One of those myriad baseball things that I've been wondering about for years - the technical differences between the various pitches. (There are a handful of these baseball things I've been wondering about for years; I've gotten answers to most of them recently, and have thusly been feeling edified.) I decided that one of my projects was going to be to figure out what the actual differences are - in throwing position (which is relatively simple) and, more importantly, in actual physics, to come up with the various strange things that thrown balls can do. In order to do this, I badgered my father into sending me a copy of The Physics of Baseball by Robert K. Adair (which I strongly recommend reading in general; it's a nifty book).
It's easy enough to deduce that the primary differences between pitches have to do with the velocity of the ball, and its rotation. The positioning of the stitches with relation to the motion of the ball is also important - this, after all, is the difference between the two-seam and four-seam fastball. For an in-depth explanation of the forces generated on a ball by its rotation, read the book; I'm not going to put the entire discussion of pitching differences up on the web. It's not my research.
In general, the axis of spin on a ball thrown by a right-handed pitcher (as the batter would see it) will angle upwards from left to right; an overhand fastball has backspin, other pitches do not. A southpaw will angle down from left to right as seen by the batter. This means that when the pitcher and the batter are favoring the same hand, a fastball will angle high and inside, and most other pitches low and outside, when aimed at the same place.
The rotation on the overhand fastball is a backspin, only slightly tilted off-center. As it happens, the force generated by a vertical backspin is counter to gravity, making this the 'rising' fastball - it doesn't fall as far between the pitcher and the plate as an unspun ball would. A split-fingered fastball, however, does not have a very strong spin on it by comparison, and thus will fall more rapidly, especially as it reaches the plate. Peculiarly, a rougher ball has lower air resistance than a smooth one, which is what the seam position modifies - a four-seamer presents a 'rougher' surface to the air it passes through than a two-seamer. Most fastballs do not curve much in the air, aside from the usual gravitic effects; for the most part they are moving too quickly for any significant curvature to be induced, and it is difficult to get the ball rotating properly for a curving effect while throwing for power.
A curve ball's spin is diagonal, and in the other direction - encouraging it to both drop and angle to one side. It is also thrown slower than the fastball; the ball curves further away the longer it is in the air. The spin on a slider is almost horizontal, instead of angled, which forces it outside and away from the batter (assuming the batter bats the same as the pitcher throws).
A screwball differs from the other pitches because the angle of its rotation is contrary to the general run of pitches. Its spin is very similar to that of a curve ball - a diagonal rotation. However, where most right-handed pitches have an axis of rotation that slopes up from the left side of the ball (again, as the batter sees it) to the right, the screwball slopes downwards - curving the ball to the inside of a right-handed batter, outside on a lefty. Since a right-hander's offspeed pitches will typically curve to the right - it's easier to put the spin on it that way - having the ball curve the other way could, indeed, be considered screwy. (The other potential definition of a screwball might be, say, 'a pitcher in a Yoda mask'.)
A knuckleball, unlike other pitches, is thrown with a specific, slow spin - about half a rotation between pitcher and batter. ("A knuckleball, when properly executed, does one full rotation before hitting the catcher?" - Avi Weiss) While other pitches depend on the force caused by the spin on the ball, the knuckleball's behaviour depends on the effects of the stitches as the ball rotates. To a certain extent, other pitches rotate fast enough that the effects of the seams are evened out to a constant effect (or at least can be approximated as such without too great an error introduced into the equations). However, in the case of the knuckleball, the slowly rotating ball slows down abruptly on one side as it rotates, curves one way, and then as the ball rotates further and the stitches are now changing the aerodynamic profile on the other side, curves back. The effects of this are notoriously unpredictable, as even a tiny difference in the rotation speed or seam angle on the ball will change the trajectory of the pitch.
The more I study pitching, the more impressed I am by pitchers. I now grasp the physics of what they do - but the ability to place the ball, through all of that, in precise points in the strike zone, is amazing to me. Pedro stands at the right hand of the baseball gods, indeed.