Pitch Movement, Part I: You Spin Me Round (Like a Baseball)

February 28, 2020 • Analysis

When I originally posted about pitch spin 11 years ago, there weren't many readily available sources of information on pitch spin beyond the basics of Magnus force. Back then, a discussion of gyro spin was somewhat advanced. It’s safe to say that, in the years since, the number of resources and the depth of topics have multiplied.

Let's quickly review what is currently "known" about Magnus force as it relates to pitching, and then we'll cover some advanced concepts before wrapping up Part I.

Magnus force basics

Magnus force is proportional to the rate of spin and the mathematical square of the velocity. At the same spin rate, faster pitches experience a greater Magnus force than slower pitches. At the same velocity, pitches with more spin experience a greater Magnus force than pitches with slower spin.

Magnus force is greatest when the spin axis is perpendicular to the path of the pitch. An axis that is not perpendicular to the path of the pitch has some amount of gyro spin. The more gyro spin there is, the smaller the Magnus force.

Magnus Effect diagram

A fastball with pure backspin creates a Magnus force straight-upward, directly opposite to gravity. A curveball with pure topspin creates a Magnus force straight-downward, in addition to gravity. These are the only two pure examples that exist because their spins do not result in a change of direction that causes a Magnus shift.

Gyro spin basics

Before getting into Magnus shift, here's a quick gyro spin primer. If you take a fastball with pure backspin and turn it left or right (like a car, not like a doorknob), you have introduced gyro spin to the pitch. The spin axis is no longer perpendicular to path of the pitch.

The more the spin axis is turned, the greater the reduction in Magnus force. If you turn the ball a full 90°, the spin axis is then completely parallel to the path of the pitch -- spinning like a football -- and the pitch becomes a pure gyro ball with zero Magnus force.

Every spin has a Magnus efficiency associated with it. On the two extremes are a purely perpendicular spin axis (with maximum Magnus, zero gyro) and a purely parallel spin axis (with zero Magnus, maximum gyro). "Spin efficiency" and "active spin" are both terms that have been used to describe Magnus efficiency. (I prefer "spin efficiency" because, frankly, all spin is active and "spin efficiency" has "efficiency" right there in the name!)

If you're into trigonometry -- and let's be real, who isn't? -- you can play around with how many degrees of gyro spin match up with what percentage of Magnus efficiency.

Magnus shift and gravity

The basic idea boils down to this: while the true spin axis remains constant relative to the pitch's initial release, the Magnus-effective spin axis changes as the pitch changes direction. This change in the effective spin axis is what I call Magnus shift.

This effect was described by David Kagan in The Hardball Times at FanGraphs a little over 2 years ago. Kagan used a lot of diagrams and illustrations that I don't feel comfortable stealing for this post. I highly recommend that you hop over there and read it, and I'll briefly offer my own words in the following paragraphs.

Kagan's discussion focuses on a pitch with pure gyro spin, which checks in at 0% spin efficiency. As gravity pulled it down and some gyro spin became side spin, the spin efficiency improved from 0%. The Magnus shift increased the spin efficiency of the pitch.

Imagine throwing a pitch with pure gyro spin out into the Grand Canyon. As it falls into the canyon, the true spin axis remains constant, but the effective spin that was initially gyro spin increasingly becomes side spin. Eventually, the pitch moves straight down and all of the initial gyro spin is then side spin. When thrown to a catcher from the mound, however, the same pitch simply does not have the time and space for gravity to dramatically alter the pitch's direction, resulting in a much, much smaller effect.

If we start with a pitch with pure side spin at 100% spin efficiency, the gravity-induced Magnus shift results in some of the side spin becoming gyro spin, and spin efficiency deteriorates from 100%. In this case, the Magnus shift decreased the spin efficiency of the pitch.

In Kagan's article, he focused specifically on this gravity effect for a pitch with pure gyro spin and found that, for an 85 MPH pitch with 1500 RPM of pure gyro spin, this effect contributes only 1/2" of movement.

The Magnus shift due to gravity is incredibly small and likely isn't worth chasing in pitch design unless the pitcher really needs to optimize an eephus (MAYBE!). Knowledge of the gravity effect is really more descriptive than it is actionable.

Magnus shift and spin movement

If you were paying attention earlier, you remember that Magnus shift is caused by the changing path of the ball, and pitches move plenty even without the help of gravity.

In September, Dan Aucoin offered some related notes on the Driveline Baseball blog in his thorough review of all things spin axis. (And for you scarce few trigonometry haters who didn't immediately whip out your calculators earlier, he also provided a nice chart for converting between degrees of gyro spin and spin efficiency. Thank him, not me.)

He compiled data on changes in spin efficiency between release and the front of the plate as measured by a Rapsodo 2.0. His numbers show that glove-side movement tends to increase spin efficiency while arm-side movement tends to decrease spin efficiency. Think about that for a minute. This suggests that, on average, breaking balls could move more as they get closer to the plate while fastballs and changeups could move less.

The above idea gets a little complicated when you consider that we already know that pitches lose velocity as they approach the plate. That has a negative impact on Magnus force, but because the pitch is moving slower, there's more time for the force to affect movement.

Aucoin continues the analysis by stating that the 8%-10% spin efficiency increase on breaking balls equates to only 1"-2" of "late" movement. That certainly isn't much, even if it's late.

Shyamalan!

You just read like 10 paragraphs about Magnus shift and the big conclusion was that it doesn't affect spin movement much at all. That would mean that spin direction and spin efficiency are all you really need to know.

Is that true? Pitching would be pretty boring if it were that easy!

Non-Magnus effects are real. Part II drops soon.