A Context-Enhanced Deep Learning Approach to Predict Baseball Pitch Location from Ball Tracking Release Metrics

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Connor Moore, Reed D. Gurchiek, Jason M. Avedesian This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5492127/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 Mar, 2025 Read the published version in Sports Engineering → Version 1 posted You are reading this latest preprint version Abstract Ball tracking systems are becoming ubiquitous in sport, creating an unprecedented opportunity for big data applications to optimize human health and performance. These applications are especially common in baseball, a sport known analyzing ball flight data to quantify performance. However, few studies adopt more advanced techniques such as deep learning to conduct these analyses. We aimed to fill this gap by developing a multi-output deep neural network (DNN) to predict final pitch location using ball tracking release metrics and contextual ball flight information (i.e., naïve projectile motion estimates) from over two million pitches thrown during National Collegiate Athletic Association Division I games. Predictions from the DNN were compared to predictions made by previously reported machine learning models, and permutation-based feature importance was used to investigate the most important features for predicting pitch location. Euclidean distance errors with the DNN were approximately 15 centimeters, outperforming linear regression models by 33% (6 centimeters). A post-hoc analysis revealed that a DNN trained without the projectile motion features performed 17% (2.8 centimeters) worse than the optimal model, suggesting the added context helped the model learn underlying physics principles that govern ball flight. Moreover, the most important ball tracking metrics for predicting pitch location were lateral release position and spin rate, which have been tied to performance and injury outcomes in elite pitchers. Thus, this model provides an enhanced framework to analyze pitcher performance, and future applications may use additional context to predict other performance metrics from ball tracking data, such as throwing arm biomechanics. baseball pitching deep learning physics human performance Figures Figure 1 Figure 2 Figure 3 1. Introduction In any sport where the athlete uses a ball, optimal performance is often explained with a description of its flight. Modern advances in optical and doppler radar technology have enabled systems that can track ball flight automatically, overcoming the limitations of qualitative analyses in the past [ 1 ]. While this technology is becoming common in many sports like golf and basketball [ 2 , 3 ], it is arguably most developed for pitched baseballs. The promising potential of ball tracking in baseball has led to rapid adoption across multiple levels of play, with TrackMan being the most common system. At the end of the 2023 season, TrackMan was in all Major League Baseball stadiums and more than 100 Minor League stadiums. At the collegiate level, the number of National Collegiate Athletic Association (NCAA) stadiums using TrackMan rose from 40 in 2021 to 182 in 2023. The advent of ball tracking technology allows researchers to readily capture the state of a pitched baseball from release to home plate. Such information provides pertinent data regarding two main skills of baseball pitching: throwing velocity and accuracy [ 4 – 6 ]. As pitchers have continued to attain new peaks in throwing velocity due to optimized training and rehabilitation routines [ 7 , 8 ], researchers have turned to machine learning models to identify the movement strategies and ball flight characteristics that allow pitchers to maintain accuracy as velocity increases [ 9 ]. Joseph et al. (2021) and Glanzer et al. (2019) developed machine learning models with biomechanical features, but ball tracking data were not included in the models [ 10 , 11 ]. Nasu and Kashino (2021) created two multiple linear regression models, one each to predict vertical and horizontal pitch location from ball tracking features, and found release angle was the strongest predictor of pitch location in each plane [ 12 ]. However, the results were based on a sample of right-handed pitchers who threw to a single location in the strike zone, and thus it is unclear how well these results generalize to a broader population of pitchers. The aforementioned studies modeled vertical and horizontal location separately, but it is likely that factors such as seam orientation and drag simultaneously moderate the relationship between release parameters and ball trajectory in all three planes of motion [ 13 ]. While some machine learning models can capture interactions between inputs (e.g., random forests), most do not natively support predicting multiple outputs and hence cannot detect interactions that span across outcomes, such as vertical and horizontal ball location [ 14 ]. Therefore, when single output models are used to predict final pitch location, they may not properly capture the underlying physics of ball flight. This issue can be overcome with deep learning, which can represent complex non-linear relationships in data and predicting multiple outputs without manually specifying interactions [ 15 ]. Although deep learning models have become more common in sports performance research, they remain less common in ball tracking research for baseball due to limited interpretability of the results [ 16 ]. To address this need, methods such as permutation-based feature importance now exist to provide insight into the features that are most important for deep learning predictions, creating new ways to interpret these complex models. The purpose of this study was thus to determine the pitching release parameters that have the most influence on final vertical and horizontal pitch location using a multi-output deep learning model. In addition to the release parameters, we included 3D projectile motion estimates of pitch location as features to provide supplemental context that we hypothesized would enhance predictive performance of the model [ 17 ]. Finally, we compared the performance of the deep learning model to previously developed linear regression models for vertical and horizontal location [ 12 ]. 2. Methods 2.1 Participants All data used for this project were retrospectively collected using TrackMan, a three-dimensional doppler radar device that quantifies the release state and flight of a pitched baseball. Access to data was granted via the TrackMan College Data Sharing Network, which provides access to in-game data for all participating NCAA teams. The project was approved by the Institutional Review Board (IRB2023-1043). All participants were active pitchers ( n = 9,476) on an NCAA baseball team from 2021–2023. Pitchers were de-identified prior to analysis using a unique number assigned by TrackMan. 2.2 Data Collection Each TrackMan unit was set up in a fixed location within a stadium. The unit collected data for all regular season games, and the same information was provided by all devices (see Supplentary Material for details). Data from each device was accessed via a file transfer protocol (FTP) server using credentials provided to the university baseball team. Data were gathered from the FTP server and subsequently stored in a restricted-access Microsoft Structured Query Language (SQL) Server database. The necessary feature and outcome data were then queried from the database into a Python environment (version 3.11.4) using a custom Python-SQL interface. Any pitches that were missing release information or met the following outlier conditions were removed during querying: release speed less than 112.7 km/hr, absolute value of induced vertical break or horizontal break greater than 0.64 meters, or vertical approach angle greater than − 3 degrees or less than − 11 degrees. After removing outliers and 622 pitches with missing information, the full dataset consisted of 2,215,013 pitches. For each pitch, all metrics characterizing initial ball state (i.e., at release from the pitcher’s hand) were used as inputs to predict resulting pitch location with three different models: physics, linear regression, and deep learning. The physics models were based on 3D projectile motion equations using the initial ball position and velocity provided by Trackman (see Supplementary Material). The remaining two models utilized the physics estimates of final ball state (i.e., at the instant it crossed home plate) as engineered features, as well as release height, release side, vertical and horizontal release angle, release speed, and spin rate taken from TrackMan. The physics estimates were included as features based on previous research suggesting the utility of incorporating domain knowledge to improve accuracy. 17 TrackMan provides the final ball location which we used as our ground truth for validation and training. Thus, induced vertical break, horizontal break, and spin axis were not included as features despite being used in previous studies, since the TrackMan stadium unit uses final ball location to infer these metrics. 12 2.3 Model Development Separate training and holdout sets were created with equal proportions of throwing hands and styles to ensure model generalizability. Each set was stratified based on throwing hand and arm angle, which was estimated by treating the release position as a right triangle and computing the inverse tangent of release height and release side (see Supplementary Material). Pitchers were then grouped into high, medium, and low arm angle categories for each throwing hand to create the stratification criteria. In total, 1,670,015 pitches from 7,121 pitchers were in the training set, and 544,998 pitches from 2,355 pitchers were in the validation set. No pitch data from the same pitcher was in both the validation and training sets. Each model was trained and evaluated using the same splits of data. Following the methods of Nasu and Kashino (2021), 12 separate linear regression models were created for vertical and horizontal location. The deep learning model was trained as a feedforward multi-output deep neural network (DNN) with multiple hidden layers. During training, the number of hidden layers was determined by choosing the number of neurons in the first hidden layer and successively halving every other layer size. The first layer size was tuned from a selection of 64, 128, 256, and 512 neurons. To ensure consistency in network depth across the compared models, the number of hidden layers was held constant at 7. This corresponded to the maximum number of layers that could be generated in a network with 64 neurons in the first hidden layer and 2 in the output layer using the halving strategy. The number of epochs (i.e., forward passes through the training set) was initially held constant at 5 across network configurations, and batch size was set to 32 for each epoch. Once the optimal first hidden layer size was determined, a new network with that configuration was trained on up to 100 epochs with early stopping, which terminated the fitting procedure after eight consecutive epochs where the improvement in validation loss was less than a tolerance of 1e-6. The activation function for the DNN was the exponential linear unit (ELU), which applies an exponential function to a neuron if the output is less than 1; otherwise, the identity function is applied. The ELU helps zero-center the mean activations of the neurons without the computational cost of batch normalization, which reduces the computational requirements of training while also preserving a more natural contour of the loss function gradient. Adam was chosen as the gradient descent optimization algorithm with an initial learning rate of 0.001. The learning rate was reduced by a factor of 10 after three consecutive epochs where the validation loss did not improve by more than 1e-6. Loss was computed as the Euclidean distance between the predicted and actual (provided by TrackMan) location, which allowed for simultaneous optimization of vertical and horizontal predictions (see Supplementary Material). Prior to model training, each feature was standardized to have zero mean and unit variance. During validation, the same scalers used for the training data were applied to the unseen data to ensure no information from the validation set influences training, and the training and holdout set features and outcomes were converted to tensors for compatibility with PyTorch when training the DNN. For each model, the mean and 95th percentile Euclidean distance errors were computed alongside the mean, 5th, and 95th percentile errors for the vertical and horizontal components. The relative importance of each feature in the DNN was then computed using permutation-based feature importance, which estimates importance by randomly shuffling the values of a feature and computing the change in loss [ 18 ]. Finally, a subanalysis of Euclidean distance errors by throwing hand and arm angle was conducted to test how well each model generalized across throwing styles, and the DNN predictions were labeled as balls or strikes based on standard strike zone dimensions to compare the model to previously reported classifiers and Major League Baseball umpires. Model development and evaluation were conducted in Python (version 3.11.4) with Scikit-learn (version 1.4.0) and PyTorch (version 2.2.2). 3. Results Pitch location predictions from the validation set were compared for each model. The optimal DNN had 64 neurons in the first hidden layer and met the early stopping criterion after 18 epochs and two learning rate adjustments (Fig. 1 ). No hyperparameter tuning was required for the other compared models. The validation set errors from the optimal DNN were consistently lower than the linear regression models and projectile motion estimates. The average Euclidean distance error from the DNN was 0.154 meters compared to 0.215 and 0.421 meters from linear regression and projectile motion, respectively (Table 1 ). The 95th percentile Euclidean distance error from the DNN was 0.362 meters compared to 0.440 and 0.624 meters from linear regression and projectile motion, respectively (Fig. 2 ). Mean absolute error (MAE) from the DNN was 0.105 and 0.093 meters for the horizontal and vertical predictions, respectively, compared to 0.165 and 0.111 for the linear regression model. The (5th, 95th) percentile errors from the horizontal and vertical predictions with the DNN were (-0.231, 0.211) and (-0.212, 0.184), respectively, and the Euclidean distance errors closely resembled a beta distribution (Fig. 2 ). Moreover, it is evident that our model is not simply regressing to the mean pitch location, but rather is sensitive to the influence of release metrics on ball flight. Using the mean pitch location from the training set to predict pitch location in the validation set, the MAE was 0.236 meters and 0.237 meters for horizontal and vertical errors, respectively, and Euclidean distance error was 0.367 meters. Visuals of the error distributions for the linear regression and projectile motion predictions can be found in the Supplementary Material. Table 1 Comparison of average validation set mean absolute errors (MAE) and Euclidean distance errors across models. Predictions were made with the optimal deep neural network (DNN), linear regression models, and projectile motion. Results are in meters. Horizontal MAE (m) Vertical MAE (m) Euclidean Distance Error (m) DNN 0.105 0.093 0.154 Linear Regression 0.161 0.111 0.215 Projectile Motion 0.279 0.280 0.421 3.1 Comparison to Linear Regression DNN predictions also outperformed linear regression within throwing hand and arm angle combinations, indicating the accurate predictions generalized across throwing styles. The Euclidean distance errors for each combination with linear regression were at least 0.199 meters, whereas the highest for any combination with the DNN was 0.158 meters (Table 2 ). Table 2 Comparison of joint Euclidean distance errors across throwing styles between linear regression and the DNN. Results are in meters. Throwing Hand Arm Angle Linear Regression DNN Left High 0.253 0.153 Left Low 0.283 0.141 Left Mid 0.286 0.158 Right High 0.199 0.154 Right Low 0.258 0.154 Right Mid 0.214 0.156 3.2 Relative Feature Importances The optimal DNN features indicated the projectile motion estimates of plate location were important to the model predictions, as the horizontal (0.214 meter increase in loss) and vertical (0.1 meter increase in loss) location estimates were two of the three most important features. (Table 3 ). The pitcher’s release side (i.e., lateral release position) was the second most important feature overall and the most important of all features directly under the influence of the pitcher (0.123 meter increase in loss). Extension had the least impact on model predictions (0.004 meter increase in loss). Table 3 Permutation feature importance results from the optimal DNN model. Change in loss is reported as the difference in validation loss between the model with the permuted feature and the optimal model (0.154 m). Relative importance is normalized such that the total sums to 1 as commonly done for machine learning models. Feature Permuted Change in Loss (m) Relative Importance Projectile Motion Prediction of Horizontal Location at Plate 0.214 0.288 Release Side 0.123 0.166 Projectile Motion Prediction of Vertical Location at Plate 0.100 0.135 Spin Rate 0.060 0.081 Projectile Motion Prediction of Flight Time 0.046 0.061 Projectile Motion Prediction of Vertical Velocity at Plate 0.045 0.060 Release Speed 0.045 0.061 Release Height 0.042 0.057 Horizontal Release Angle 0.031 0.042 Vertical Release Angle 0.029 0.039 Extension 0.004 0.006 3.4 DNN Performance as a Classifier Despite predicting a continuous outcome, the DNN predictions were also sensitive to whether a pitch landed in the strike zone. 79.1% of the validation set predictions were correctly labeled as strikes or balls based on typical strike zone dimensions (0.43 meters wide by 0.58 meters tall), which is higher than previously reported classifiers (e.g., Manzi et al.) and nears the level of accuracy (87%) demonstrated by Major League Baseball umpires from 2008 to 2018, prior to the adoption of ball tracking in stadiums [ 19 ]. Figure 5 provides a density plot showing the most frequently predicted locations for pitches from the validation set that were strikes and balls. 4. Discussion The study at hand utilized in-game ball tracking data from 9,476 NCAA pitchers and 6,899 games, making it one of the largest machine learning studies of baseball performance to-date. Previous studies using ball tracking data were conducted in a laboratory and typically limited the sample of pitchers to less than 30 [ 6 , 12 ]. Consequently, many of the machine learning techniques used are conventional regression or classification methods. While these methods benefit from improved interpretability relative to more flexible methods, they suffer from the fact that they may not generalize beyond the study sample, and hence they may overstate model performance [ 20 ]. To address this limitation, we used deep learning to estimate pitch location from initial ball state. Deep learning estimates outperformed previously studied linear regression models by over 25%, suggesting that the flexibility of the model architecture is better suited to the complex physical process of ball flight and may provide better insight into the factors that influence ball trajectory. The physical process of ball flight has been studied extensively over time. Recently, efforts have focused on better understanding the complex relationship between spin, seam orientation, and the Magnus force acting on the ball throughout its flight [ 21 , 22 ]. These factors directly contribute to curvature between release and home plate, but despite advances in modern computing technology, they have proven exceedingly difficult to model mathematically [ 23 , 24 ]. Instead, a far more simplified conceptualization of these factors is that they cause deviations from the parabolic trajectory that would be predicted with basic projectile motion. We therefore hypothesized that using basic projectile motion estimates as features in the deep learning model would improve predictive performance, and a post-hoc analysis revealed that predictions with this model were 17% (2.8 centimeters) more accurate than the same DNN architecture trained without any physics features. Since the deep learning model had multiple hidden layers with up to 64 neurons and a non-linear activation function, it was designed to learn complex relationships between the ball’s initial state and the physical properties that govern its flight. Indeed, four of the six most important features from the deep learning model were those derived from projectile motion: estimated horizontal and vertical location, estimated flight time, and estimated vertical direction speed at home plate (Table 3 ). The importance of each feature provides insight into the predictive process of the deep learning model. The most important feature in the DNN was the estimated horizontal location from physics (Table 3 ). In the linear regression models, horizontal location estimates were 39% (5 centimeters) worse than vertical location estimates. The dynamics influencing the lateral component of ball flight are highly non-linear and difficult to model with regression, and previous attempts to do so have suffered from poor performance due to its overly simplistic representation of ball flight [ 24 ]. The physics estimate of horizontal location was an even simpler portrayal of ball flight based on projectile motion (see Supplementary Material), but discrepancies between the estimated and actual location may have revealed implicit information about the aerodynamic interactions of lift, drag, turbulence, and seam orientation influencing ball flight [ 21 , 25 ]. These forces are also affected by the amount of spin imparted on the ball at release, the fourth most important feature in the DNN and second most under direct control of the pitcher [ 25 ]. Taken together, this relationship leads to non-linear horizontal ball trajectories, but the horizontal linear regression model was unable to predict them. Given that the horizontal location predictions with the DNN substantially outperformed those from linear regression, it is possible that the deep learning model implicitly created a representation of the aerodynamics influencing lateral flight. One of the main components that distinguishes a neural network from linear regression is the non-linear activation function in the hidden layers to determine the output of neurons. The presence of neurons that are not activated leads to networks that learn more complex relationships between features and outcomes than linear regression, such as how ball velocity and spin lead to deviations from the parabolic flight predicted by projectile motion. When these relationships are disrupted, as occurred when permuting the features to estimate importance, the predictions suffer because the implicit relationships no longer hold. For the deep learning model, permuting the projectile motion derived estimates rendered the model unable to make predictions using sound principles of ball flight physics. Since the model appears to leverage these principles to make accurate predictions, this finding suggests that deep learning may be able to represent the underlying physics of ball flight. Future research may engineer additional features to compare the performance of deep learning algorithms with state-of-the-art physics models. An additional benefit of deep learning models is the ability to customize the loss function. Unlike linear regression, which is constrained by ordinary least squares to a single output, the final layers of a deep learning model can produce multiple outputs. These outputs were optimized jointly by using Euclidean distance as the loss criterion. In addition to a better representation of the physics of ball flight, which is governed by forces that affect vertical and horizontal pitch location together, the multi-output model is more aligned with the need for pitchers to throw to 2D locations rather than a single vertical or horizontal target. Unsurprisingly, most important features in the model were related to both components of pitch location, and two of them are under direct control of the pitcher. Following the estimated horizontal location at home plate, the next most important features were release side (i.e., lateral release position), estimated vertical location at home plate, and spin rate at release (Table 3 ). Previous studies have found that a consistent lateral release position leads to better performance and reduced injury risk throughout a season [ 26 , 27 ], while ball spin simultaneously affects both components of pitch location through lift forces, drag, and side spin during flight [ 21 , 25 ]. Different spin rates characterize the variety of pitch types thrown during games (e.g., fastballs, changeups, and breaking balls), and those who can generate unique amounts and direction of spin on these pitches have demonstrated more success during competition [ 25 , 28 ]. Although the relationship between release position, spin rate, and pitch location had been previously studied with linear models, the DNN outperformed linear regression in the vertical plane by 19% (1.8 centimeters) and the horizontal plane by 42% (5.6 centimeters), suggesting a more robust representation of ball flight. Notably, previous studies have found release angle to be a significant predictor of pitch location [ 12 ], but vertical and horizontal release angle were found to be two of the three least important features in the DNN. This may be attributed to the use of release angle in the projectile motion estimates, which provided a more explicit relationship between release angle, subsequent flight, and resulting location. Critically, this introduced correlated features and potentially limited our approach. However, when models rely on correlated features for predictions, the resulting permutation-based feature importance for each is typically suppressed, as the model can still utilize the non-permuted features to make predictions and suffer minimal increase in loss [ 29 ]. This was clearly not the case for the DNN, as perturbations to projectile motion estimates led to larger increases in loss, but changes to release angle caused negligible increases. Therefore, the previously identified effect of release angle on pitch location likely holds true through the underlying ball flight physics related to projectile motion, but other factors (e.g., release side and spin rate) are more actionable for the pitcher. Furthermore, the improved performance of the DNN relative to linear regression and a DNN without the projectile motion features suggests these results provide a more valid representation of ball flight and release metrics that influence baseball pitch location. Several other limitations exist in our approach. First, the tuning process did not adapt the number of hidden layers to reflect the number of neurons in the first hidden layer. Instead, the number was held constant at 7 across all candidate models. Since this number was chosen to accommodate the 64-neuron model, it is possible that it was favored over the other models during the tuning process. The 64-neuron model was also the shallowest configuration, meaning that deeper neural networks with more hidden layers and neurons per layer may have performed better. It is also unclear how the benefits of improved predictive performance with deep learning compare to the reductions in interpretability, particularly from the perspective of pitching coaches and trainers. The tradeoff between interpretability and flexibility of models is commonly discussed in sports science literature, as black box algorithms are becoming more common across studies of performance and injury risk [ 5 ]. Sports performance presents a need for immediately actionable insights, which usually favors interpretable models such as linear regression when athletic development is the goal [ 30 ]. Linear regression was used in previous studies that sought to predict pitch location [ 11 , 12 ], but it is difficult for such models to generalize when deployed on much larger sets of data [ 20 ]. The interpretations from those models may be invalid if the predictions they generate are highly inaccurate, and more flexible model architectures such as deep learning are necessary to attain satisfactory predictive performance. The DNN from the study at hand outperformed linear regression across throwing hands and delivery styles, and permutation-based feature importances provided insight into the predictive process of the model. Future research should seek to improve upon this feature importance method, which can help push the field of sports science towards gathering more advanced insights into optimal sports performance through deep learning. 5. Conclusion As technology for capturing in-game performance data continues to become ubiquitous in sport, more opportunities will emerge for big data applications to optimize health and performance. This is particularly true in baseball, a sport that is notorious for its use of ball tracking to quantify performance. This study included ball tracking data from 9,476 pitchers, making it one of the largest studies of baseball pitching performance. The overall size and variety of pitchers included in the dataset rendered conventional machine learning methods such as linear regression impractical for the study objective, which was to develop a model that predicts pitch location from initial ball state information. The initial ball state information was supplemented with physics derived estimates of final ball state, including location, speed, and flight time. The critical role of the physics derived features in these predictions further suggests that deep learning may be able to represent the underlying physical processes that govern ball flight. Moving forward, enhanced models may move towards a framework for understanding the biomechanical factors that influence pitch trajectory, providing valuable insight into predictors of in-game performance and injury risk. Declarations Acknowledgments The authors report no funding for this research. Disclosure Statement The authors declare no potential conflict of interest. Data Availability Statement All data used for this study were obtained through an agreement with the TrackMan College Data Sharing Network. Due to privacy restrictions in the agreement, supporting data are not available. 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Cross-validated permutation feature importance considering correlation between features. Anal. Sci. Adv. 3, 278–287 (2022). Bullock, G. S. et al. Black Box Prediction Methods in Sports Medicine Deserve a Red Card for Reckless Practice: A Change of Tactics is Needed to Advance Athlete Care. Sports Med. 52, 1729–1735 (2022). Additional Declarations No competing interests reported. Supplementary Files supplementarymaterial.docx Cite Share Download PDF Status: Published Journal Publication published 28 Mar, 2025 Read the published version in Sports Engineering → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5492127","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":385374904,"identity":"2533c084-64e2-4ede-bc9f-278b024325b1","order_by":0,"name":"R. Connor Moore","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYHACxgcfGCxgHGaitDAbzmCQIE0LmzQPSVrM208nG9vUSMjp9h8+9oChwjqxgZAWmTO5Gx/nHJMwNruRlm7AcCadsBYJCd7NxrkNEonbbvCYSTC2HSZKyzZpywaJ+m3nzwC1/CNWC2ODRILZgRyglgZitPDkbjbsOSZhuO1GWppEwrF0Y8Ja2M9ufPCjxkbe7PzhYxIfaqxlCWpBBQmkKR8Fo2AUjIJRgAsAAD4LOPdkqbHtAAAAAElFTkSuQmCC","orcid":"","institution":"Clemson University","correspondingAuthor":true,"prefix":"","firstName":"R.","middleName":"Connor","lastName":"Moore","suffix":""},{"id":385374905,"identity":"008977c8-2915-4baf-98cd-7ef8f326aba8","order_by":1,"name":"Reed D. Gurchiek","email":"","orcid":"","institution":"Clemson University","correspondingAuthor":false,"prefix":"","firstName":"Reed","middleName":"D.","lastName":"Gurchiek","suffix":""},{"id":385374906,"identity":"d02072a4-0292-4968-9ad1-ebd7406526c3","order_by":2,"name":"Jason M. Avedesian","email":"","orcid":"","institution":"Cleveland Cavaliers","correspondingAuthor":false,"prefix":"","firstName":"Jason","middleName":"M.","lastName":"Avedesian","suffix":""}],"badges":[],"createdAt":"2024-11-20 15:38:40","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5492127/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5492127/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s12283-025-00497-5","type":"published","date":"2025-03-28T15:57:16+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":70540904,"identity":"9a069b15-8736-4252-87bb-5ed3a7a77c38","added_by":"auto","created_at":"2024-12-04 08:31:47","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":45830,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eTraining (blue) and validation (red) loss curves for the DNN. The black dashed lines indicate epochs after which adjustments were made to the learning rate.\u003c/strong\u003e\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5492127/v1/1edeb3eec2aeef752ba8f410.png"},{"id":70540908,"identity":"eb1329dd-ce2e-4fec-b851-c5be4d02eaed","added_by":"auto","created_at":"2024-12-04 08:31:47","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":107375,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eError distributions for horizontal (a, left) vertical (b, middle), and Euclidean distance predictions (c, right) made with the DNN. Errors were computed as predicted minus actual. The solid black line is a standard normal distribution scaled to the histogram data (gray bars). The black dashed lines indicate the 5th (left) and 95th (right) percentile errors, respectively.\u003c/strong\u003e\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5492127/v1/b5eb75e112741704e159f2be.png"},{"id":70540905,"identity":"48437b7a-53b3-45e4-b835-e6069ccaeec7","added_by":"auto","created_at":"2024-12-04 08:31:47","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":264377,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eDensity plots for predictions made from validation set strikes (a, left) and balls (b, right). The predicted horizontal location (x-axis) and vertical location (y-axis) are given in meters. The black shaded line outlines the standard strike zone dimensions used for labeling pitches (0.43 meters wide by 0.58 meters tall). Darker shaded points indicate a greater density of predictions made in the region.\u003c/strong\u003e\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5492127/v1/55a2a7d3bb36859f3c5c36c3.png"},{"id":79605124,"identity":"8b99b4b8-0836-442e-a98f-09dde1d1f6f3","added_by":"auto","created_at":"2025-03-31 16:10:42","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1511447,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5492127/v1/e0b381d0-3d1b-41bb-b3e7-abe43db2ca82.pdf"},{"id":70540907,"identity":"afbfb5a1-0cbb-49f4-94c5-7d7bade1717b","added_by":"auto","created_at":"2024-12-04 08:31:47","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":384212,"visible":true,"origin":"","legend":"","description":"","filename":"supplementarymaterial.docx","url":"https://assets-eu.researchsquare.com/files/rs-5492127/v1/2ec0c788ca6cdb6472bfe821.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eA Context-Enhanced Deep Learning Approach to Predict Baseball Pitch Location from Ball Tracking Release Metrics\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn any sport where the athlete uses a ball, optimal performance is often explained with a description of its flight. Modern advances in optical and doppler radar technology have enabled systems that can track ball flight automatically, overcoming the limitations of qualitative analyses in the past [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. While this technology is becoming common in many sports like golf and basketball [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], it is arguably most developed for pitched baseballs. The promising potential of ball tracking in baseball has led to rapid adoption across multiple levels of play, with TrackMan being the most common system. At the end of the 2023 season, TrackMan was in all Major League Baseball stadiums and more than 100 Minor League stadiums. At the collegiate level, the number of National Collegiate Athletic Association (NCAA) stadiums using TrackMan rose from 40 in 2021 to 182 in 2023.\u003c/p\u003e \u003cp\u003eThe advent of ball tracking technology allows researchers to readily capture the state of a pitched baseball from release to home plate. Such information provides pertinent data regarding two main skills of baseball pitching: throwing velocity and accuracy [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. As pitchers have continued to attain new peaks in throwing velocity due to optimized training and rehabilitation routines [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], researchers have turned to machine learning models to identify the movement strategies and ball flight characteristics that allow pitchers to maintain accuracy as velocity increases [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Joseph et al. (2021) and Glanzer et al. (2019) developed machine learning models with biomechanical features, but ball tracking data were not included in the models [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Nasu and Kashino (2021) created two multiple linear regression models, one each to predict vertical and horizontal pitch location from ball tracking features, and found release angle was the strongest predictor of pitch location in each plane [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. However, the results were based on a sample of right-handed pitchers who threw to a single location in the strike zone, and thus it is unclear how well these results generalize to a broader population of pitchers.\u003c/p\u003e \u003cp\u003eThe aforementioned studies modeled vertical and horizontal location separately, but it is likely that factors such as seam orientation and drag simultaneously moderate the relationship between release parameters and ball trajectory in all three planes of motion [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. While some machine learning models can capture interactions between inputs (e.g., random forests), most do not natively support predicting multiple outputs and hence cannot detect interactions that span across outcomes, such as vertical and horizontal ball location [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Therefore, when single output models are used to predict final pitch location, they may not properly capture the underlying physics of ball flight. This issue can be overcome with deep learning, which can represent complex non-linear relationships in data and predicting multiple outputs without manually specifying interactions [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Although deep learning models have become more common in sports performance research, they remain less common in ball tracking research for baseball due to limited interpretability of the results [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. To address this need, methods such as permutation-based feature importance now exist to provide insight into the features that are most important for deep learning predictions, creating new ways to interpret these complex models.\u003c/p\u003e \u003cp\u003eThe purpose of this study was thus to determine the pitching release parameters that have the most influence on final vertical and horizontal pitch location using a multi-output deep learning model. In addition to the release parameters, we included 3D projectile motion estimates of pitch location as features to provide supplemental context that we hypothesized would enhance predictive performance of the model [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Finally, we compared the performance of the deep learning model to previously developed linear regression models for vertical and horizontal location [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Participants\u003c/h2\u003e \u003cp\u003eAll data used for this project were retrospectively collected using TrackMan, a three-dimensional doppler radar device that quantifies the release state and flight of a pitched baseball. Access to data was granted via the TrackMan College Data Sharing Network, which provides access to in-game data for all participating NCAA teams. The project was approved by the Institutional Review Board (IRB2023-1043). All participants were active pitchers (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;9,476) on an NCAA baseball team from 2021\u0026ndash;2023. Pitchers were de-identified prior to analysis using a unique number assigned by TrackMan.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Data Collection\u003c/h2\u003e \u003cp\u003eEach TrackMan unit was set up in a fixed location within a stadium. The unit collected data for all regular season games, and the same information was provided by all devices (see Supplentary Material for details). Data from each device was accessed via a file transfer protocol (FTP) server using credentials provided to the university baseball team. Data were gathered from the FTP server and subsequently stored in a restricted-access Microsoft Structured Query Language (SQL) Server database. The necessary feature and outcome data were then queried from the database into a Python environment (version 3.11.4) using a custom Python-SQL interface. Any pitches that were missing release information or met the following outlier conditions were removed during querying: release speed less than 112.7 km/hr, absolute value of induced vertical break or horizontal break greater than 0.64 meters, or vertical approach angle greater than \u0026minus;\u0026thinsp;3 degrees or less than \u0026minus;\u0026thinsp;11 degrees. After removing outliers and 622 pitches with missing information, the full dataset consisted of 2,215,013 pitches.\u003c/p\u003e \u003cp\u003eFor each pitch, all metrics characterizing initial ball state (i.e., at release from the pitcher\u0026rsquo;s hand) were used as inputs to predict resulting pitch location with three different models: physics, linear regression, and deep learning. The physics models were based on 3D projectile motion equations using the initial ball position and velocity provided by Trackman (see Supplementary Material). The remaining two models utilized the physics estimates of final ball state (i.e., at the instant it crossed home plate) as engineered features, as well as release height, release side, vertical and horizontal release angle, release speed, and spin rate taken from TrackMan. The physics estimates were included as features based on previous research suggesting the utility of incorporating domain knowledge to improve accuracy.\u003csup\u003e17\u003c/sup\u003e TrackMan provides the final ball location which we used as our ground truth for validation and training. Thus, induced vertical break, horizontal break, and spin axis were not included as features despite being used in previous studies, since the TrackMan stadium unit uses final ball location to infer these metrics.\u003csup\u003e12\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Model Development\u003c/h2\u003e \u003cp\u003eSeparate training and holdout sets were created with equal proportions of throwing hands and styles to ensure model generalizability. Each set was stratified based on throwing hand and arm angle, which was estimated by treating the release position as a right triangle and computing the inverse tangent of release height and release side (see Supplementary Material). Pitchers were then grouped into high, medium, and low arm angle categories for each throwing hand to create the stratification criteria. In total, 1,670,015 pitches from 7,121 pitchers were in the training set, and 544,998 pitches from 2,355 pitchers were in the validation set. No pitch data from the same pitcher was in both the validation and training sets.\u003c/p\u003e \u003cp\u003eEach model was trained and evaluated using the same splits of data. Following the methods of Nasu and Kashino (2021),\u003csup\u003e12\u003c/sup\u003e separate linear regression models were created for vertical and horizontal location. The deep learning model was trained as a feedforward multi-output deep neural network (DNN) with multiple hidden layers. During training, the number of hidden layers was determined by choosing the number of neurons in the first hidden layer and successively halving every other layer size. The first layer size was tuned from a selection of 64, 128, 256, and 512 neurons. To ensure consistency in network depth across the compared models, the number of hidden layers was held constant at 7. This corresponded to the maximum number of layers that could be generated in a network with 64 neurons in the first hidden layer and 2 in the output layer using the halving strategy. The number of epochs (i.e., forward passes through the training set) was initially held constant at 5 across network configurations, and batch size was set to 32 for each epoch. Once the optimal first hidden layer size was determined, a new network with that configuration was trained on up to 100 epochs with early stopping, which terminated the fitting procedure after eight consecutive epochs where the improvement in validation loss was less than a tolerance of 1e-6.\u003c/p\u003e \u003cp\u003eThe activation function for the DNN was the exponential linear unit (ELU), which applies an exponential function to a neuron if the output is less than 1; otherwise, the identity function is applied. The ELU helps zero-center the mean activations of the neurons without the computational cost of batch normalization, which reduces the computational requirements of training while also preserving a more natural contour of the loss function gradient. Adam was chosen as the gradient descent optimization algorithm with an initial learning rate of 0.001. The learning rate was reduced by a factor of 10 after three consecutive epochs where the validation loss did not improve by more than 1e-6. Loss was computed as the Euclidean distance between the predicted and actual (provided by TrackMan) location, which allowed for simultaneous optimization of vertical and horizontal predictions (see Supplementary Material).\u003c/p\u003e \u003cp\u003ePrior to model training, each feature was standardized to have zero mean and unit variance. During validation, the same scalers used for the training data were applied to the unseen data to ensure no information from the validation set influences training, and the training and holdout set features and outcomes were converted to tensors for compatibility with PyTorch when training the DNN. For each model, the mean and 95th percentile Euclidean distance errors were computed alongside the mean, 5th, and 95th percentile errors for the vertical and horizontal components. The relative importance of each feature in the DNN was then computed using permutation-based feature importance, which estimates importance by randomly shuffling the values of a feature and computing the change in loss [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Finally, a subanalysis of Euclidean distance errors by throwing hand and arm angle was conducted to test how well each model generalized across throwing styles, and the DNN predictions were labeled as balls or strikes based on standard strike zone dimensions to compare the model to previously reported classifiers and Major League Baseball umpires. Model development and evaluation were conducted in Python (version 3.11.4) with Scikit-learn (version 1.4.0) and PyTorch (version 2.2.2).\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003ePitch location predictions from the validation set were compared for each model. The optimal DNN had 64 neurons in the first hidden layer and met the early stopping criterion after 18 epochs and two learning rate adjustments (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). No hyperparameter tuning was required for the other compared models.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe validation set errors from the optimal DNN were consistently lower than the linear regression models and projectile motion estimates. The average Euclidean distance error from the DNN was 0.154 meters compared to 0.215 and 0.421 meters from linear regression and projectile motion, respectively (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The 95th percentile Euclidean distance error from the DNN was 0.362 meters compared to 0.440 and 0.624 meters from linear regression and projectile motion, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Mean absolute error (MAE) from the DNN was 0.105 and 0.093 meters for the horizontal and vertical predictions, respectively, compared to 0.165 and 0.111 for the linear regression model. The (5th, 95th) percentile errors from the horizontal and vertical predictions with the DNN were (-0.231, 0.211) and (-0.212, 0.184), respectively, and the Euclidean distance errors closely resembled a beta distribution (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Moreover, it is evident that our model is not simply regressing to the mean pitch location, but rather is sensitive to the influence of release metrics on ball flight. Using the mean pitch location from the training set to predict pitch location in the validation set, the MAE was 0.236 meters and 0.237 meters for horizontal and vertical errors, respectively, and Euclidean distance error was 0.367 meters. Visuals of the error distributions for the linear regression and projectile motion predictions can be found in the Supplementary Material.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of average validation set mean absolute errors (MAE) and Euclidean distance errors across models. Predictions were made with the optimal deep neural network (DNN), linear regression models, and projectile motion. Results are in meters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e Horizontal MAE (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVertical MAE (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEuclidean Distance Error (m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eDNN\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.093\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.154\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLinear Regression\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.161\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.111\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.215\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eProjectile Motion\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.421\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Comparison to Linear Regression\u003c/h2\u003e \u003cp\u003eDNN predictions also outperformed linear regression within throwing hand and arm angle combinations, indicating the accurate predictions generalized across throwing styles. The Euclidean distance errors for each combination with linear regression were at least 0.199 meters, whereas the highest for any combination with the DNN was 0.158 meters (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of joint Euclidean distance errors across throwing styles between linear regression and the DNN. Results are in meters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThrowing Hand\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eArm Angle\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLinear Regression\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLeft\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eHigh\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.253\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.153\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLeft\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eLow\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.283\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.141\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLeft\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eMid\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.158\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRight\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eHigh\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.199\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.154\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRight\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eLow\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.258\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.154\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRight\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eMid\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.156\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Relative Feature Importances\u003c/h2\u003e \u003cp\u003eThe optimal DNN features indicated the projectile motion estimates of plate location were important to the model predictions, as the horizontal (0.214 meter increase in loss) and vertical (0.1 meter increase in loss) location estimates were two of the three most important features. (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The pitcher\u0026rsquo;s release side (i.e., lateral release position) was the second most important feature overall and the most important of all features directly under the influence of the pitcher (0.123 meter increase in loss). Extension had the least impact on model predictions (0.004 meter increase in loss).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePermutation feature importance results from the optimal DNN model. Change in loss is reported as the difference in validation loss between the model with the permuted feature and the optimal model (0.154 m). Relative importance is normalized such that the total sums to 1 as commonly done for machine learning models.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeature Permuted\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eChange in Loss (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRelative Importance\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eProjectile Motion Prediction of Horizontal Location at Plate\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.288\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRelease Side\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.123\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.166\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eProjectile Motion Prediction of Vertical Location at Plate\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.135\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSpin Rate\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eProjectile Motion Prediction of Flight Time\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.061\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eProjectile Motion Prediction of Vertical Velocity at Plate\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRelease Speed\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.061\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRelease Height\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eHorizontal Release Angle\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.042\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eVertical Release Angle\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.039\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eExtension\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.006\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.4 DNN Performance as a Classifier\u003c/h2\u003e \u003cp\u003eDespite predicting a continuous outcome, the DNN predictions were also sensitive to whether a pitch landed in the strike zone. 79.1% of the validation set predictions were correctly labeled as strikes or balls based on typical strike zone dimensions (0.43 meters wide by 0.58 meters tall), which is higher than previously reported classifiers (e.g., Manzi et al.) and nears the level of accuracy (87%) demonstrated by Major League Baseball umpires from 2008 to 2018, prior to the adoption of ball tracking in stadiums [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Figure\u0026nbsp;5 provides a density plot showing the most frequently predicted locations for pitches from the validation set that were strikes and balls.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThe study at hand utilized in-game ball tracking data from 9,476 NCAA pitchers and 6,899 games, making it one of the largest machine learning studies of baseball performance to-date. Previous studies using ball tracking data were conducted in a laboratory and typically limited the sample of pitchers to less than 30 [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Consequently, many of the machine learning techniques used are conventional regression or classification methods. While these methods benefit from improved interpretability relative to more flexible methods, they suffer from the fact that they may not generalize beyond the study sample, and hence they may overstate model performance [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. To address this limitation, we used deep learning to estimate pitch location from initial ball state. Deep learning estimates outperformed previously studied linear regression models by over 25%, suggesting that the flexibility of the model architecture is better suited to the complex physical process of ball flight and may provide better insight into the factors that influence ball trajectory.\u003c/p\u003e \u003cp\u003eThe physical process of ball flight has been studied extensively over time. Recently, efforts have focused on better understanding the complex relationship between spin, seam orientation, and the Magnus force acting on the ball throughout its flight [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. These factors directly contribute to curvature between release and home plate, but despite advances in modern computing technology, they have proven exceedingly difficult to model mathematically [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Instead, a far more simplified conceptualization of these factors is that they cause deviations from the parabolic trajectory that would be predicted with basic projectile motion. We therefore hypothesized that using basic projectile motion estimates as features in the deep learning model would improve predictive performance, and a post-hoc analysis revealed that predictions with this model were 17% (2.8 centimeters) more accurate than the same DNN architecture trained without any physics features. Since the deep learning model had multiple hidden layers with up to 64 neurons and a non-linear activation function, it was designed to learn complex relationships between the ball\u0026rsquo;s initial state and the physical properties that govern its flight. Indeed, four of the six most important features from the deep learning model were those derived from projectile motion: estimated horizontal and vertical location, estimated flight time, and estimated vertical direction speed at home plate (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe importance of each feature provides insight into the predictive process of the deep learning model. The most important feature in the DNN was the estimated horizontal location from physics (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). In the linear regression models, horizontal location estimates were 39% (5 centimeters) worse than vertical location estimates. The dynamics influencing the lateral component of ball flight are highly non-linear and difficult to model with regression, and previous attempts to do so have suffered from poor performance due to its overly simplistic representation of ball flight [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The physics estimate of horizontal location was an even simpler portrayal of ball flight based on projectile motion (see Supplementary Material), but discrepancies between the estimated and actual location may have revealed implicit information about the aerodynamic interactions of lift, drag, turbulence, and seam orientation influencing ball flight [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. These forces are also affected by the amount of spin imparted on the ball at release, the fourth most important feature in the DNN and second most under direct control of the pitcher [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Taken together, this relationship leads to non-linear horizontal ball trajectories, but the horizontal linear regression model was unable to predict them.\u003c/p\u003e \u003cp\u003eGiven that the horizontal location predictions with the DNN substantially outperformed those from linear regression, it is possible that the deep learning model implicitly created a representation of the aerodynamics influencing lateral flight. One of the main components that distinguishes a neural network from linear regression is the non-linear activation function in the hidden layers to determine the output of neurons. The presence of neurons that are not activated leads to networks that learn more complex relationships between features and outcomes than linear regression, such as how ball velocity and spin lead to deviations from the parabolic flight predicted by projectile motion. When these relationships are disrupted, as occurred when permuting the features to estimate importance, the predictions suffer because the implicit relationships no longer hold. For the deep learning model, permuting the projectile motion derived estimates rendered the model unable to make predictions using sound principles of ball flight physics. Since the model appears to leverage these principles to make accurate predictions, this finding suggests that deep learning may be able to represent the underlying physics of ball flight. Future research may engineer additional features to compare the performance of deep learning algorithms with state-of-the-art physics models.\u003c/p\u003e \u003cp\u003eAn additional benefit of deep learning models is the ability to customize the loss function. Unlike linear regression, which is constrained by ordinary least squares to a single output, the final layers of a deep learning model can produce multiple outputs. These outputs were optimized jointly by using Euclidean distance as the loss criterion. In addition to a better representation of the physics of ball flight, which is governed by forces that affect vertical and horizontal pitch location together, the multi-output model is more aligned with the need for pitchers to throw to 2D locations rather than a single vertical or horizontal target. Unsurprisingly, most important features in the model were related to both components of pitch location, and two of them are under direct control of the pitcher. Following the estimated horizontal location at home plate, the next most important features were release side (i.e., lateral release position), estimated vertical location at home plate, and spin rate at release (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Previous studies have found that a consistent lateral release position leads to better performance and reduced injury risk throughout a season [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], while ball spin simultaneously affects both components of pitch location through lift forces, drag, and side spin during flight [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Different spin rates characterize the variety of pitch types thrown during games (e.g., fastballs, changeups, and breaking balls), and those who can generate unique amounts and direction of spin on these pitches have demonstrated more success during competition [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Although the relationship between release position, spin rate, and pitch location had been previously studied with linear models, the DNN outperformed linear regression in the vertical plane by 19% (1.8 centimeters) and the horizontal plane by 42% (5.6 centimeters), suggesting a more robust representation of ball flight.\u003c/p\u003e \u003cp\u003eNotably, previous studies have found release angle to be a significant predictor of pitch location [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], but vertical and horizontal release angle were found to be two of the three least important features in the DNN. This may be attributed to the use of release angle in the projectile motion estimates, which provided a more explicit relationship between release angle, subsequent flight, and resulting location. Critically, this introduced correlated features and potentially limited our approach. However, when models rely on correlated features for predictions, the resulting permutation-based feature importance for each is typically suppressed, as the model can still utilize the non-permuted features to make predictions and suffer minimal increase in loss [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. This was clearly not the case for the DNN, as perturbations to projectile motion estimates led to larger increases in loss, but changes to release angle caused negligible increases. Therefore, the previously identified effect of release angle on pitch location likely holds true through the underlying ball flight physics related to projectile motion, but other factors (e.g., release side and spin rate) are more actionable for the pitcher. Furthermore, the improved performance of the DNN relative to linear regression and a DNN without the projectile motion features suggests these results provide a more valid representation of ball flight and release metrics that influence baseball pitch location.\u003c/p\u003e \u003cp\u003eSeveral other limitations exist in our approach. First, the tuning process did not adapt the number of hidden layers to reflect the number of neurons in the first hidden layer. Instead, the number was held constant at 7 across all candidate models. Since this number was chosen to accommodate the 64-neuron model, it is possible that it was favored over the other models during the tuning process. The 64-neuron model was also the shallowest configuration, meaning that deeper neural networks with more hidden layers and neurons per layer may have performed better. It is also unclear how the benefits of improved predictive performance with deep learning compare to the reductions in interpretability, particularly from the perspective of pitching coaches and trainers. The tradeoff between interpretability and flexibility of models is commonly discussed in sports science literature, as black box algorithms are becoming more common across studies of performance and injury risk [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Sports performance presents a need for immediately actionable insights, which usually favors interpretable models such as linear regression when athletic development is the goal [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Linear regression was used in previous studies that sought to predict pitch location [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], but it is difficult for such models to generalize when deployed on much larger sets of data [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The interpretations from those models may be invalid if the predictions they generate are highly inaccurate, and more flexible model architectures such as deep learning are necessary to attain satisfactory predictive performance. The DNN from the study at hand outperformed linear regression across throwing hands and delivery styles, and permutation-based feature importances provided insight into the predictive process of the model. Future research should seek to improve upon this feature importance method, which can help push the field of sports science towards gathering more advanced insights into optimal sports performance through deep learning.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eAs technology for capturing in-game performance data continues to become ubiquitous in sport, more opportunities will emerge for big data applications to optimize health and performance. This is particularly true in baseball, a sport that is notorious for its use of ball tracking to quantify performance. This study included ball tracking data from 9,476 pitchers, making it one of the largest studies of baseball pitching performance. The overall size and variety of pitchers included in the dataset rendered conventional machine learning methods such as linear regression impractical for the study objective, which was to develop a model that predicts pitch location from initial ball state information. The initial ball state information was supplemented with physics derived estimates of final ball state, including location, speed, and flight time. The critical role of the physics derived features in these predictions further suggests that deep learning may be able to represent the underlying physical processes that govern ball flight. Moving forward, enhanced models may move towards a framework for understanding the biomechanical factors that influence pitch trajectory, providing valuable insight into predictors of in-game performance and injury risk.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003e\u003cem\u003eAcknowledgments\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eThe authors report no funding for this research.\u003c/p\u003e\n\u003ch2\u003e\u003cem\u003eDisclosure Statement\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eThe authors declare no potential conflict of interest.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e\u003cem\u003eData Availability Statement\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eAll data used for this study were obtained through an agreement with the TrackMan College Data Sharing Network. Due to privacy restrictions in the agreement, supporting data are not available.\u0026nbsp;\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eRCM conducted data aggregation, data analysis, results visualization, and manuscript writing. JMA conducted data supervision and assisted with methodology and manuscript review. RDG also assisted with methodology and manuscript review, in addition to helping with results visualization.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLiu, J. \u003cem\u003eet al.\u003c/em\u003e A survey on location and motion tracking technologies, methodologies and applications in precision sports. Expert Syst. Appl. 229, 120492 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBishop, C. \u003cem\u003eet al.\u003c/em\u003e Trackman 4: Within and between-session reliability and inter-relationships of launch monitor metrics during indoor testing in high-level golfers. J. 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Sports Med. 52, 1729\u0026ndash;1735 (2022).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"baseball, pitching, deep learning, physics, human performance","lastPublishedDoi":"10.21203/rs.3.rs-5492127/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5492127/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBall tracking systems are becoming ubiquitous in sport, creating an unprecedented opportunity for big data applications to optimize human health and performance. These applications are especially common in baseball, a sport known analyzing ball flight data to quantify performance. However, few studies adopt more advanced techniques such as deep learning to conduct these analyses. We aimed to fill this gap by developing a multi-output deep neural network (DNN) to predict final pitch location using ball tracking release metrics and contextual ball flight information (i.e., na\u0026iuml;ve projectile motion estimates) from over two million pitches thrown during National Collegiate Athletic Association Division I games. Predictions from the DNN were compared to predictions made by previously reported machine learning models, and permutation-based feature importance was used to investigate the most important features for predicting pitch location. Euclidean distance errors with the DNN were approximately 15 centimeters, outperforming linear regression models by 33% (6 centimeters). A post-hoc analysis revealed that a DNN trained without the projectile motion features performed 17% (2.8 centimeters) worse than the optimal model, suggesting the added context helped the model learn underlying physics principles that govern ball flight. Moreover, the most important ball tracking metrics for predicting pitch location were lateral release position and spin rate, which have been tied to performance and injury outcomes in elite pitchers. Thus, this model provides an enhanced framework to analyze pitcher performance, and future applications may use additional context to predict other performance metrics from ball tracking data, such as throwing arm biomechanics.\u003c/p\u003e","manuscriptTitle":"A Context-Enhanced Deep Learning Approach to Predict Baseball Pitch Location from Ball Tracking Release Metrics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-04 08:31:42","doi":"10.21203/rs.3.rs-5492127/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b18d2bd6-3297-40da-9258-e65ec0570f4e","owner":[],"postedDate":"December 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-03-31T16:07:03+00:00","versionOfRecord":{"articleIdentity":"rs-5492127","link":"https://doi.org/10.1007/s12283-025-00497-5","journal":{"identity":"sports-engineering","isVorOnly":false,"title":"Sports Engineering"},"publishedOn":"2025-03-28 15:57:16","publishedOnDateReadable":"March 28th, 2025"},"versionCreatedAt":"2024-12-04 08:31:42","video":"","vorDoi":"10.1007/s12283-025-00497-5","vorDoiUrl":"https://doi.org/10.1007/s12283-025-00497-5","workflowStages":[]},"version":"v1","identity":"rs-5492127","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5492127","identity":"rs-5492127","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}