On Oct. 6, 2010 Roy Halladay became only the second pitcher in major league history to throw a no-hitter in the postseason. He had thrown a perfect game earlier in the season, marking the only time a major league pitcher has thrown a no-hitter and a perfect game in the same season. A good portion of his success was due to his ability to throw the sinker ball.

Manny Acta described a sinkerballer’s outing as follows, “He pounded the strike zone with that heavy sinker. It was going down like a bowling ball.” The sinker is often referred to as “heavy,” but what can that mean? Certainly, a sinker ball weighs no more than a fastball or a curve. A baseball “…shall weigh not less than five nor more than five and one-quarter ounces avoirdupois…” according to MLB rules. The bottom line is major leaguers are excellent experimental physicists, so there must be something real behind their observations.

Here we’ll explore this idea of a heavy sinker from the point of view of physics. We’ll begin by reviewing the Magnus force on a fastball, a curveball, and a sinker. Then some data on the properties of these three pitches will be presented. Finally, three possible scientific explanations of the term “heavy sinker” will be suggested.

The forces on a pitched baseball

Figure 1 shows the three forces that act on a baseball in flight (reference 1). The gravitational force pulls the ball downward. The drag force acts opposite the velocity and slows the ball down. The Magnus force, sometimes called the lift force, is perpendicular to both the velocity and the spin direction which is defined in an interesting way.

Figure one shows a ball that has backspin, that is, the top of the ball is spinning against the velocity while the bottom is moving with it. The rule to determine the spin direction is to curl the fingers of your right hand around with the spin of the ball, stick out your right thumb, and the thumb will point in the “spin direction.” In this case the spin direction is into the page resulting in a Magnus force that is nearly vertical. If the ball had had topspin, the spin direction would be out of the page and the Magnus force would be almost completely downward.

Figure 2 shows the ball from the point of view of the catcher, so the velocity vector is predominantly pointed toward you, out of the page. The Magnus force is perpendicular to the spin direction, ω, which makes an angle, θ, with the x-axis. Notice that a ball with complete topspin would have θ = 0˚ = 360˚. The resulting Magnus force would be downward causing the ball to drop more rapidly than if gravity acted alone. On the other hand, a ball with just backspin has θ = 180˚. The resulting Magnus force would be upward causing the ball to drop less rapidly than gravity dictates. A ball with only sidespin could have θ = 90˚ resulting Magnus force would be toward the catcher’s right or θ = 270˚ resulting Magnus force would be toward the catcher’s left. The ball should drop just due to gravity.

In summary, a ball with only backspin will fall slower than g, a ball with only topspin will fall faster than g, and a ball with just sidespin will fall at g.

Fastballs, curves and sinkers—oh my

Using PITCHf/x data [ref. 2 and 3], Figure 3 shows a game’s worth of fastballs (green triangles) and curveballs (red squares) from Clayton Kershaw of the Los Angeles Dodgers. The sinkers thrown by Halladay during his playoff no-hitter are shown as blue diamonds. You should notice the fastballs are thrown with almost complete backspin as the angle is clustered around 180˚. The Magnus force will provide lift, keeping them from falling at the rate determined by the gravitational force alone.

The curveballs are thrown with mostly topspin. Remember, complete topspin would be 360˚ while these average about 340˚. The Magnus force will be nearly downward, causing them to falling more rapidly than just the gravitational force alone. This explains why curveballs “drop off a table.”

Halladay’s sinkers travel at the same speed as Kershaw’s fastballs, yet their spin is quite different. Their spin angle is about 255˚, which is close enough to the 270˚ to say that the Magnus force is nearly horizontal. Therefore, the ball will fall at nearly the same rate as a ball thrown without spin. In addition, this sinker will move toward the catcher’s left. That is, it will ride in on a right-handed batter and drift away from a left-hander.

He ain’t heavy…

The trajectories of a fastball (green), a sinker (blue), and a curve (red) are shown in figure 4, with home plate located at x=50. Since the Kershaw fastball and the Halladay sinker are both hurtling toward the plate at the same rate, they both take the same amount of time to get there. The fastball has less downward acceleration due to the upward Magnus force caused by its backspin. So, a fastball won’t drop as much as a sinker. That is why a sinker is called a sinker! It is not sinking more than gravity requires, but it sinks measurably more than most pitches of equal speed. As a result, batters tend to underestimate this drop and hit the top of the ball. This explains why sinker ball pitchers generally induce far more ground balls than traditional pitchers. Since hitters find it difficult to get the ball off the ground, they describe the pitch as “heavy.”

It might be worth noting that a curveball drops substantially more than a sinker because it has topspin. In addition, a curveball is thrown 10 to 20 mph slower than either the fastball or the sinker giving the ball more time to fall. This also gives batters more time to adjust to the curve than the sinker.

There are at least two more physical reasons to expect batters to describe the sinker as heavy. The goal of an at-bat is to hit the ball hard. This is most easily accomplished by hitting the ball on the “sweet spot” of the bat [ref. 4 and 5]. When the ball is hit on the sweet spot, the batter feels little vibration in his hands, giving him the sense he struck the ball well. Figure 5 shows the rotation of the spin and the resulting Magnus force on the ball. We’ve seen for a fastball, or even a curveball, the pitch is mostly moving vertically. However, a sinker has a substantial amount of horizontal movement due to its sidespin.

The typical spin on these fastballs is 2,500 revolutions per minute, while for the sinker it is only about 10 percent smaller at 2,200 rpm. So, a fastball will be just slightly more above its gravitational trajectory than a sinker will move horizontally along the bat. It is far easier for a hitter to adjust up and down during his swing than in or out. So, a sinker is far more difficult to hit on the sweet spot than a fastball or even a curve. Hitting a sinker more often results in an off sweet spot collision. The resulting vibrations felt in the hands create the sense that the ball is heavy.

The second reason that the word “heavy” might be used has to do with the forces the ball exerts on the bat during their collision. A well-hit 5.125-ounce baseball coming in at 90 mph will leave at about 110 mph changing velocity in about 1.5 milliseconds. A quick calculation gives a value around 2,000 pounds!

A Hardball Times Update by Rachael McDaniel Goodbye for now.

This force on the bat is mostly horizontal and directed toward the catcher. Batters are used to and expect this sensation when they hit the ball. This force is there regardless of the spin on the ball.

There are also forces exerted on the bat created by the spin of the ball as shown in figure 6. A fastball with backspin will exert an upward force on the bat. A sinker will exert a force along the bat. These forces are known to exist because the reaction force the bat exerts on the ball is known to stop the ball’s rotation [ref. 6] during their collision.

We can get a rough estimate of the size of this force for a fastball using the radius of the ball, the time to stop the spin which is about half the collision time ∆t = 0.75ms, the initial spin rate of 2,500rpm, and by assuming a final spin rate is zero. Plugging in the values yields the upward force on the bat from a fastball of 170 pounds. The value for the force felt when hitting a sinker can be found using the slower spin rate of 2,200 rpm and is about 150 pounds. These two spin caused forces are small compared to the 2,000 pounds associated with the direct collision, but they might still be large enough to sense.

The spin-caused forces, while around the same size, act different directions. The force due to the fastball acts upward while the force due to the sinker acts along the bat. The directional change in the force might also give a batter the sense that something is different about hitting a fastball as opposed to a sinker. The difference would be the lack of an upward force which might create the feeling that the sinker ball is “heavier.”

In summary, this paper proposes three physical theories to explain why hitters might describe a sinker as heavy:

{exp:list_maker}Sinkers fall more than fastballs, so they tend to get hit toward the ground.

Sinkers move a substantial amount horizontally due to their side spin, making them harder to hit on the sweet spot.

Batters are used to feeling a slight vertical force when they hit a fastball, but this force is exerted along the bat for a sinker. {/exp:list_maker}

Baseball is a human endeavor where feelings and senses matter nearly as much to the outcome as physical reality. While “heavy” to a physicist means feeling more gravitational force, the word has a less precise meaning in the world of baseball. This was an attempt to reconcile these two views. In the final analysis, when it is your turn at bat and you’re swinging at a fastball, all you know for sure is you don’t want to get that sinking feeling.

References & Resources

1. For a complete and thorough discussion of the forces on a baseball in flight see A. M. Nathan, “The effect of spin on the flight of a baseball,” Am. J. Phys., 76, 119 – 124 (2008).

2. For instructions to get to and use the PITCHf/x data set see D. T. Kagan, “The Anatomy of a Pitch: Doing Physics with PITCHf/x Data,” The Physics Teacher Vol. 47, No. 7, 412 (2009).

3. This particular data set was collected from the PITCHf/x Tool at Brooks Baseball.

4. A. M. Nathan, “Dynamics of the Baseball-Bat Collision,” Alan M. Nathan, Am. J. Phys., 68, 979-990 (2000).

5. For a humorous look at the physics of the sweet spot see http://phys.csuchico.edu/baseball/DrBaseball/SweetSpot/.

6. The ball has been shown to come to rest before the bat then induces the ball to start spinning again. See A. M. Nathan, J. Cantakos, R. Kesman, B. Mathew, and W. Lukash, “Spin of a Batted Baseball,” Procedia Engineering, 34, 182-187 (2012). Proceedings of 9th ISEA Conference, Lowell, Mass., July 2012.