Pitch Movement, Part II: Sweet Seams (Are Made of This)

March 15, 2020 • Analysis

In Part I, we quickly reviewed how spin creates movement via Magnus force and the different characteristics of a pitch's spin that alters its impact. Here in Part II, we're going to look at the role the seams play in determining pitch movement.

Laminar Express: Theory vs Reality

Laminar flow sort of entered the baseball vernacular thanks to a January 2012 post at The Hardball Times by Dr. Alan Nathan that took a hard look at a Freddy Garcia pitch to explain its movement. In the course of describing it, he offered an extensive explanation of the results of experiments undertaken by Professor Rod Cross that illuminated a laminar-turbulent gradient effect. I recommend reading it and trying to wrap your head around it, even going down the rabbit hole of links he provided, but if you don't have time for that, Cross published a YouTube video that amounts to a crash course:

The criminally short version is this: if you can create a persistent smooth patch on the leading surface of a baseball, it creates a laminar-turbulent air flow gradient, and the ball's flight will deflect away from the smooth patch.

For a while, Trevor Bauer and Driveline Baseball believed this gradient influenced the flight of a special two-seamer, but that always struck me as curious because all video of this special pitch appeared to show the ball moving toward the smooth patch.

When Barton Smith wrote a post about how Trevor Bauer's Laminar Express two-seamer might work, Driveline Baseball paid him a visit. The initial results showed the effect, but it took several more posts and a realization about the spin axis itself before the explanation truly fit with previous findings. He uncovered a surprise: the magic of the smooth patch appeared to be what it meant about the location of the seams rather than the supposed laminar-turbulent gradient.

The key appears to be putting and keeping a seam in a location that causes boundary layer separation as early as possible on one side of the ball, which tends to delay boundary layer separation on the opposite side thanks to the ball's unique seam pattern.

PIV seam separation.
Smith's PIV data for a ball moving straight up. The seam on the left creates turbulence that delays boundary layer separation, and the seam on the right causes boundary layer separation. An asymmetrical wake is created, indicating a force to the left. (Source: baseballaero.com, used with permission.)

Enter: Seam-based Wake Effects

Was this the first observed and explained seam effect? Only kind of because, of course, Dr. Mike Marshall published a description similar to this in 2003 in Chapter 19 of his online book:

With two figure eight patterns sewn together, baseballs formed four loops. I determined that baseballs could rotate in such a manner as to have one of these loops constantly on its leading surface. In this way, this loop could create a circle that constantly collided with air molecules. I call the circle that this loop creates, ?The Circle of Friction.?

That sure sounds an awful lot like what's going on with the Laminar Express, doesn't it? Further reading of Chapter 19, however, fails to reveal where exactly The Circle of Friction should be, leaving the reader with nothing more than "different places ... on its leading surface". At best, Marshall's was a partial explanation.

This seam shifted wake effect is somewhat possible with a standard two-seam orientation and some gyro spin, but that isn't the only way to use a seam to cause early boundary layer separation. Smith was able to tweak the seam orientation and create this effect without any gyro spin. He explained it in a short video that appears to reveal The Circle of Friction around a smooth patch. While spinning, it looks a lot like the ball that Cross used to demonstrate this effect.

The Circle of Friction
A baseball spinning quickly, showing The Circle of Friction on the right side of the ball.

If simply changing the seam orientation can create The Circle of Friction shown above, where else can we put seams to create similar effects?

Smith asked himself this same question and very quickly produced a couple of orientations that produce an effect similar to a scuff on the ball. He called these two pitches: scuffball and looper. If you've ever seen a red-dot slider or tried to learn to throw one, they might look a little familiar to you.

A looper puts a seam near a pole of the spin axis; imagine the Laminar Express shown above with a smaller smooth area. A scuffball puts a seam directly on a pole of the spin axis (and specifically not at the other pole); imagine the Laminar Express shown above with the smooth patch shrunken all the way out of existence.

Both pitches create a rough area at or near one of the poles of the spin axis that acts like just like a scuff. The rough area creates an early and significant boundary layer separation, shifting the wake and creating movement away from the rough area.

Now remember from Part I how gyro shift changes the effective spin axis. A change in spin axis changes the leading surface of the ball, which changes what's happening on the hemisphere line -- the "edge" of the ball's leading surface. With a rough area at or near one of the poles, a change in effective spin axis also changes the effective location of the rough area.

In other words, in the same way that a change of direction alters spin effects, it can also alter seam effects.

In the video below, you'll see a simple demonstration of how the hemisphere line (indicated by the green lines) moves around the ball as the ball's trajectory (indicated by the blue arrow) changes. This spin axis remains mostly fixed, and pitches don't actually have big changes in direction, so we're talking about relatively small changes that result in a couple of inches of more or less movement.

Consider a scuffball with a little bit of gyro that moves the rough area forward on the ball's leading surface. The rough area will not cause as dramatic a boundary layer separation at first because it isn't at the edge, but as the rough area forces a change of direction, the edge effectively moves forward toward the rough area allowing it to create a more dramatic boundary layer separation resulting in a bigger shift in the wake and more movement. This is one way to create late break!

Magnus force complications

By now, you should know that it's still not that easy. Smith's preliminary research on the looper revealed something extremely curious and entirely unexpected. At 90 MPH with 3:00 tilt and no gyro at 1200 RPM, a looper with the loop on the bottom adds about 1.5" of sideways movement on average while a looper with the loop on the top subtracts about 3" of sideways movement.

Looper locations at 90 MPH.
Relative looper movement at 90 MPH, 1200 RPM, 3:00 tilt. Black: normal 2-seam orientation, control. Orange & Red: loop on the bottom. Blue & Green: loop on the top. (source: baseballaero.com, used with permission)

Think about that for a minute. In addition to the wake effect from the loop, a looper can positively or negatively impact the Magnus effect depending on which side of the ball the loop is on!

The same pitch with standard two-seam orientation was already at 100% Magnus efficiency. Somehow, a looper with the seam on the bottom -- still 100% Magnus efficient by all current definitions -- caused it to move more than a 100% efficient pitch moves.

More research is needed at higher RPM and different velocities, and I both welcome and invite that research because, frankly, that's the most ridiculous thing I've ever heard about pitch spin.

Why on earth would one add to Magnus effect while the other substracts from it? Smith has told me that he has a suspicion that one of the effects will increase and the other effect will decrease with increased RPM, and I think I know what we'll see.

The loop on the bottom of the ball creates an upward force that reduces the gyro shift caused by gravity. The loop on the top creates a downward force that increases the gyro shift caused by gravity. In other words, the bottom loop allows the pitch to spin more efficiently over the entire distance of the pitch, and the top loop reduces efficiency practically as soon as it is released.

The above is specifically true for pitches with 3:00 tilt or 9:00 tilt, but the same driving principles would apply to any looper or scuffball in terms of Magnus efficiency, at least theoretically.

The Take-Away

Depending on how well you've followed everything up to this point, the next sentence may or may not change your entire perspective on pitch spin.

Pitches with different movement patterns can have identical velocity and spin characteristics.

Stated that way, it's pretty crazy, but what if you think about it this way:

Pitches with identical velocity and spin characteristics can have different movement patterns.

Somehow, even though it says the exact same thing, the second version is a little bit more intuitive, isn't it?

For example: a Laminar Express, a looper, and a scuffball can all be thrown with the same velocity (90 MPH), same spin axis (12:00 Tilt w/100% Magnus efficiency), and same spin rate (2250 RPM) as a two-seam or four-seam fastball, but each produces a unique movement pattern.

The difference between these pitches is merely the seam orientation relative to the spin axis. This means -- and has always been true -- that seam orientation is a vital characteristic of pitch movement.

In Part III, I will get into how to describe seam orientation and discuss the pros and cons of different approaches. We've already decided to change a few things since Smith published the post we co-authored on his blog.


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.


2011 Texas Rangers: Wins, Attendance, and Playoffs

March 10, 2011 • Analysis

For two years in a row, my attendance prediction model has come extremely close to predicting the actual attendance at the team's win level.

In 2009's prediction, my model overshot actual attendance by 1.15%. In 2010, it overshot actual attendance by 0.85%.

The model has been updated to include data from 2010.

Texas Rangers, Wins vs Estimated Attendance, 2011

Again, the model predicts an increase in attendance. At last year's win level -- 90 wins -- the model predicts an average attendance of 33,645 per home game. To fall below last year's attendance level, the model says that the Rangers would have to win fewer than 77 games.

Coming off a World Series appearance, it will be interesting to see how the model holds up for 2011.

Regression Notes

The standard error is down from last year's 2,602 attendees per game to 2,560. The R-square and Adjusted R-Square values are nearly identical to the previous year's -- all three years have been right around 0.90 for both values.

Thanks to the accuracy of last year's prediction, the t Stat and P-value numbers for all three independent variables improved. The growth factor variable (inflation) is still the least significant of the three with a t Stat of 1.415, but again, removing it from the calculations results in larger errors.

Playoff Probability

There were no significant changes to the playoff probabilities for each win level in the AL West. The 90% barrier is crossed at 95 wins, and the 50% barrier is crossed at 91 wins.

I'm keeping it short-and-sweet this time to avoid repeating what I've said in the past. If you'd like to read my previous articles, which are good if you'd like to read about how I constructed my model, check out the links below:

Texas Rangers Win-Curve Part I: Wins vs Attendance

Texas Rangers Win-Curve Part II: Playoff Probability

2010 Texas Rangers: Wins, Attendance, and Playoffs

If you're fascinated by this stuff and haven't read Vince Gennaro's book Diamond Dollars, I strongly encourage you to take a look at it.


Measuring pitch variability through PITCHf/x

January 3, 2011 • Analysis

For a while, I've been wondering what can be measured and analyzed using PITCHf/x data that hasn't already been measured and analyzed. A few things crossed my mind, but the most interesting thought was about the degree of variability of a pitcher's pitches.

It would be relatively easy to measure how much variability a pitcher has in velocity and movement if all things were equal. Of course, they aren't.

The two biggest problems for analyzing this type of variability are, as I see them, pitch type identification and park-to-park measurement error. Variability would mean little if half of a pitcher's "two-seam fastballs" are actually change-ups. Variability also runs into problems when parks like Kansas City -- whose radar gun readings are notoriously high -- are included in a data set with other ballparks.

Fortunately, if we only look at a single ballpark -- usually the pitcher's home ballpark because it has the greatest sample size -- park-to-park measurement error should be less of a factor. Without some form of park-to-park normalization, though, interpark comparisons shouldn't necessarily be taken at face value.

Additionally, 2010 saw a huge improvement in pitch type identification. While it still isn't 100% accurate, it is close enough on many pitchers to give me confidence while playing around with my ideas.

I haven't really dug into the numbers yet, but I will be looking to see if variability within a pitch type helps or hurts a pitcher. My gut feeling is that the number itself won't have much meaning.

To calculate the variability, I plan to capture the 95% window using two measurements of the standard deviation in both directions from the mean. By definition, this eliminates the outliers, but it will take some study to determine if that's really the measurement to use.

It may be beneficial to use a pythagorrean measure to find the variability for pitch movement; however, this would not appropriately model pitches that have greater variability vertically than horizontally (and vice versa, of course).

Look for a follow-up after I play around with this idea.


Thinking about run values

December 30, 2010 • Analysis

For some time, I've been looking for a way to appropriately integrate run values into the PITCHf/x database. I have read articles at Beyond the Boxscore, Inside The Book, and Cubs f/x, but I am no closer to getting what I want. Unfortunately, I lack the resources and time to find the answers myself.

Many tables have been published with run expectancies for the 12 ball/strike count states for various time periods. Tables have also been published for the 24 base/out states. Because the two tables contain different representations of the same data, there's no way to combine them. What I would like to see -- and I'm sure this makes me a sadist -- is a run expectancy table for the 288 ball/strike/base/out states.

Yes, that's one hell of a matrix to process, but there are two thoughts that seem to be the beginning of arguments against the two relatively simple approaches:

  • The thought against only using the 12 ball/strike count states table: a first-pitch strike in a bases loaded, no out situation has to effect the run expectancy more than a first-pitch strike in a bases empty, two out situation, right?
  • The thought against only using the 24 base/out states table: an 0-2 single with a runner on first base has to effect the run expectancy more than an 3-0 single with a runner on first base, right?

Admittedly, I don't have the knowledge or skills necessary to issue either of those thoughts as facts, so I have posed them as questions. It seems logical, though, doesn't it?

I think an appropriate time period for the analysis to cover is 1998-present -- since the last expansion.

Does anyone know if anyone has tackled this subject, successfully or otherwise? Is this covered in a book that I have not yet read -- possibly even one that I have read?

Consider this an open call for help in this matter.

[UPDATE: Tom Tango finally calculated the 288 states after the 2018 season, but his website was not working when I tried to grab the link.]