Anatomy of a pitch: the 12-6 Curveball

With pitchf/x being all the rage these days, I thought I would give a primer on what makes pitches do the crazy things they do. I’ll start with the curveball, since I’ve always found it to be the most interesting. As we will see, curveballs are also pretty simple to analyze. Note: I’m doing this entirely from a physics perspective, not a baseball perspective, and I know nothing about pitchf/x. I have never personally thrown any of these pitches (other than maybe a ‘fast’ ball), and certainly don’t know much about the more subtle strategies that pitchers use with specfic pitches (i.e. I know sinkers = ground balls, knuckleballs are essentially randomly moving pitches, changeups fool batters due to speed differences, etc. but not what lefthanders tend to use to get lefties out). Let’s look a simple model of how this pitch works. For the moment, let’s assume that our ball is completely smooth and is thrown without any spin, and remember Newton’s second law: F = ma. In fact, let’s be mathematicians here and set the mass equal to one, since dimensional quantities annoy us (you can tell that I am not a physicist). Thus, any change in the initial velocity (acceleration = change in velocity) when it is released by the pitcher has to be caused by external forces acting on the ball. Obviously, we have a downward force acting on the ball (gravity), which causes the ball to drop, and drag forces due to air resistance, which cause the ball to slow down. What happens when we add (a purely vertical) spin? Due friction between the air particles and the surface of the ball, the spinning ball exterts some force on the air particles around it. Thus, in the picture above, the upper half of the ball is causing the air around the ball to move at a greater velocity, while at the bottom the ball is causing the air nearby to move at a lesser velocity. Since drag force depends on speed, there is a bigger drag force at the top of the ball than at the bottom, which deflects the ball downward. This resulting downward force is called the Magnus force. The faster you can spin a ball, the bigger the differential in the velocities at the top and bottom of the ball, and thus the Magnus force is larger. In fact, there is little difference in the amount of force that you obtain (with the same amount of spin) once you start throwing curveballs above 60 mph or so, which is why you see a lot of slow 12-6 curve balls. If you throw them too fast, there isn’t a lot of time for the spin effects to do their thing. Of course, if you can get a ridiculous RPM on the ball *and* throw it really fast, you still get all of the spin effects and it’s nearly impossible for the batter to pick up (see Kerry Wood, circa 1998). However, from what I understand that’s hell on your elbow (see Kerry Wood, circa 1999). Likewise if you can get crazy spin on the ball and throw it too slowly, it will hit the ground before it gets to the plate, which is another reason why those slow 12-6 curve balls have a lot of arc to them (the pitchers have to add some vertical velocity for the Magnus force to kill off). I would imagine that it’s really tough to throw those for strikes, since by the time they get to the plate they’re diving like crazy. Just like a pitcher can add and subtract from a fastball, I would imagine that a pitcher could add and subtract spin on a curveball as well, to ensure that all of his curveballs don’t break at the same rate. Of course, a hanging curveball is a curveball that doesn’t have enough spin. Without the effects of spin (and the usual slow speed at which it is thrown) it is very easy for a hitter to time, which is why so many of them end up going a long, long way.