Note that this post has been updated to reflect an change in the origin of Orientation.
One of our main messages has been that:
The ball Orientation relative to the axis is important.
And for the people who are willing to consider that idea, the obvious question is :how do you quantify the Orientation. I finally decided to take this on, and rather than doing the heavy lifting, I put Trip Somers (@one_pitch_man) on to it and he killed it. Much of the following ideas are his.
Note that I am capitalizing Orientation, because I want it to be a thing.
As motivation, consider the “Looper” changeup described in Post 49. This is a 3:00 tilt pitch, meaning that it’s axis is vertical. But as you can see from this rear view, it also has a funny Orientation. And that Orientation is critical to how it behaves. So how can we describe Orientation?
First, let me emphasize that Orientation will be described relative to the spin axis. That means a looper fastball has the same Orientation as a looper changeup, even thought the spin axis is 90 degrees different.
To start, we need an origin. I realized that, but Trip is the one who further realized that the origin must be based on a single position of the ball. We will use the picture below to help. For simplicity’s sake, I have the axis straight horizontal. Zero Orientation is Mr. Manfred’s signature horizontal to the pitcher. As he has not signed every baseball in the world, take note of the seams. The “landing strip” is horizontal. Note that no matter what axis you want the ball to be on, Orientation should be based on this horizontal axis.
Remember that in the baseball world, from the pitcher’s perspective, X is to the right, Y is the direction of pitch travel and Z is up. With the axis fixed along X, we modify the Orientation by rotating the ball around Y or Z. We need a sign convention, and we have chosen clockwise to be positive when the ball is viewed from the pitcher’s perspective for the Y rotation or viewed from above for the Z rotation.
Given this convention, every pitch I have talked about — laminar express or discoball changeup, looper, scuffball — are all+Z rotations in increasing order. While I originally spent hours arranging speared balls on a piece of 2X4 and photographing them, this is much more easily shown using Trip Somer’s new tool that you can find here. Note that he calls Z rotation “Top” and Y “front”. Also note that none of these have the tilt or efficiency of the pitches mentioned, just the orientation.
Here is a 2-seamer,
A laminar express (or discoball, using a different Tilt)
A looper,
And a scuffball
For a 90º Z rotation, you have a 4-seamer. I could go on, but so far, this is all I need.
Once Orientation is known, you can change the axis to whatever you want and the orientation remains the same. Our Looper experiment had 3:00 tilt and a 39º Z rotation.
These Orientations are easy to visualize for fastballs with 12:00 tilt, but keep in mind that Orientation is relative to the spin axis, so the same Orientations for a pitch with 6:00 tilt moves the seams to the other side of the ball. This is because the spin axis (and therefore the ball itself) has flipped to go from 12:00 tilt to 6:00 tilt.
To illustrate this, a looper fastball with 39º Z rotation and 12:00 tilt has its loop on the right side of the ball, while a looper curveball with 39º Z rotation and 6:00 tilt has its loop on the left side of the ball. If the same looper curveball had -39º Z rotation, its seams would be on the right side, just like the fastball.
An easier way to think about it: to keep the seams on the same side for a pitch spinning in the opposite direction, just flip the Z rotation angle! (This gets more complicated when considering Y rotation, so ignore that for now.)
If you view these orientations from the axis end, they look like this.
Mentioned above but not discussed, Orientation can also have Y rotation. Y rotation alone would leave the seams roughly symmetric as the pitch spins, likely producing little useful effect unless it is paired with some degree of Z rotation or some gyro spin.
Both Trip and I feel strongly that it is important to get these things right, so if you have a better suggestion, we are happy to hear it.
Trip plans to write about how seam orientation affects pitch movement in an upcoming post on his blog at texasleaguers.com. Have a look.
It was my understanding that a laminar express pitch is not thrown with 100% efficiency, but I see here that the laminar express you modeled does have 100% active spin. Could you explain how the above pitch qualifies as a laminar express? I have read a lot of your earlier posts but have a fairly limited understanding of physics.
You are correct, and I am sorry that my post is confusing on that point. The animation shows the necessary orientation of a laminar express relative to its axis, but it does not show a laminar express axis. Let me know if that doesn’t make sense. I may have to update this post because it didn’t occur to me how confusing this is, but I see it now. Thank you.