routinely exceeds 100-mph on the radar gun. On September 6, 2014, Chapman faced SS Wilmer Flores of the New York Mets in the ninth inning, with the Reds up 2–1. On the sixth pitch of the encounter, Chapman poured a fastball over the outside part of the plate.

As the ball came out of the lefty’s hand, it was moving at 102-mph and rotating at 2600 RPM with nearly pure backspin. Chapman’s release was tilted slightly – the angle of his arm was between three-quarters and directly overhead – so there was also a bit of sidespin. You can see the slight horizontal deflection caused by that sidespin in the umpire’s view.

This was a nasty pitch, but Flores managed to foul it off. After two more foul tips, Flores earned a walk on the ninth pitch of the plate appearance. Major league batters may struggle to catch up to a 100-mph fastball, but they can still make contact now and then.

Of course, there are other ways to be successful with a fastball. Boston’s Koji Uehara rarely reaches 93-mph with any of his pitches, but he can still be effective. Facing Jose Molina of the Rays in the ninth inning of a game on July 26, 2014, Koji threw just about his fastest pitch of the night: a fastball moving at only 87.9-mph. In the figure below, you can watch as this pitch (shown in blue) falls farther and farther behind Chapman’s, (in red) losing the race by about six feet, or 0.06 seconds.

The spin rate, though, was just about the same as Chapman’s pitch, 2600 RPM, leading to a similar Magnus force. Both pitches drop a bit more slowly than the average fastball, which spins at roughly 2200 RPM. From the umpire’s point of view, these pitches thrown by Uehara and Chapman appear to “rise” as they approach the plate. They aren’t really rising, as the graph shows, but give that impression relative to the average pitches the batter has faced.

This Is Just The Beginning

We hope you’ve enjoyed meeting the basic fastball: You’ll see him and his backspin quite frequently in any game. He stands at the head of the Fastball Clan, one of the two great families of pitches. Next time, we’ll visit with the leader of the other family, the basic curveball. After these introductions, we can spend some time learning about their cousins: the cutter, the slider, the changeup, and many others. See you then!

Follow us on Twitter at @SoSHBaseball.

Ian York assisted with graphical work for this piece.

About Mike Richmond 12 Articles
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.

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