Part I in this series covered the basics of the Magnus effect and how pitch spin creates movement. Part II covered some interesting research being done by Barton Smith to explain non-Magnus seam effects.
At his blog, baseballaero.com, Smith has logged research results as he's worked through several experiments aimed at analyzing and describing a baseball's aerodynamic wake as it relates to the position of the baseball's seams. As the posts stacked up and more impactful conclusions could be drawn, he realized he needed a way to describe seam orientation.
A few emails later, he and I had worked out the basics of a simple system, and a couple of days after that, we co-authored the first post about describing seam orientation.
Based on a few subsequent conversations and work done to produce visualizations, we realized that describing seam orientation wasn't the only missing piece needed to completely describe a pitch's spin.
In this post, I'm going to discuss the system as it is currently implemented by the pitch spin modeler. (You may want to have that open in another tab while you continue reading.)
A preview of the modeler, for those that don't care to click the link above.
Describing spin basics
There are already three extremely common and well understood components of spin description. There is no reason to mess with them really.
"Spin rate" is a simple measure of how fast the pitch is spinning, typically in rotations per minute (RPM) though you may see a different unit of measure in a math-heavy analytics post or article.
"Tilt" is the two-dimensional representation of the direction of the Magnus effect created by the spin. For example, a fastball with pure backspin has a tilt of 12:00 because the force created by the Magnus effect points straight up which is 12:00 on a clock face.
This clock-face-based description was popularized by Rapsodo and widely welcomed as a solution to the rather constant confusion that resulted from trying to communicate spin axis as an angle. (Astute readers will notice that, while tilt doesn't directly describe the spin axis, it does do so indirectly via the right-hand rule.)
"Spin efficiency" is commonly used to represent the percentage of spin that contributes to the Magnus effect. A lower efficiency means there is more gyro spin. A less common term for this is "Active Spin", though it is still represented as a percentage. In the pitch spin modeler, I have labeled it "Active Spin" under the Efficiency header.
UPDATE (4/16/2020): To more accurately reflect the role of gyro spin in pitch movement, the "Efficiency" header has been renamed "Magnus Efficiency", and the "Active Spin" slider has been converted to "Gyro Angle" with the efficiency percentage following in parentheses.
Improving the basics: gyro spin is missing something
On the pitch spin modeler you'll see another setting under Efficiency called "Gyro Pole". This setting indicates which of the two spin axis poles is "responsible" for the efficiency percentage. Technically speaking, both spin axis poles are equally responsible since one can't move without the other, but for now "responsible" means that the particular pole is forward on the leading surface of the ball.
Generally speaking, RHPs will have a "negative" gyro angle, and LHPs will have a "positive" angle. So... Why not establish a positive pole and a negative pole? Why not just use positive and negative angles? My short answer is this: for something that sounds so simple, it is rather confusing and non-descriptive when it comes to practicality.
Take, for example, a curveball with 6:00 tilt thrown by a RHP with 80% spin efficiency thanks to a gyro angle of 36.9°. Should that angle be positive or negative? What if a LHP threw it? Take another example: a fastball with pure side spin. If the bottom pole is forward, is that positive or negative? Is the answer to that question the same for both a RHP and a LHP?
Identifying the specific pole on the same clock face as the tilt is easy and perfectly descriptive. The two poles will always be at +3 hours and -3 hours, respectively, from the pitch's tilt. The pitch modeler already identifies them for you, so you simply select which pole should be angled forward!
Back to seam orientation
This one was a little tricky. The clock face was already taken, and this really can't be solved by a two-dimensional model anyway. The general baseball audience probably doesn't understand Euler angles or quaternions. (I barely do, and I coded a pitch spin modeler that depends on them!)
As far as I could determine -- with the help of Barton Smith and Tom Tango -- there were really only two options for eloquently describing seam orientation: (1) a coordinate system that uses latitude and longitude like a globe and (2) a pair of angles that tell you how to turn the ball.
The coordinate system has its advantages. It's well known. It's fairly commonly understood in general terms. It's precise, and it's specific. It also has some important disadvantages. Though it's fairly commonly understood in general terms, I'd venture to say that players and coaches don't have a lot of practical experience using it every day. What would an orientation of (34, -117) actually mean even if they could find that spot on the ball?
So I decided to push forward with what seems like the simplest possible approach: rotate the ball from the top, rotate the ball from the front. Both rotations, for descriptive purposes, are clockwise for positive and counter-clockwise for negative.
Orientation redundancy and pitch grips
Due to the pattern of the seams on the baseball, there are a lot of different ways to grip the baseball to create identical spins. For example, from the origin position, a 180° Top rotation gives you a different look but produces the same spin as the 0° origin! Likewise, -90° and +90° both produce a standard four-seam spin.
The original release of the pitch spin modeler restricted Top rotation to a range of -90° to +90° to avoid confusion regarding unique spin models, but I quickly felt that it unnecessarily prevented useful visualization of two-seam grips that use vertical seams.
With it extended to a full 180° in both directions, you can use the tool to model any grip you can think of!
The pitch spin modeler has 6 variable inputs that are used to completely describe a baseball's spin. That is twice as many as were widely used just a few weeks ago. Take any one of those 6 inputs away, and you create a blind spot in the pitch description.
With all 6 given, it becomes a matter of math to determine where movement-critical seams are located. Once the math is ready, this will fantastically complicate both the standard constant acceleration model and the more advanced Nathan model for pitch movement that do not currently account for seam-based wake effects.
The next entry in this series will discuss currently available tracking technologies and what they can and can't tell you about a pitch. (Don't hold your breath, though. It's going to take some time because there will be a lot to verify ahead of posting. There will probably be several unrelated posts between now and then.)