In the midst of researching the haphazard nature of JP Sears’ fastball command for my weblog Pitch Plots, I noticed I used to be lacking the reply to a elementary query: Why does the ball go the place it goes?
Particularly, I had no thought which variables decide the bodily location the place a pitch crosses residence plate. My first guesses revealed nothing: a mix of velocity, extension, spin, and launch peak had no relationship to a pitch’s eventual location. If it wasn’t any of those elements, what might Sears change to throw his fastball to higher areas?
I used to be lacking the important thing variable: the discharge trajectory. Trajectory, as outlined right here, is not only launch peak and width but in addition the vertical and horizontal launch angles of the pitch, which aren’t broadly obtainable to the general public on a pitch-by-pitch foundation.
The discharge trajectory, it seems, explains almost every little thing in regards to the final location of a pitch.
Even with out incorporating any details about what occurs after the ball is launched — the spin, the pace, the motion, the air — launch angles, alongside launch peak and width, can inform us with nearly excellent certainty the place a pitch inside a given pitch sort will find yourself.
With this discovering, we will do a greater job of quantifying command. Location+ and PitchingBot Command — two command fashions hosted right here at FanGraphs — reveal so much about how good pitchers are at avoiding walks, however they take a big pattern to grow to be dependable. Each fashions depend on count-based location outcomes, and it takes a number of hundred pitches to assemble sufficient information to meaningfully consider areas in every depend. In addition they aren’t notably “sticky” from yr to yr, that means {that a} pitcher’s 2023 Location+ doesn’t reveal a lot about what it is perhaps in 2024. What these fashions seize, it appears, is perhaps fleeting.
Many have tried to quantify command over the previous twenty years. Eno Sarris went by the historical past of those makes an attempt in his 2018 article debuting the STATS LLC metric Command+. Within the article, he instructed that it is perhaps unimaginable to measure the true intent of a pitcher. Among the many extra bold efforts to take action was COMMANDf/x, which tried to seize the place a catcher’s mitt was arrange previous to the supply of the pitch. However its preliminary makes an attempt produced questionable outcomes. One limitation is the character of catcher targets: It’s true that typically the catcher is ready up precisely the place he needs the pitcher to throw, however simply as usually the catcher could gesture towards the supposed goal earlier than establishing center, or just maintain his glove beneath the zone till the pitch begins its flight path. Novel technological approaches are opening up new pathways for pre-pitch glove monitoring, however the aforementioned issues stay.
Launch trajectories, by comparability, reliably present details about pitcher intent like no different variable within the public sphere. In principle, pitchers who’ve higher command ought to have trajectories — vertical and horizontal launch angle pairs — that cluster tightly in particular areas. My statistic — the Kirby Index, named for Mariners beginning pitcher George Kirby — would be the first public metric that exams this principle.
For simplicity’s sake, the Kirby Index measures command of a single pitch: the four-seam fastball. However fastballs additionally current extra problems: 4-seamers will be up, down, in, away, and something in between.
The Kirby Index doesn’t try and account for these complexities, however even with important limitations, it’s nonetheless “stickier” year-to-year than the 2 FanGraphs command fashions. I hope the Kirby Index will likely be simply the primary of many efforts to harness the immense energy of launch trajectories to higher perceive the elusive idea of pitcher command.
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Once I went on the lookout for the lacking variable, I had two preliminary theories: Both environmental elements have been at play, or there was one thing in private biomechanical information that might clarify pitch areas.
Enter launch angles. Launch angles — each vertical and horizontal — aren’t a broadly obtainable statistic. Many Division I faculty groups measure it utilizing Trackman items, however that information is saved in-house. Main league groups use fancier monitoring expertise than faculty groups and certain have their very own inside measurements that seize not simply launch angles but in addition ball trajectory on a granular, millisecond-by-millisecond degree. Alex Chamberlain began providing aggregated VRA and HRA calculations on his indispensable Pitch Leaderboard in February, however aside from a partial VRA leaderboard posted by Andrew Baggarly in a 2021 story about Tyler Rogers, main league VRA has not been mentioned a lot within the public sphere.
In academia, not less than one statistics division has thought of the thought. In a 2022 article titled “SEAM methodology for context-rich participant matchup evaluations,” College of Illinois statistics professors Julia Wapner, David Dalpiaz and Daniel J. Eck modeled matchups with a slew of Statcast variables in addition to internally calculated vertical and horizontal launch angles. In that article, they offered a “rudimentary” option to calculate implied VRA utilizing the identical three-dimensional velocity and acceleration figures which are utilized in vertical strategy angle (VAA) calculations:
I started with their equations. Then, after consulting with Alex Chamberlain (who printed groundbreaking analysis on vertical strategy angles for FanGraphs in 2021 and 2022 and horizontal strategy angles in 2023), I made additional tweaks to the implied launch angle formulation to account for acceleration and extension in all three bodily dimensions.
After calculating vertical and horizontal launch angles for all four-seam fastballs thrown in the course of the 2023 season, I dialed up a machine studying device that excels at making predictions with massive obtainable samples of knowledge: RandomForestRegressor.
A very powerful factor to learn about how RandomForestRegressor works is that the mannequin primarily makes lots of of various predictions primarily based on “resolution timber.” Afterwards, it averages the outcomes of these predictions to create a grasp prediction. To take action, it develops the optimum mannequin on a “coaching” set — 75% of the dataset, on this case — utilizing bootstrapping methods (principally, many trials and plenty of errors); as soon as the mannequin is shaped, it deploys the mannequin on a “check” set — the opposite 25% of the dataset — guaranteeing that the mannequin isn’t simply making good predictions as a result of it’s already seen that information. Use of this system is dependent upon a big dataset.
Fortunately, this dataset is large. There have been just below 230,000 four-seam fastballs thrown in the course of the 2023 season, that means I might prepare my mannequin on lots of of 1000’s of fastballs and nonetheless have a big dataset left over for testing.
To start out, I checked out our first mannequin, which included every little thing apart from launch angles — spin, extension, velocity, launch peak, and launch width. Right here’s the way it did, with a 45-degree dotted line included on the plot to indicate what an ideal relationship would seem like:
The R-squared between the anticipated values and the precise values for vertical areas was 0.06; for horizontal areas, it was 0.05. Briefly, it did a horrible job of predicting fastball areas — even with all of that info at its disposal.
I then eliminated every little thing from the mannequin apart from launch peak and width, and added vertical and horizontal launch angles. Right here’s how the mannequin did at predicting vertical and horizontal areas utilizing solely launch trajectories, omitting every little thing else about what occurred to the ball after launch:
The R-squared between the precise and predicted values was 0.92 for vertical pitch areas and 0.85 for horizontal pitch areas, that means that the discharge trajectory defined nearly the entire variation within the final location of four-seam fastballs.
This, to me, was a shocking consequence: Practically every little thing in regards to the eventual location of the pitch 60.5 ft away will be recognized earlier than the ball is even launched. And if launch angles are this highly effective at explaining fastball location on a pitch-by-pitch degree, might this info be leveraged to quantify a pitcher’s fastball command?
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Command, traditionally, is probably the most troublesome aspect of a pitcher’s arsenal to quantify. At this level, there are a variety of Stuff fashions on the market, all of which do an excellent job at describing the bodily traits of pitches. As a result of they have a look at bodily traits and never outcomes, they stabilize shortly. In different phrases, they offer us helpful info quick, quicker than one thing like FIP or ERA would possibly.
Launch trajectories permit for a chance to develop a command mannequin that matches the Stuff fashions of their skill to stabilize shortly. If these trajectories seize a lot of the details about the situation of a pitch earlier than the pitcher has launched the ball, they in principle can inform us so much in a brief period of time in regards to the skill for pitchers to hit their spots. The query, then, turns into leverage this information to quantify fastball command — and which outcome-based statistics are an correct reflection of this elusive idea.
On the primary a part of the query: A crude option to harness launch trajectories for measuring command could be to first calculate the usual deviation of the 4 foremost determinants of location — vertical launch angle, horizontal launch angle, vertical launch level, and horizontal launch level — kind these customary deviations into percentiles, and weigh every variable primarily based on the significance every has to the final word location of the pitch. This spits out a single command determine, which I’ll name the Kirby Index, named after George Kirby, who ranked first within the Kirby Index in 2022, second in 2023, and first in the course of the 2024 season till a weird begin at Coors. (The mechanics of the Kirby Index will be seen on my Github web page.)
(As an apart: Calculating the density of precise pitch areas would end in very comparable rankings, which raises the query of why launch trajectories are preferable to only trying on the areas themselves. My view is that by protecting the main target particularly on mechanical variables throughout the pitcher’s management and eradicating any exterior environmental elements like wind or climate, the metric higher explains command; it additionally has the additional benefit of capturing year-to-year results with better accuracy.)
The Kirby Index has a evident limitation. The baked-in assumption is that pitchers are throwing to a single goal, and that every pitch that deviates from that single goal is a mistake. This, after all, doesn’t utterly align with actuality. Zac Gallen, for instance, ranks close to the underside of the 2024 Kirby index partially as a result of he’s aiming at eight or 9 separate targets inside a given begin. Kirby is probably aiming for barely fewer areas, however hitting all of them with exceptional frequency. The only-target assumption of the Kirby Index implies that it’s not coming notably near harnessing the total energy of the connection of launch angles to command — however as you’ll see, it nonetheless captures one thing important.
Here’s a plot of Kirby’s launch angle clusters to this point this season in comparison with one of many Kirby Index laggards: Patrick Sandoval.
Discover the unfold of Sandoval’s launch angle pairs in comparison with the density of Kirby’s. There’s clearly one thing right here in regards to the repeatability of launch angles that factors to command skill, not less than on the extremes. Which brings us to the second query: How can we measure how “good” the Kirby Index is at predicting command?
One potential reply could be stroll charge. Stroll charge, or BB%, is commonly related to command, however as Eno Sarris wrote in 2018, it is perhaps higher to say that walks are extra intently associated to regulate, or the power to keep away from balls. Command requires use of not simply the strike zone however the areas on its instant edges. A’s reliever Ryan Buchter instructed Eno that he misses the strike zone on function, and is keen to stroll a batter to be able to transfer onto a extra favorable matchup.
“I’m simply not giving in to hitters,” Buchter instructed Eno. “Even when it’s a lefty up and a righty on deck, and I fall behind, I don’t give in. That’s my recreation.”
So stroll charge is probably not the most effective proxy for command. A greater reply is perhaps one thing like weighted runs, a stat that tries to depend up each occasion that happens when the pitch is thrown and defines the outcomes primarily based on the runs saved (or misplaced) on the precise pitch.
Right here, the Kirby Index matches up surprisingly effectively over small samples in comparison with Location+ FA and botCMD FA in predicting fastball run values — although you will need to make clear right here that these two fashions and the Kirby Index are doing barely various things. Location+ FA and botCMD FA are grading the situation of the pitch; the Kirby Index is making no judgments in regards to the precise location, solely assessing whether or not launch angles are being replicated. In that sense, evaluating these two fashions to the Kirby Index is like evaluating apples to oranges. However maybe that makes its efficiency in opposition to these fashions much more attention-grabbing: Whereas Location+ FA and botCMD FA have a considerably stronger relationship than the Kirby Index to the Statcast model of wFA/C, or weighted fastball runs per 100 pitches, the Kirby Index holds sturdy when measured up in opposition to the PitchInfo model, even surpassing Location+ so far within the 2024 season:
None of those metrics do an incredible job of explaining the variation in weighted runs. I checked out 4 separate month-long samples, and the best performer reached an R-squared of 0.14 between the mannequin and the run worth of a pitcher’s fastball. As we already know, modeling command is troublesome, and our present methods are lacking key details about intent.
However that is the place the Kirby Index might doubtlessly level towards a means ahead. One trace is in the way in which the Index stands out in opposition to its rivals in its year-to-year stability. Intuitively, this is smart: As a result of it’s primarily based on information that’s sourced from bodily attributes, it ought to higher predict itself from yr to yr than a stat derived from pitch outcomes. This seems to be true in each latest full season samples and slivers of recent seasons; in each these samples, the Kirby Index has been “stickier” than its mannequin rivals. Beneath is a plot of Kirby Index stickiness from the 2022 season to the 2023 season for all pitchers with not less than 500 fastballs thrown in each seasons. The R-squared of 0.5 of between-year stickiness surpasses Location+’s R-squared of 0.39:
It additionally seems stickier in small samples. Right here’s the way it compares to each PitchingBot and Location+ in stickiness between the 2023 season and the early a part of 2024:
That results in our ultimate query: How shortly does the Kirby Index grow to be dependable inside a given season? To check this, I regarded on the start-to-start stability of vertical launch angle customary deviations, the important thing enter of the Kirby Index. I calculated the utmost and minimal VRA customary deviation for all appearances the place the pitcher threw not less than 25 four-seam fastballs, and checked out all pitchers with not less than 10 appearances that met this threshold.
For single begins, the median distinction between customary deviations was 0.39, that means that the “true” full season VRA worth was 0.2 customary deviations away from probably the most excessive begin. For 2-start rolling averages, that distinction dropped to 0.26, that means a niche of about 0.1 customary deviations between the true worth and probably the most excessive two-start window. In different phrases, it usually takes someplace between one or two begins to get a powerful sense of the place a pitcher’s “true” VRA — and subsequently their true Kirby Index — actually stands.
In principle, the Kirby Index might grow to be much more highly effective. Main league pitchers, in any case, don’t simply throw to 1 location; the most effective attempt to purpose at eight, 9, even perhaps 10 distinct targets. Can we construct a Kirby Index that accounts for this actuality?
Utilizing Okay-Means, we will attempt — however at current, the weighted customary deviation percentiles outperform extra subtle approaches. I examined two, three, and 6 clusters; I break up the info by handedness; I checked out solely vertical areas — and throughout these combos, the easy Kirby Index performs finest. Theoretically, there ought to be a option to incorporate Okay-Means and just a little little bit of trigonometry to measure how effectively pitchers hit these particular launch trajectory combos and subsequently enhance the power of this mannequin, however that may be a topic for a future submit (or one other researcher!). That course of would possible begin by first figuring out “perfect” areas as outlined by international trajectory clusters, after which seeing how often a pitcher comes shut to those perfect targets. Sadly, that will require normalizing launch angles by launch peak and arm angle of the supply, and I’ve already carried out means an excessive amount of math on this article.
For now, it is sufficient to say that the Kirby Index factors at one thing actual — with the promise of much more.
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The subsequent frontier of knowledge evaluation in baseball is biomechanics. Statcast measures outputs; biomechanics are the inputs that produce the xwOBAcon and Stuff+ figures that we presently consider as “course of” stats. For good privacy-related causes, that info is basically restricted to the direct data of the groups that pay gamers’ salaries, nevertheless it doesn’t take a lot creativeness to see how that info could possibly be enormously precious in predicting the place the subsequent George Kirby would possibly come from.
Considerably extremely, this biomechanical proxy will be calculated — or not less than estimated — utilizing a handful of Statcast inputs and borrowing from physics and geometry. Let’s imagine then that launch angles are at each the literal and metaphorical threshold of the shifting motion from process-related statistics, freely offered in a Statcast .csv, towards biomechanical variables, largely the purview of the groups. In any case, launch angles themselves are solely an output of a sequence of biomechanical inputs, a product of pelvises, elbows, wrists, shoulders and fingers, all coming into live performance to supply a specific trajectory of a thrown ball.
This research is simply a restricted try and seize the potential energy that launch angles would possibly supply to command modelers. It’s not likely even a mannequin, only a weighted set of ordinary deviation percentiles. And it’s constructed merely: On this iteration, Okay-Means clustering is left on the chopping room ground, leaving garden-variety customary deviations for measuring variations in launch trajectories. Lastly, the research solely seems to be at four-seam fastballs, that are turning into much less necessary in the fashionable recreation; future research will undoubtedly look into offspeed pitches, differentiate by handedness, and higher establish perfect targets.
For now, the Kirby Index is a helpful shorthand for understanding, if not essentially predicting, command over small samples. As one high-profile Stuff modeler wrote on Twitter, “A location metric for a single recreation received’t inform us a lot.” The Kirby Index means that maybe it could possibly.
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The 2024 Kirby Index
Minimal 125 four-seam fastballs in 2024 season. All information as of Might 2.
Until famous, all stats are by April 19.