George Kirby had Javier Báez right where he wanted him. It was October 3, 2022, the last start of Kirby’s excellent rookie year, and Kirby had Báez, the king of chasing sliders off the plate, in an 0-2 count. His catcher, Cal Raleigh, set up off the plate, suggesting that Kirby would be targeting the outer edge.
Kirby hit his target with a well-executed slider. And Báez, instead of whiffing, hit it out of the park.
Báez wasn’t fooled; at seemingly no point did he think that pitch was a fastball. And Kirby’s lack of deception — defined here as a lack of overlap between the horizontal release angle (HRA) of his fastball and slider — may have played a part.
My research shows that HRA similarity between fastballs and sliders explains a batter’s swing decisions at the pitch level. When a given slider matches the average (or expected) HRA of the pitcher’s fastball, it makes the hitter more likely to swing. If the slider is farther from the pitcher’s average fastball HRA, the hitter is more likely to take the pitch — even if it’s in the strike zone.
My findings track with an intuitive understanding of how these pitches interact with one another. If a slider is released from the same horizontal release angle as a fastball, the arm action between the two pitches will be identical and the initial flight of the pitch will pass through the same “tunnel.” The hitter, unable to initially tell the slider apart from the fastball, is more likely to pull the trigger on a swing. And the reverse is also true — a lack of deception in slider release angles makes a swing less likely.
The importance of the fastball and slider release angle interaction leads to two separate insights. One, it tells us something important about the reasons hitters decide to swing at sliders. The deception effect, in concert with the initial trajectory, explains more about a hitter’s swing decision on a slider than how much it’s moving or how fast it’s released. Second, it spotlights an interesting trade-off between release angle repeatability and deception, suggesting that there may be a secret cost to precise command.
Last month, I wrote about the Kirby Index, which captures how precisely a fastball can be located by a given pitcher. Now there is the Kirby Corollary: Too much precision can backfire.
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It’s maybe helpful to think about why Báez generally swings and misses at sliders. Is it because the pitch is going so fast he can’t tell it apart from a fastball? Is it because it’s moving so much that he can’t tell it’s a slider until the last minute? Or is this question infinitely complex, with a constantly changing set of answers?
Most likely, it’s that last one. But my sense is that one key element is the idea of the “illusion of waste.”
Alex Chamberlain coined the phrase “illusion of waste” in his article on release angles and Immediately Obvious Waste Pitches, or IOWPs, in April. I’ll quote him at length here:
When a pitcher throws a pitch, the pitch reaches home plate in a fraction of a second. The opposing hitter, then, has a fraction of a fraction of a second to discern a great many things about the pitch: its velocity, its shape, its probable final location, all to then ascertain whether or not he should swing. Given the impossibly small window of time in which to make a swing decision, much of a hitter’s behavior is influenced by the untold thousands of pitches he’s seen before, like a mental library of pitch shapes. One of the very first visual cues a hitter receives, aside from the pitcher’s release point, is the angle at which a pitch leaves the pitcher’s hand.
As Alex wrote, a pitcher could leverage a batter’s mental library to their advantage. From his piece: “In the ever-evolving game of baseball chess, a skilled pitcher could command good pitches with ‘bad’ release angles, finding the zone with pitches that appear to have no business doing so.” Operationalizing this idea, Alex looked at all pitch types and sorted them into IOWPs.
I wanted to take a different approach to the IOWP idea. Instead of thinking about all pitch types agnostically, I wanted to look at how a batter’s mental model might relate to the relationship between two pitch types. Specifically, I wanted to understand the interplay between a fastball and a slider.
What actually makes a slider good is a surprisingly difficult question to answer. For instance, we can look at Stuff+, which is modeled on explaining and predicting slider run value. Let’s see how it did at describing the stat it is trained against at the individual pitcher level in 2023:
It’s surprisingly uninformative! The r-squared between slider Stuff+ and slider run value was 0.08. There’s a lot we don’t know about why a slider works at any given point in time. As Max Bay, one of the creators of Stuff+, wrote on Twitter in response to this finding, “Turns out humans are not static stochastic response generating machines.” In other words, batters and pitchers are constantly responding to each other, and what made a hitter swing and miss on a slider last week might be completely different this week. Identifying the specific factors that make a slider good over extended periods of time is tougher than it looks.
Nevertheless, one of these factors, without question, relates to the ability of a pitcher to throw their slider in the same “tunnel” as their fastball. In 2017, Bret Sayre, Harry Pavlidis, Jonathan Judge, and Jeff Long of Baseball Prospectus coined the concept of the “tunnel point,” defined as the location roughly 24 feet in front of home plate where the batter must decide whether or not to swing. (Later, they updated the “tunnel point” to be roughly 150 milliseconds before reaching home plate.)
Using the concept of a tunnel point, they generated a suite of statistics that measured tunneling quality among individual pitchers, including speed change and release differential between two pitches (like a fastball and a slider, for example) thrown in sequence. The inability of a batter to tell two pitches apart, further research from Baseball Prospectus showed, “can have a significant effect on how likely a batter is to swing through a pitch.”
In a 2017 Hardball Times article, Dan Blewett described his own theory of tunneling, concluding that the tunneling effect is a function of repeating the same physical delivery. Quoting Blewett:
If a pitcher repeats his delivery, then the flight of each pitch, to each location, is essentially predetermined by physics. To make them take the same tunnel, then a pitcher would need to pair pitches based on where they start, not where they end. The deviation from a tunnel, for a pitcher who repeats his delivery well, will then only come from deviations in starting location, or focal point (used interchangeably).
What’s cool is that we now have a variable that captures that starting location exactly: the release angle. The release angle guides the initial trajectory of a pitch out of the pitcher’s hand; as we know, it also determines the ultimate location of the pitch.
As both Blewett and the Baseball Prospectus team note, tunneling is inseparable from sequencing. Theoretically, the tunnel is the result of a fastball and a slider thrown back to back. The initial fastball sets the image in a hitter’s mind; the follow-up slider plays on the mental image the previous fastball has created.
I wanted to know if this same “tunneling” effect applied not just to pitches in sequence but to the relationship between all fastballs and all sliders from a given pitcher. My idea was that a hitter is usually trying to time up a fastball. Sometimes they swing like they think it’s a fastball, but instead it’s a slider. Perhaps they give up on the pitch, thinking it’s a fastball off the plate, but boom, actually it’s a slider. The batter’s perception of the interplay between the fastball and slider, in other words, likely plays some role in the effectiveness of the pitch, independent of whether it is specifically sequenced after a fastball.
In a recent piece of research on his BaseTunnel Substack, Eli Ben-Porat found evidence of release angle synergy between fastballs and gyro sliders leading to better results on the sliders. Using the average vertical release angle (VRA) on fastballs and sliders within a given start, Eli created a gyro slider deception statistic, finding that this statistic had a relationship to whiff rates. As Eli notes, Clayton Kershaw excels at this: He overlaps his horizontal release angles between fastball and slider to the maximum extent possible and gets tons of swings as a result. To achieve maximum overlap, he throws fastballs low and outside, and sliders just below that point:
Spencer Strider, perhaps unsurprisingly, does the same thing as Kershaw:
Taking a slightly different approach, I looked at pitchers at the other extreme of deception, those who struggle to generate “the illusion of waste.” Methodologically, instead of release angle averages, I used kernel density estimates (KDEs), which are fancy histograms. (If someone has a better way to describe KDEs, feel free to leave a comment below.) I also ignored vertical release angles completely, focusing specifically on the horizontal element of a slider.
For this exercise, the variables are the distributions of fastball and slider release angles, respectively. I then calculated the area under the curve of the overlapping fastball and slider KDEs to get a single “overlap” metric, which I’ll call the Corollary Index (CI).
(A quick methodological note: fastballs are defined as all four-seamers, sinkers, and cutters; sliders are pitches classified as either sliders or sweepers.)
The graphs are helpful in showing this visually. Let’s look at Kirby’s 2023 release angle KDEs. Up until recently, Kirby was a guy who almost never released his fastball from the same release angle as his slider. This is reflected in the graph below by the amount of gray shading between the two curves:
Compare Kirby to someone like Kershaw or Tarik Skubal, whose fastball and slider release angles looked virtually identical last season. That’s a lot more gray:
I figured that the quality that Skubal, Strider, and Kershaw exhibit — and that Kirby lacks — would have some relationship with how much batters swung at their sliders. The effect, according to Eli’s article about Kershaw, is real for whiffs; my research found that for called strikes, a pitcher’s CI has a statistically meaningful relationship to their ability to generate takes on the slider.
First, let’s look at the relationship between slider Stuff+ and slider called strike percentage. This will help get a sense of whether a common set of non-location-based pitch factors (velocity, movement, release point) affect a pitcher’s ability to get called strikes on their slider:
The r-squared was 0.001 — in other words, there was no relationship between a pitcher’s slider Stuff+ and how many called strikes they achieved with the pitch. Now let’s look at the relationship between CI and called strike percentage, where the r-squared was 0.12:
This relationship was even stronger in 2022. That year, CI and called strike percentage had an r-squared of 0.20:
That might not sound like much of a relationship, but remember that the r-squared between slider Stuff+ and slider run value — the thing that Stuff+ is built to describe best — is just 0.08. The reasons for certain pitches doing certain things are complex and always evolving. The strength of the relationship between CI and called strike rate is a strong suggestion that the overlap of horizontal release angles is a factor in determining why certain pitchers achieve a lot of called strikes on their pitches, even as pitchers and hitters are constantly changing in response to one another.
To make this point clearer, I used a machine learning technique called RandomForestClassifier, which helps create a model that is used for assessing binary variables (variables that either happen or don’t happen, like a swing). Given enough data, machine learning models are pretty good at describing the relationship between certain variables. If I wanted to know which factors related to a pitch result in a batter swinging, I can just throw a bunch of numbers into the machine learning soup and make it try to predict a swing using only that information. I know that it isn’t just repeating what it already knows because I then test the model on data it’s never seen before.
I built two predictive frameworks for guessing whether a batter would swing at a slider after filtering the data to all sliders thrown by right-handed pitchers in 2022. The first used some of the main inputs for a model such as Stuff+ — release point, velocity, and vertical/horizontal movement. The second framework relied on a single number: HRA differential. HRA differential is the difference between the slider thrown and the pitcher’s average fastball HRA. (I could have used league-wide HRA as well; some exploratory unpublished research suggests that there isn’t much of a difference between the two.)
The second model outperformed the first model — the HRA differential model had a 59% accuracy score, and the Stuff model had a 54% accuracy score. In other words, a lack of release angle overlap along with the pitch’s initial trajectory tells you more about why a batter swung than where the pitch was released from, how fast it was going, and how much it was moving. I also ran the same exercise using 2023 data on sliders thrown by left-handed pitchers, and the results were virtually identical.
Here are some counterarguments you might be considering. One might be that the location is by far the most influential variable in determining whether a batter will swing, and because HRA differential contains location information, that is the only reason it might do a better job predicting swings than a dumbed-down Stuff model. Other potential counterarguments include that it’s perhaps just capturing pitchers who throw more backdoor sliders, or those who have amazing slider command.
I think that the Corollary Index is specifically capturing the effect of overlapping (or non-overlapping) release angles for three reasons.
One is that pure horizontal location information only achieves 66% accuracy in its own RandomForestClassifier model. Knowing the slider’s ultimate horizontal location doesn’t automatically tell you why a batter will or won’t swing at it — it gives you a pretty good sense, but is far from a full explanation. The second is that location information is also included in the dumbed-down Stuff model in the form of vertical and horizontal release points. The third is that HRA on its own predicted swings with 52% accuracy. Adding the overlap component makes the model go from less likely to predict swings than the dumb Stuff model to more likely to predict a swing. It’s a crucial missing piece.
That means I am suggesting that how much a slider does or does not look like a fastball out of the hand is a major reason why a batter swings at it — in concert with initial trajectory, it’s perhaps just as or even more important than the slider’s speed and movement.
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I’m thinking of the inherent trade-off between the precision of locations and the illusion of waste as the Kirby Corollary. Alex Chamberlain captured the central idea in a DM, writing, “It’s such a catch-22 because Kirby has superb command, which means because of his pitch shapes he has to have different release angles to sustain his command.”
Since the beginning of 2023, 103 pitchers have thrown at least 500 sliders. Kirby ranks sixth in zone rate — and 96th in swing rate. His zone-to-swing ratio is above any other starting pitcher in the league. He throws his sliders for strikes a ton and yet batters still don’t swing.
Some of the hitter passivity on the slider is due to his command, like when he dots up a backdoor slider to a lefty. Some of it is the counts in which he chooses to throw the slider — often in 0-0 or 1-0 counts, when the batter is going to be more likely to take a pitch. But command and count aren’t the full story.
The slider doesn’t look like the fastball out of the hand, and so batters can more easily dismiss it. This is the Kirby Corollary — his commitment (and ability) to repeatedly throw four-seam fastballs inside to right-handed hitters is so strong that those hitters choose to give up on the outside part of the plate. Kirby has so far struggled to channel the illusion of waste — he is stymied by the lack thereof.
Getting tons of called strikes isn’t necessarily a problem, but it hurts him when he’s searching for strikeouts, specifically against right-handed batters. Earlier in counts, hitters will let the pitch go, but as the count goes deeper, their approach becomes more defensive, fouling pitches off if they’re over the plate or ignoring them if they’re not. In two-strike counts, Kirby’s slider is no longer as effective — it can get strikes early in counts, but when it comes time to put a hitter away, it isn’t likely to induce chase off the plate. To underscore this point: 205 pitchers threw at least 100 sliders and/or sweepers in two-strike counts in 2023. George Kirby’s whiff rate on those two-strike sliders (16%) ranked 202nd.
The Kirby Corollary allows us to differentiate between two different types of command. There is the ultra-precise command that the Kirby Index captures. And then there is a subtler form of command, best exemplified by Kershaw, that is the ability to deceive one’s pitches by making them look the same out of the hand. They are both valuable, and they both involve trade-offs.
Fastballs can be very effective on the inside part of the plate, especially if thrown high in the zone. But if a pitcher never throws their fastball on the outer edges of the zone, they will have a tough time getting hitters to bite on their sliders. It’s tricky, because fastballs that are farther over the plate can get crushed. But they also unlock swing-and-miss.
I have to acknowledge that by the time this is published, it could well be old news. After all, Kirby himself appears to be actively changing. Compare his 2023 HRA overlap on the left to his 2024 overlap:
His slider KDE, indicated by the orange, has two distinct humps; in other words, Kirby is showing signs of a skewed bimodal distribution. In 2024 — and specifically in his last four starts — he’s throwing his slider more often from trajectories that look like the fastball. And hitters are finally starting to chase the pitch off the plate.
You do a bunch of analysis on data from the past, and while you’re coming up with a conclusion about that data, the ground shifts underneath your feet. As Eno Sarris wrote about the decreasing efficacy of the sweeper on Monday, echoing Max Bay’s comment about static stochastic response generating machines, “The game is itself one big training device, the more hitters see (the sweeper) the more they are trained to hit it (or not swing at it as the case may be).” But I think my research suggests that even as the game evolves at this impossible pace, the Kirby Corollary will remain true — in order to get batters to swing at the slider, you have to convince them it might be a fastball.
