As Ted Williams once said, “The hardest thing to do in baseball is to hit a round baseball with a round bat, squarely”. In my opinion, hitting a baseball consistently is one of the most difficult things to do in all of sports, and there are many components involved in being a successful hitter at the Major League level. Not only does the batter have to decide within a matter of milliseconds when to swing, but the batter also has to make hard, solid contact in order to translate their swings into offensive production.
Since its introduction to the public sphere in 2015, Statcast data has provided analysts with new insights into how batted ball quality relates to offensive production. By utilizing metrics such as Hard Hit% and Barrel%, evaluators no longer have to “guess” how hard each hitter hits the ball, and metrics such as xwOBA eliminate some of the subjectivity in the process of determining how “lucky” or “unlucky” a hitter has been in regards to their batted ball results. In May, Statcast released its first batch of public bat tracking metrics, including bat speed and swing length, adding another layer of advanced metrics that analysts can utilize for predictive modeling of offensive production.
While there have been numerous metrics created using Statcast data to evaluate batted ball quality over the past handful of seasons, there have also been a few attempts to assess swing decisions, notably Robert Orr’s SEAGER metric and Drew Haugen’s SwRV model. I have been fascinated by both of these models since they were released and in this article, I will unveil my swing decision model, SOTO.
Methodology:
Plate discipline and swing decisions are currently evaluated in the public sphere using a variety of different metrics. Two prominent metrics include O-Swing% (or “chase rate”), dividing a player's swings out of the strike zone by the number of pitches faced outside of the strike zone, and Z-O Swing%, which takes a hitter’s in-zone swing minus their chase rate. O-Swing% is generally thought of as an effective predictor for walk rate, as takes out of the zone will nearly always result in balls, while Z-O Swing% is thought of as a means to measure a player’s overall swing decisions, as the best offensive outcomes are a product of swinging the bat.
These metrics are effective because it makes intuitive sense that it is ideal for a hitter to swing at pitches that are located in the strike zone and it is not ideal for a hitter to swing at pitches outside of the strike zone. Two factors that these models don’t take into account, however, are the location coordinates and the count of each pitch. When calculating Z-Swing%, a swing the hitter takes on a pitch at the corner of the zone on 0-0 is weighted the same as a swing the hitter takes on a pitch right down the middle on a 1-2 count. Likewise, a take on a pitch well outside of the strike zone on the first pitch of an at-bat is valued the same as a take on a pitch just outside the zone on a 3-2 count when calculating O-Swing%. In my opinion, these metrics do not properly weigh the value of a swing or take, since swing decisions deeper in the count are more important (given the fact they often directly lead to a strikeout or walk), and results on pitches located at the edges of the zone can be impacted by factors outside of the hitter’s control (such as catcher framing or umpire tendencies.)
To create a more effective method to evaluate swing decisions, I have created a swing decision model, SOTO. Similar to the construction of my pitch quality model, aStuff+, I created my swing decision model as an XGBoost regression model. To predict the expected run value of a Swing Or Take Only, I have created two models (one for swings, the other for takes) that utilize the location and count of each pitch to predict the expected run value of each pitch. The model also includes a variable to adjust each event for batter and pitcher handedness. In order to create a target variable to predict the expected run value of each pitch, I calculated the average run value of each result and count and applied these values to their respective outcomes. For example, each 1-2 swinging strike will have the same expected run value using this method.
I decided to train my model on all pitches thrown during the 2021, 2022, and 2023 Major League Baseball seasons. I went back and forth in determining whether or not to include 2021 data in the training set since this was the last season that pitchers hit in the National League and it can be safely assumed that the average pitcher made worse swing decisions than the average hitter. I decided to keep 2021 data in the training set since the inclusion of at-bat by pitchers does not appear to tamper with the results of the model, however, it does add some complexity to the interpretation of the results of SOTO when the predictions are scaled relative to league average (to be discussed in more depth later).
As mentioned earlier, I trained two separate models (one for swings, and another for takes) using an XGBoost regression model. To improve the accuracy of the model, I improved the model’s hyperparameters using the Hyperopt package in Python. To make predictions, the models are applied to each hitter’s swing and takes, and then a weighted average is taken of each hitter's expected run value on swings and expected run value on takes. This weighted average is then expressed in the form of xRV/100 pitches, creating SOTO. With that being said, onto the model performance!
Feature Importance:
The table above displays the feature importance of all the variables in the XGBoost regression models for swings and takes. As expected, the location and count of each pitch are significant variables in predicting the expected run value of each swing or take. Unlike my pitch quality model, there are not many interesting takeaways to draw from the feature importance, given the limited number of variables utilized as predictors in the model. To further demonstrate the impacts these variables have on the model, I applied the swing and take model to all pitches in my dataset, took the difference in expected run value between these two models, and created the following plot to illustrate the locations within the strike zone where swings and takes are more favorably valued.
As shown by the heat maps above, the expected run value for swings and takes appear to be successfully valued based on pitch location, as swings down the heart of the plate and takes on pitches well out of the strike zone are more heavily valued than pitches located on the edges of the strike zone.
Descriptive + Predictive Performance:
Creating a model whose results make intuitive sense is only one step of the equation. Ensuring that the model is able to predict future performance, as well as describe the current performance of a hitter regarding their swing decisions is the real value of creating a model like SOTO. To measure the descriptive and predictive abilities of my swing decision model, I will evaluate the correlations of SOTO, O-Swing%, and Z-O Swing% with BB%, wOBA, and ISO. I will construct three separate tables for each analysis, grouped by minimum plate appearances (100, 250, and 500). For the descriptive analysis, I will compare Y1 data to itself, while I will compare Y1 data to Y2 for the predictive analysis.
As shown by the tables above, SOTO is largely a superior descriptive and predictive metric in evaluating a hitter’s swing decisions than O-Swing% and Z-O Swing%. Compared to Z-O Swing%, SOTO more effectively describes and predicts BB%, wOBA, and ISO in small and large sample sizes. Compared to O-Swing%, SOTO more effectively describes BB%, wOBA, and ISO, while O-Swing% has a slight advantage in predicting BB%. SOTO is a more effective predictive metric for wOBA and ISO than O-Swing%.
My conclusion from these correlations is that SOTO takes the best attributes of both of these swing decision measurements and combines them into one metric. While O-Swing% is good at describing BB% and Z-O Swing% is good at describing wOBA and ISO, SOTO is more effective at describing and predicting all three of these measures of offensive production.
Stickiness + Stabilization:
For use as a predictive statistic, it is important that SOTO is able to be “sticky” and have the ability to predict itself year-to-year. To calculate the stickiness of SOTO, I conducted a simple linear regression of year-to-year SOTO to evaluate how much variance in Y2 SOTO can be explained by Y1 SOTO. For comparison, I also conducted regressions to evaluate the stickiness of O-Swing% and Z-O Swing%. Similar to the descriptive/predictive analysis, I ran three separate regressions for each metric, grouped by minimum plate appearances (100, 250, and 500).
As shown by the tables above, SOTO is quite sticky from year-to-year, with an r-squared of at least .5318 depending on the sample size. SOTO is more sticky in larger sample sizes, with an r-squared of .6006 among hitters with a minimum of 500 plate appearances in consecutive seasons. While SOTO is stickier year-to-year than Z-O Swing% at all three plate discipline thresholds, O-Swing% is stickier year-to-year than SOTO in both small and large sample sizes. Since the intention behind creating SOTO was to improve upon Z-O Swing%, I consider SOTO’s level of stickiness to be more than suitable, however, O-Swing%’s improved ability to predict itself year-to-year should be taken into account when attempting to predict a hitter’s future walk rate.
It is also important to analyze when SOTO stabilizes, as this provides insight into when it can be useful to utilize the statistic without concern of having an insufficient sample size. There are multiple methods by which the stabilization point of a machine learning model like SOTO can be calculated. Some baseball machine learning models, such as FanGraphs Stuff+, use Cronenbach’s Alpha to identify stabilization points, however, I am not familiar with how to complete this analysis. Similar to how I proceeded when I created my pitch quality model, I instead took direct inspiration from Thomas Nestico’s tjStuff+ model and determined the stabilization point by identifying when a player’s SOTO does not deviate by more than 0.025 SOTO over every 10 pitches, starting with 10 pitches (for more detail regarding Thomas’s method for calculating stabilization, please click on this link).
As shown by the table above, this analysis indicates that the median stabilization point for SOTO is approximately 255 pitches. Assuming that each plate appearance averages 5 pitches, this would indicate that the median stabilization point for SOTO would be 51 plate appearances.
SOTO Leaderboards:
Now that we have established all the factors that go into SOTO, it is time to analyze how well each hitter performs. To more easily interpret the results of this swing decision model, I scaled each hitter’s SOTO relative to the league average in a given season (SOTO+). SOTO+ is scaled so that league average swing decisions are graded as 100, with 10 equaling one standard deviation. For example, a hitter who displays swing decisions that are one standard deviation above the mean would be graded as a 110.
As mentioned earlier, the lack of a universal designated hitter during the 2021 season had a significant effect on the league average and standard deviation for that season, as the presence of pitchers batting resulted in worse overall swing decisions across the league. Please keep this in mind when evaluating SOTO+ values from the 2021 season.
For the leaderboards, I calculated the SOTO and SOTO+ for each hitter from the 2021, 2022, 2023, and 2024 seasons. In these leaderboards, 2024 data runs through August 31st. Here are the top 10 SOTO leaders and bottom 10 SOTO laggards from the past three full seasons:
As shown by the table above, it is a good indicator of SOTO’s effectiveness that hitters who are known for having plus plate discipline are at the top of the leaderboard while the bottom of the leaderboard is filled with hitters who are known for having poor plate discipline. The namesake of the model, Juan Soto, ranks as the hitter who has led the league in swing decisions by a large margin over the past three seasons, while one of baseball’s most infamous “free-swingers”, Javier Báez appears twice amongst the bottom 10 laggards.
So far this season, Kyle Tucker has taken a slight advantage over Juan Soto regarding swing decisions, with Tucker displaying a 126 SOTO+ compared to Soto’s 125 SOTO+. While Tucker has missed a large portion of the season due to injury, he projects to be the first player other than Juan Soto to finish with a SOTO+ greater than 120. One player I am particularly intrigued by is Richie Palacios, as his 117 SOTO+ ranks as third-best in all of Major League Baseball. If he can find a way to improve his power output, either by lowering his swinging strike rate and pulling the ball in the air more or by continuing to add bat speed, Palacios could be a candidate to significantly increase their level of offensive production next season.
SOTO Aging Curves:
Another means of utilizing a swing decision model like SOTO can be as a tool to project how well or poorly a player’s swing decisions can be expected to age over the course of their career. To analyze how a player’s swing decisions age over the course of their career, I constructed a simple aging curve, utilizing the “delta method” to analyze each player’s year-to-year difference in SOTO, grouped by age. To enhance the interpretability of the aging curve, I also implemented LOWESS to create a smoothed aging curve.
Consistent with some older research conducted by Bill Petti on aging curves for plate discipline metrics, hitters typically display an improved ability to make swing decisions early in their careers, peaking around age 28. After age 28 (especially after age 30), each hitter’s ability to make good swing decisions can be expected year-to-year throughout the remainder of their careers. After age 35, there is a lot of variance present in the aging curve, likely due to survivorship bias and a smaller population of players in these age groups. While the results of the aging curve past age 35 can be largely ignored, perhaps this phenomenon indicates that making good swing decisions is a skill that is imperative for hitters to have to keep playing at the Major League level deep into their 30s.
Incorporating SOTO w/ Bat Tracking Metrics:
In May, Statcast released its first batch of public bat tracking data, including bat speed and swing length for each swing taken during the 2024 season. In addition to this raw data, Statcast also released a variety of metrics such as Blast% and Squared Up% that can be used to better measure contact efficiency across Major League Baseball.
Another bat tracking metric that Statcast released was Fast Swing%, which is calculated as the percentage of swings that each hitter takes with a bat speed of at least 75 MPH (I view this statistic as the bat speed equivalent to Hard Hit%). 75 MPH is an important benchmark for bat speed, as batted balls typically yield better results on “fast swings” as opposed to slower swings.
Upon creation of SOTO, I wondered if I could take this metric one step further and incorporate the quality of swing decisions into Fast Swing%. It makes intuitive sense to me that it is more important to take your fastest swings at pitches in ideal locations to swing, as opposed to taking your fastest swings at pitches unlikely to result in production. Therefore, I created the new bat tracking metric, Best Swing%.
To calculate Best Swing%, I applied the swing and take model to each pitch thrown during the 2024 season. Then, I subtracted the expected swing value from the expected take value to create an “expected difference” value. If the “expected difference” of a pitch is positive (the expected value of a swing is greater than the expected value of a take), then it is classified as a pitch the hitter should swing at. If the ‘“expected difference” is negative, then the hitter should take. Best Swing% is then calculated as the percentage of swings that each hitter takes on pitches with a positive “expected difference” with a bat speed of at least 75 MPH.
As shown by the correlation table above, Best Swing% is a marginally better metric at describing wOBAcon, xwOBAcon, wOBA, and ISO than Fast Swing%. Best Swing% is also a better metric at describing wOBAcon, xwOBAcon, and wOBA than average Bat Speed. While bat tracking metrics are still in their infancy on the public side, with the release of more metrics such as contact point and year-to-year data needed in order to create effective descriptive and predictive swing models, the performance of Best Swing% indicates that there is demonstrable value in taking “fast swings” at pitches in ideal locations.
Concluding Thoughts:
While SOTO does a good job at evaluating each player’s ability to make good swing decisions, there are a couple of limitations to the model that I wish to improve upon in the future. The first limitation is that the model does not take into account the pitch type of the incoming pitch, treating all pitch types the same. I primarily decided to leave this variable out of my model for two reasons. One reason is that there is some ambiguity between pitch classifications (such as pitchers who throw a sweeper, but it is classified by Statcast as a slider), and I did not want these differences to have an impact on the results of the model. While including the physical characteristics of each pitch into the model could’ve resolved any classification issues, this would raise an additional question of which features make an impact on a hitter’s decision-making process at the plate. To make the swing decision model as simple as possible, I simply elected to keep any pitch type related metrics out of the model.
Another limitation of the model is that it assumes that each hitter has the same “nitro zone”, while in reality, hitters have different locations throughout the zone where they frequently make their loudest contact. I have been intrigued by this concept since Rylan Domingues published in 2022 that hitters perform better when they swing less at pitches located outside of their nitro zone. While I would have liked to include a nitro zone feature in SOTO, I have been unsuccessful in my attempts to create a convex hull that identifies the shape of each hitter’s nitro zone. Perhaps SOTO v2 will include a nitro zone feature, which will hopefully improve the performance of the model.
Making good swing decisions provides a hitter with a solid foundation to generate offensive production, however, improving a hitter’s swing decisions can often be a difficult task. While nearly every hitter steps into the batter’s box with the intention to only swing at pitches in the strike zone, it is the ability to decide within milliseconds whether to swing or take that separates the hitters with good swing decision ability from those with poor swing decision ability. Utilizing the “expected difference” method to identify pitches that hitters should swing at, Major League Baseball hitters still have a ways to go before reaching complete swing decision optimization.
Good Swing% is calculated as swings that hitters took at pitches with a positive “expected difference” divided by total number of pitches, and Good Z-Swing% is calculated as swings that hitters took at pitches in the strike zone with a positive “expected difference” divided by total number of pitches in the strike zone.
It should be expected that the ideal swing rate according to my swing decision model would be lower than the actual swing rate since it is unreasonable to expect Major League hitters to chase out of the zone at a near-zero rate, however, there is a consistent gap between Z-Swing% and ideal Z-Swing%. Over the past four seasons, Z-Swing% has consistently been around 68%, while the ideal Z-Swing% has hovered around 60%.
In my opinion, the next competitive advantage in Major League Baseball as it pertains to developing hitters will be having an effective means to improve a hitter’s swing decisions. With realistic pitching machines such as Trajekt available in many Major League organizations, players now have the opportunity to receive many more repetitions against Major League-quality pitching than was previously available, which can result in an improvement in swing decision ability. Perhaps this is also an area of player development where neuroscientists and sports psychologists can provide insights into how to put a hitter’s mind in the right condition for making quick, important decisions such as deciding whether to swing or take at a given pitch. Compiling a detailed game plan also plays a valuable role in improving a hitter’s swing decisions at the plate, as the quality of today’s pitching necessitates that each hitter has a plan of attack at the plate in order to maximize their level of offensive production.
I am currently working on a SOTO leaderboard and other visualization tools that should be available on Substack in the coming days, weeks, and months. I am excited to release my swing decision model to the public and I am excited to see all of the insights that SOTO will provide in the future.
Thanks for reading!
Follow @MLBDailyStats_ on X and Adam Salorio on Substack for more in-depth MLB analysis. Photo credits to Charles Wenzelberg.
*View the current SOTO leaderboards at the attached hyperlink*
Special thanks to Robert Orr, Drew Haugen, and Thomas Nestico, as my swing decision model would not be possible without their respective publications on the topic.
