# Nathan: Everything you wanted to know about baseball spin

From SABR member Alan Nathan at Baseball Prospectus on March 31, 2015:

Ever since the early days of PITCHf/x, we have had unprecedented information about the movement of pitches. We now have a precise quantitative measure of how much and in what direction a pitch moves—i.e., deviates from a straight-line path. The movement is the result of the combined forces of gravity pulling the ball downward and the so-called Magnus force on a spinning baseball. It has become conventional to remove the effect of gravity, which is easily calculable, so that the resulting movement—pfx_x and pfx_z in PITCHf/x lingo—is due only to the Magnus force. I will utilize that convention in this article. It seems sort of reasonable that there ought to be some simple relationship between the movement to the spin rate. For example, if a pitch is spinning at a higher rate, the expectation is that there will be more movement. But is that expectation correct? In fact, it is not correct because, as the title of this article suggests, all spin is not alike. And that is the issue I want to discuss here.

So why is it that all spin is not alike? The reason has to do with the vector nature of the spin: It has a magnitude and a direction. The magnitude is pretty simple, since it is just the number of revolutions per minute, or rpm. Let’s talk about the direction. The easiest way to determine the direction of the spin is to use a right-hand rule: Wrap the fingers of your right hand around the ball so that they point in the direction that the ball is turning. Your thumb will then point in the direction of the spin axis.

Here are some examples. A straight overhand fastball has pure backspin and the spin axis points to the pitcher’s right. An overhand “12-6” curveball has pure topspin and the spin axis points to the pitcher’s left. A ball thrown with pure sidespin has its spin axis pointing up or down. In all these examples, the spin axis is perpendicular to the direction of motion. On the other hand, a gyroball is a pitch thrown with the spin axis perfectly aligned along the direction of motion, much like a spiral pass in football. Indeed, it is often called “bullet spin”, since that is how a bullet will spin when shot from a rifle. All of these pitches are special cases, since in general the spin axis could be pointing in any direction whatsoever.