When a ball spins, it creates an envelope of air around it called the boundary layer. This boundary layer moves with the ball whether it spins forward or backward or sideways. The interaction of this boundary layer with the surrounding air results in an outside force that changes the path of the baseball. This is the Magnus effect.
Named for German scientist Heinrich Magnus, this effect is a principle of fluid dynamics that describes the lift created by the spin of an object that is moving through a fluid (gas or liquid).
To better understand lift, here is a brief look at how airplane wings create lift. The shape of airplane wings causes air to move faster over the top of the wings than it moves beneath the wings. The faster moving air results in lower air pressure above the wing and greater air pressure beneath the wing. The greater air pressure pushes the wing up; this is lift.
HOW SPIN CREATES LIFT
The spin of the ball dictates the rotation of the boundary layer. When the ball has back-spin, like a fastball, the boundary layer under the baseball shoots air forward into the air that is trying to move around the baseball. The opposing air flows result in slower air movement and higher air pressure underneath the baseball.
On top of the ball, the boundary layer shoots air backward in the same direction as the air that is trying to move around the baseball. These air flows compliment each other and combine to create faster air movement and lower air pressure on top of the baseball.
The combination of slower air movement under the ball and faster air movement over the ball creates lift that opposes gravity - a "rise". The Magnus effect, in this case, acts just like an airplane wing.
For a curveball, the top-spin is like turning that wing upside-down. The opposing air flows are now on top of the baseball, and the complimentary air flows are on bottom. Here, the Magnus effect creates lift that compliments gravity - a drop.
With a tilted spin axis, the Magnus effect creates a tilted lift. A left tilt adds right-to-left movement when the pitch has back-spin and left-to-right movement when the pitch has top-spin. A right tilt has the opposite effects.
When a pitch spins perfectly sideways, like a screwball or a sweeping curveball, the Magnus effect does not create a "rise" or drop. Instead, it creates sideways lift. Viewed from the top, clockwise spin results in left-to-right lift, and counter-clockwise spin results in right-to-left lift.
MAGNUS EFFECT ON OTHER PITCHES
The Magnus effect is greatest when the ball's spin axis is perfectly perpendicular to the velocity of the baseball. As the spin axis turns (or yaws, if you're into that sort of thing) from perpendicular to parallel to the baseball's velocity, the Magnus effect decreases accordingly. Likewise, the magnitude of the Magnus effect increases as the spin axis moves from parallel to perpendicular to the baseball's velocity.
Gyroball
When the ball's spin axis is perfectly parallel to its velocity, the Magnus effect is null, barring crosswinds. In this case, the ball spins like a bullet - clockwise for righties and counter-clockwise for lefties when viewed from the pitcher's perspective - and no part of the boundary layer opposes or compliments the surrounding air flow.
A pitch with this spin is called a gyroball, and despite what was widely reported when Daisuke Matsuzaka came to the states, the null Magnus effect makes this the straightest pitch that can be thrown.
Wind tunnel studies have shown that this type of spin results in a smaller wake behind the ball. A smaller wake means less wind resistance which means a gyroball does not slow down as much as a fastball does on its way to the plate.
Slider
A slider is intended to have glove-side lift, but Pitch-f/x data suggests that sliders move less than any other commonly thrown pitch. On Pitch-f/x charts, sliders are usually grouped around or very near to the chart's origin where zero horizontal movement meets zero vertical movement. This suggests that most sliders spin like gyroballs. I tend to agree.
Good sliders, though, will have a spin that is somewhere between that of a curveball and that of a gyroball. Such spin will create the sliding movement and, depending on the degree of tilt, a varied amount of additional drop for the pitch.
Cut fastball
If a slider's spin is between that of a curveball and that of a gyroball, the spin of a cut fastball should be between that of a fastball and that of a gyroball. Where a slider ideally has some top-spin, a cut fastball has a large amount of back-spin.
The combination creates lift nearly identical to a fastball, but because the spin axis is turned slightly to the pitcher's glove-side, it also has glove-side run.
Split-finger fastball
Split-finger fastballs can be thrown with one of two different spins. The first spin is simply a slower back-spin than a normal fastball that creates less lift than a normal fastball would. When thrown at nearly the same speed as a normal fastball, the split-finger fastball appears to drop due to the smaller lift.
The second spin is actually top-spin. This is the ideal spin for an effective split-finger fastball because the forward tumble creates a drop like a curveball. The velocity of the pitch is similar to a fastball, but the spin is like a curveball albeit with a much slower rotation.
When top-spin is present in this pitch, it is sometimes called a forkball. A forkball is usually held with a deeper grip than a split-finger fastball, but the two pitches are practically identical give or take a couple of ticks on the radar gun.
Sinker
Some sinkers spin like reverse-cut fastballs, and some sinkers spin like reverse-sliders. Most are somewhere in between. A power sinker, like the one thrown by Brandon Webb, spins almost like a screwball but with fastball velocity.
The same rules that apply to cut fastballs and sliders also apply to sinkers. The difference is that cut fastballs and sliders have glove-side lift while sinkers have arm-side lift.
THE ROLE OF SEAMS
The 108 stitches on a baseball grab the air around the ball and create a larger boundary layer than a ball with no seams would create. The horseshoe shape all around the baseball allows a pitcher to throw just about any pitch as a two-seam pitch, a four-seam pitch, or something that isn't quite either of those (a three seamer?). Most sliders fall into the third category.
A four-seam pitch spins on an axis that allows four seams to influence the boundary layer. The four seams are evenly spaced (balanced) around the baseball. This symmetry creates a stable and relatively predictable Magnus effect.
A two-seam pitch, though, spins on an axis that unbalances the seams even though all four seams still influence the boundary layer. This axis puts a seam loop on either side of the ball, leaving the two connecting seams close together on one side of the ball.
With the axis turned slightly to the left or the right, one of the seam loops moves toward the point of pressure (where the ball breaks through the surrounding air and experiences the greatest wind resistance), and the other seam loop moves away from it. This axis exaggerates the Magnus effect of the seam that moves toward the point of pressure, and reduces the Magnus effect of the seam that moves away.
The dominant seam, because of its almost circular shape, creates a point of nearly constant friction as it pushes boundary layer air almost directly into the air breaking across the point of pressure. When the seam catches that angle just right, the baseball will dart left or right depending on which seam is dominant.
CLOSING THOUGHTS AND OTHER NOTES
I've talked a lot about how a pitch spins and why it moves the way it does, but I haven't yet touched on the magnitude of the Magnus effect. The obvious part is that greater movement is due to a greater Magnus effect. The not so obvious part is how to increase the Magnus effect to create even more movement. The simple answer is to give the ball more spin.
The faster a ball spins, the greater the resulting Magnus effect will be. Squeezing just one extra rotation out of a pitch can have dramatic results on the pitch's movement.
You may have noticed that I didn't talk about the knuckle ball at all. Well, the knuckle ball doesn't spin, so it has no Magnus effect. A knuckle ball's movement is strictly an aerodynamics issue where the seams cause immediate disruption in the surrounding air flow rather than through a boundary layer. On the pitch's way to the plate, chaos theory takes over and the knuckle ball waivers as the seams catch air and unpredictably change the path of the ball.
Finally, release angles play a sizable role in creating "hidden" movement. For example, if a pitcher releases the ball two feet outside of the rubber, it has to move roughly 3 1/2 feet to reach the opposite corner of the plate. Sliders and curveballs with glove-side lift will look like they are moving nearly 4 feet as they cross that corner, even though they only break about 3 to 5 inches.