This is Michael Rosen’s first piece as a FanGraphs contributor. You may have read his previous work at the site, including his article about the Kirby Index, a metric he created to measure command using release angles. He lives in Los Angeles and works as a transportation planner.
Earlier this year, I tried to solve the riddle of how Shota Imanaga threw his invisible fastball. The pitch had (and still has) a rare combination of traits: At the time of writing, only Imanaga and Cristian Javier threw fastballs from super flat vertical approach angles (VAA) with elite induced vertical break (IVB). A fastball with a flat VAA or high IVB plays a trick on the hitter’s perception; a fastball with both qualities becomes nearly unhittable, or invisible, when located at the top of the zone. I posed two questions in that piece: Why was this invisible fastball so rare? And what was Imanaga specifically doing to throw a fastball with these traits?
The first question can be answered, my research shows, by looking directly at release angles. Release angles reflect the direction that the pitcher is aiming the ball at release, which I wrote about at length in my article on the Kirby Index from May. That act of aiming — specifically, the direction the ball is oriented out of the pitcher’s hand — also affects the amount of backspin on a four-seam fastball.
The plot below shows the relationship between backspin (measured as x-axis spin) and vertical release angle for four-seam fastballs during the 2024 season through August 5. The plot captures the linear relationship between the two variables. As the release angle flattens, the amount of backspin drops:
Fastballs resist gravity — in other words, they have more IVB — when they are thrown with more backspin. They essentially trick the batter into thinking that the pitch is rising. As a result, batters tend to swing under pitches with lots of backspin, resulting in an increase in both whiffs (misses) and harmless fly balls from contact made underneath the ball.
When a pitcher releases a fastball from a steeper vertical release angle — in other words, when the ball is pointed more toward the ground — it allows the pitcher to get “behind the ball,” creating the carry or ride effect that IVB measures. When the pitch is released at a flatter vertical release angle, it is more difficult for the pitcher to backspin the ball.
Riley McCauley, a former minor league pitcher who now works as a coach in the Phillies’ system, explained why a pitch with a steeper release angle would generate more backspin.
“The higher the slot is, the more behind the ball, the lower the vertical release angle is, typically the better opportunity you probably have to backspin the ball,” McCauley told me.
This relationship between fastball backspin and release angle flatness explains why there is an inherent tradeoff between VAA and IVB. Throwing a fastball from a flatter (and therefore more advantageous) release angle generally results in a concurrent sacrifice of IVB.
Imanaga, on the other hand, throws his fastball high in the zone with relatively flat release angles and still manages to produce elite carry. This leads into my second question: How is he doing this?
The answer appears to boil down to outlier mechanical skills. Not only is Imanaga a Kirby Index king — one of the best pitchers in the league at repeating his release angles — he is also capable of throwing a fastball that optimizes for swing-and-miss like almost no other pitcher. Both these skills can be understood, in some way, in relation to his release angles.
Measuring these mechanical skills, as I wrote in my Kirby Index article, is the next frontier of baseball analysis. But the most sophisticated analysis will not be performed by the public — it will happen in big league front offices, with teams deploying dozens of analysts to parse the outputs provided by companies like KinaTrax, who track every single part of a pitcher’s body as it goes through the pitching delivery.
Release position was our first hint of the influence of mechanics on spin; release angles get even closer. Further down the rabbit hole, there will be variables like hand position, finger pressure, wrist action, arm speed, and other mechanical influences. Driveline Baseball, through their OpenBiomechanics Project, is giving the public a sense of what kind of data teams might have at their disposal. (Their Github documentation has a good rundown of the specific variables that are measured with motion capture data.)
To understand why Imanaga throws a great fastball, it is necessary to look at the biomechanical components of his delivery. Analysis of these components may well open up the next data advantage for teams. As Eric Longenhagen wrote in his 2024 draft recap, quoting a member of a front office: “We are all making decisions looking at the same data and, increasingly, based on similar interpretations of that data.” Biomechanical data could allow teams to differentiate themselves once again, building biomechanical models that can spot the next Imanaga after looking at a single pitch. Release angles are at the threshold of all of this, but behind the biomechanical curtain, whole worlds of modeling possibilities exist. Behind the scenes, the arms race is on.
…
Four forces act on a spinning four-seam fastball in flight. The Magnus force follows the direction of the pitcher’s fingertips, pushing in the direction that the front of the ball is moving. Gravity drags the ball toward the ground at roughly 32 feet per second squared. Seam-shifted wake sends the ball in unpredictable directions if the ball’s spin orientation is uneven. Drag goes in the opposite direction as ball flight, slowing it down as it approaches home plate.
For a four-seam fastball, the Magnus force is responsible for the common phenomenon that we describe as ride, hop, and carry. It is commonly measured using IVB or drop. If a ball spins more, it stays up longer, resisting the pull of gravity.
I wanted to investigate which mechanical elements influence fastball carry. What is the pitcher specifically doing to create carry on the fastball?
Release height is one biomechanical variable known to relate strongly to fastball carry. The relationship between release height and fastball carry is well documented, to the point that smart analysts like Alex Chamberlain have pointed out that a pitcher’s carry must be understood within the context of their release height. The logic goes that hitters expect a certain carry from a given release height because of the tight relationship between these two variables.
I wanted to explore the other factors that allow pitchers to generate carry. Yes, fastball carry is a function of backspin, but which factors allow for maximum backspin on the pitch?
(A quick methodological aside: There are a few ways to evaluate the carry of a fastball. The two most common ways are IVB and drop. Both of these variables are influenced by the velocity of the pitch toward home plate. Slower fastballs get a boost in IVB; faster fastballs are rewarded by drop simply for being fast. If we are primarily interested in the specific carry characteristics of a given fastball, it makes the most sense to look specifically at its vertical acceleration, or “az” in Statcast parlance, from which both IVB and drop are derived. Az is measured in feet of drop per second per second, so a pitch that drops exactly with gravity would have an az of -32.)
It appears that a fastball’s vertical release angle is a major factor. I cooked up a linear regression with five independent variables: pitch location, vertical release angle, velocity, release height, and release extension. The regression explained 99% of the variation in fastball carry; when the variables were unit normalized, vertical approach angle had the strongest effect size, even stronger than release height:
When the pitch is released from a steeper angle — in other words, when the pitch is aimed more downward, with a greater initial vertical velocity — it generates more carry. When a pitch has a flatter aim, or a release angle closer to zero degrees, it generates less carry. Here is a plot of every four-seam fastball thrown in the 2023 season, with release angle on the x-axis and vertical acceleration on the y-axis. You can see that as the release angle flattens out, the pitch drops more with gravity:
The relationship is even stronger when averaging results at the individual pitcher level. Below is a plot of the average vertical release angle of each starting pitcher plotted against their fastball carry:
One might think that the relationship between release angle and carry is mediated by arm angle and release height, but this does not appear to be the case. Even within a given pitcher — and therefore holding arm angles and release heights relatively constant — this relationship holds up. The average R-squared of within-pitcher release angle to acceleration for four-seam fastballs sits at about 0.2. Here’s Miles Mikolas, for example:
The relationship of release angles to both location and fastball carry explains why there is no apparent relationship between fastball carry and location. Consider this plot of all four-seam fastballs through July 4:
On the x-axis is vertical acceleration; on the y-axis is the location of the pitch. It looks like there’s no relationship between the carry of a fastball and where it crosses home plate vertically, right? Not so fast.
Here’s the same plot, except this time with each pitch colored in as a function of its vertical release angle:
It turns out there is a relationship between fastball carry and location — it’s just mediated by the release angle.
The blob illuminates the various ways that a pitch can end up high in the zone. It can be thrown with a flat release angle and almost no carry, or it can be thrown with a steeper release angle and more gravity-resisting backspin. They are different paths to the same location.
I emailed Dr. Alan Nathan about this, and he offered his theory for the relationship between fastball carry and release angles.
“If the initial direction is too steeply downward, then the ball might end up below the bottom of the zone,” Nathan wrote. “That can be countered with backspin. So I am guessing that the steeper the downward release angle, the more backspin is needed to keep the ball in the strike zone, which means a lower [vertical acceleration].”
…
A few readers of my Kirby Index article expressed skepticism that the metric revealed novel insights about pitcher command. After all, release angles are calculated as a function of nine parameters that have been available since the advent of PITCHf/x. Researchers like Scott Powers and Stephen Sutton-Brown have leveraged those nine parameters to push command modeling to the cutting edge; if there was juice to squeeze here, these models would be squeezing it.
What at least one reader suggested is that if the public had access to biomechanical release angle data — not just release angles derived from initial attributes like velocities and accelerations — these data could lead to promising insights. While the public may not have access to this biomechanical data, major league teams do, whether it is through third-party providers like KinaTrax, or through data provided directly by MLB through Hawk-Eye Pro in partnership with Reboot Motion. And release angles are just the tip of the iceberg.
If command and stuff are downstream of release angles, then release angles are downstream of processes even further back in the delivery. McCauley, the Phillies coach, explained how all of these variables connect.
“I think a lot of times we do look at the wrists and the release point, but I think the lower half going down the mountain sets that up,” McCauley told me. “I think guys like [Justin] Verlander and [Tyler] Glasnow have pretty upright, linear lower halves, whereas guys like Josiah Gray and Joe Ryan have these low, slingy slots with tons of VAA [and] are typically kind of crossfire [with] very rotational lower halves. The lower half sets up what happens with the rest of the delivery, and the delivery affects ball flight at the same time.”
KinaTrax is one of the most prominent providers of biomechanical data. They came on the scene nearly a decade ago when the Tampa Bay Rays installed their software at Tropicana Field. According to Scott Coleman, the director of biomechanics at KinaTrax, the company took a major step forward following the 2020 season when they realized the ease of collecting markerless motion capture data.
Using their improved technology, KinaTrax could train their cameras on major league players and capture dozens of biomechanical variables along the way — not just release angles, but the pitcher’s external rotation, shoulder abduction, hip/shoulder separation, and dozens of other variables. Technology like this makes it possible to measure each aspect of the kinematic chain in detail.
This biomechanical information — not just release angles, which have a strong relationship to both command and stuff, but everything downstream of these release angles — can potentially be leveraged to build better predictive models, identifying hidden draft prospects, spotting injuries, and accelerating the player development revolution.
And unlike the older generation of ball flight data, which basically every team is equally capable of utilizing at this point, there appears to currently be a range of expertise when it comes to implementing biomechanical insights. There are 20 teams that contract with KinaTrax, for example, but not all of them engage with the data in the same way.
“There are some teams out there that have a lot of people that handle just our data,” Coleman told me. “And then there’s some teams that have, you know, one or two people.”
Back in 2022, Eno Sarris and Alec Lewis wrote about the future of biomechanics and pitching analysis for The Athletic. In that story, they suggested that “one of the last frontiers for biomechanics will come in linking the way pitchers move to actual results on the field.” The relationship of release angle to both command (the Kirby Index) and fastball carry shows how pitching outcomes can be linked directly to how pitchers move.
On the public side, release angles, and their importance to quantifying both command and movement, point to the power of biomechanical variables in explaining pitcher quality. But the real research is occurring behind closed doors, using terabytes of complex biomechanical data to unearth the next great pitcher.
Every team has a “stuff” model, and those models likely all look pretty similar at this point. But modeling pitcher performance based on biomechanical inputs — that is where the next information asymmetry could emerge. Perhaps it already has.
