Can Machine Learning Robustly Predict Grade of Execution in Figure Skating Jumps from Kinematic Features Across Competitions—A Case Study of Ladies' Double Axel at the World Championships

Can Machine Learning Robustly Predict Grade of Execution in Figure Skating Jumps from Kinematic Features Across Competitions—A Case Study of Ladies' Double Axel at the World Championships | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Can Machine Learning Robustly Predict Grade of Execution in Figure Skating Jumps from Kinematic Features Across Competitions—A Case Study of Ladies' Double Axel at the World Championships Seiji Hirosawa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6233774/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract In the current figure skating scoring system, a jump's score is determined by the sum of its base value, which represents difficulty, and the grade of execution (GOE), which reflects execution quality. The criteria for evaluating the GOE allow for subjective judgment by the judges. Consequently, skaters may train without concrete guidelines for maximizing their scores. If execution quality could be robustly predicted based on kinematic characteristics, it could contribute to improving the performance of skaters. This study examined whether the GOE assigned by judges to double Axel jumps performed by female skaters at the 2019 and 2023 World Championships could be robustly predicted based on kinematic features and explored the features that contribute to these predictions. The results demonstrated that three simple kinematic features—vertical height (VH), horizontal distance (HD), and landing distance—explained 42.9% of the variance in GOE, even in a dataset that included different competitions. The mean absolute error of the prediction was 0.528. Although the GOE evaluation criteria mentioned "very good height and length," the VH had little impact in practice. Instead, jumps with a greater HD and good flow on landing resulted in higher GOE. However, in this study, ratio-based derived features, previously shown to be relevant, were not significantly related to GOE, suggesting that their influence was competition-specific rather than consistent across different competitions. This study contributes to an objective understanding of performance evaluation in judged sports from a kinematic perspective, in which scoring is inherently subjective and based on complex criteria. Judged sports Performance evaluation Sports biomechanics Sports analytics Kinematic analysis Scoring prediction Application of machine learning in sports Elastic Net regression Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1 Introduction In the current figure skating scoring system, the technical score is determined by summing the scores of the executed technical elements, including jumps, spins, and steps. The score for each element is the sum of the base value, which represents the difficulty, and the grade of execution (GOE), which reflects the execution quality. Previously, Technical Merit was scored on a scale of 0.0–6.0 in 0.1-point increments for the entire performance. However, to ensure greater transparency in judgment, the system was changed to the current International Judging System (IJS), where each technical element is scored individually and summed to determine the final technical score. In the IJS, a jump's score is determined by its base value—predefined based on the jump type and rotation count—and adjusted by GOE-based bonuses or deductions reflecting execution quality. In recent years, more skaters have attempted high-difficulty triple and quadruple jumps in European and World Championships ( 1 ). However, to win competitions, simply landing difficult jumps without falling is not sufficient; skaters must also perform jumps that judges recognize as high quality. Table 1 presents the positive, and Table 2 the negative, criteria for jump GOE. Judges assess each jump in real time, assigning a score on an 11-point scale from − 5 to + 5. The scoring guidelines for positive GOE are based on the number of bullets (evaluation items officially listed in the ISU judging guidelines) fulfilled: +1 for one bullet, + 2 for two, + 3 for three, + 4 for four, and + 5 for five or more bullets. For GOE scores of + 4 and + 5, the first three bullets highlighted in bold in Table 1 must be included. GOE is a complex evaluation criterion determined by multiple factors. Compared with the negative aspects shown in Table 2 , the positive aspects in Table 1 leave greater room for interpretation, as they include more qualitative and subjective elements. The evaluation criteria encompass not only kinematic characteristics of jumps, such as 'very good height and very good length' or 'good take-off and landing,' but also aspects related to creativity and musical expression, such as 'unexpected or creative entry' and 'element matches the music,' making the evaluation system highly complex. Additionally, even among criteria related to kinematic characteristics, the term "good" is used, leaving room for subjective judgment by the judge. As skating techniques continue to advance, current figure skaters refine even successfully landed jumps to ensure they are judged as high in quality. However, because the criteria for GOE remain ambiguous and clear coaching indicators are lacking, skaters may feel compelled to pursue excessive refinement of jumps that are already successful. This tendency appears to be related to the higher prevalence of overuse injuries reported in previous studies ( 2 – 5 ), as the pursuit of aesthetic perfection is likely to increase physical strain. Table 1 Guidelines for the Positive Aspects of Grade of Execution (GOE) ( 6 ) 1. very good height and very good length (of all jumps in a combo or sequence) 2. good take-off and landing 3. effortless throughout (including rhythm in Jump combination) 4. steps before the jump, unexpected or creative entry 5. very good body position from take-off to landing 6. element matches the music Table 2 Guidelines for Establishing GOE for Errors (Negative Aspects) ( 6 ) Reduction for errors (Jump Elements) Jump element not according to requirements, final GOE must be -5 Downgraded (sign <<) -3 to -4 Fall -5 Under-rotated (sign <) -2 to -3 Landing on two feet in a jump -3 to -4 Landed on the quarter (sign q) -2 Stepping out of landing in a jump -3 to -4 Less than quarter missing (no sign) -1 Two three-turns in between (jump combo/sequence) -2 to -3 Euler executed as step over -1 to -2 Change of edge in between jump combo -1 to -2 Poor speed, height, distance, or air position -1 to -3 Wrong edge take-off Flip/Lutz (sign “e”) -2 to -4 Touch down with both hands in a jump -2 to -3 Unclear edge take-off Flip/Lutz (sign “!”) -1 to -2 Touch down with one hand or free foot (including in between jumps) -1 to -2 Unclear edge take-off Flip/Lutz (no sign) -1 Loss of flow/direction/rhythm between jumps (combo/seq.) -1 to -3 Poor take-off -1 to -3 Weak landing (bad position/wrong edge/scratching etc.) -1 to -3 Long preparation -1 to -3 Since the 2018–2019 season, a broadcast-oriented tracking system called “Ice Scope” has been utilized in figure skating competitions (Fig. 1 ). The system calculates jump height, horizontal distance, and landing speed. These kinematics metrics are provided for media presentation only and are not used in the official judging process. By integrating such biomechanical data with scoring outcomes, it becomes possible to examine whether quantitative features can explain or predict subjective evaluations such as GOE. Therefore, this study aimed to determine whether the GOE assigned by judges to jumps can be robustly predicted using kinematic features obtained from the Ice Scope tracking system and to identify the specific kinematic characteristics associated with higher-quality execution. The key contributions of this study are as follows: Three interpretable kinematic features explain a substantial portion of GOE variance across competitions, providing a basis for objectifying subjective evaluations. Despite GOE criteria emphasizing “height and length,” horizontal and landing distances are more critical than vertical height, offering a new perspective on jump quality. Ratio-based features previously reported to be related to GOE did not show a consistent relationship in this study, suggesting that their importance may be competition-specific. 2 Related work Regarding the kinematic characteristics of figure skating jumps, previous research has primarily focused on increasing difficulty and examining how skaters can successfully land jumps with a higher number of rotations. Among the six types of jumps, the Axel jump has been the most extensively studied ( 7 ). The Axel jump is the only jump that takes off in a forward direction. Additionally, skaters are required to perform an Axel jump in both the short program and free skating. According to the principles of mechanics, maximizing rotations in the air requires both sufficient jump height (vertical velocity) and a high rotational speed (angular velocity). Multiple biomechanical studies have reported that skaters maintain the same jump height, even when performing jumps with more rotations and skaters achieve more difficult jumps by increasing their rotational speed ( 8 – 11 ). Some studies have proposed the use of weighted gloves to further increase rotational speed. ( 12 ). However, recent studies have reported that the only skater in the world to have successfully landed a quadruple Axel achieved a significantly greater maximum jump height compared with skaters performing triple Axel jumps at the World Championships. This suggests that skaters aim to increase their jump height to master new jumps ( 13 ). This finding is consistent with case studies conducted when only a few skaters were capable of performing a triple Axel ( 14 ), highlighting the ongoing debate on the relationship between jump height and the achievement of high-difficulty jumps. While the debate on jump height and difficulty continues, an equally important aspect of competitive success is the quality of execution. From the perspective of GOE, an analysis based on kinematic features obtained from a tracking system named IceScope—the Japanese media-oriented tracking system developed by Qoncept Inc. and used in selected competitions ( 15 )—was performed on double Axel jumps in the women's short program at the 2019 World Championship. The results showed that greater horizontal distance and landing distance compared with vertical height, and greater horizontal distance compared with landing distance, contributed to higher GOE. However, since this study was limited to the short program of a single competition, it remains unclear whether these trends are consistent across different competitive contexts ( 16 ). Building on such efforts to link kinematics with subjective evaluation, research in the field of computer vision has explored figure skating as a subject for score prediction within the broader task of action quality assessment (AQA), which involves predicting a score from a video sequence of actions ( 17 – 21 ). Most studies use broadcast videos as inputs and predict technical and program component scores using RGB-based image features or pose estimation-based features as inputs to deep learning models ( 22 – 28 ). Among these models, deep learning approaches are commonly employed to automatically extract features from consecutive video frames. By learning hierarchical patterns related to body posture, motion dynamics, and visual appearance, deep learning models can map these features to performance scores assigned by judges. The evaluation of technical scores in figure skating has shifted from an overall performance-based assessment to the sum of individual technical elements. Therefore, using the entire performance as input may be suitable for predicting program component scores; however, its applicability to technical scores remains limited. Predicting an individual jump score could provide valuable feedback to skaters and coaches. In AQA-related research focusing on the prediction of GOE, deep learning models such as convolutional neural networks (CNNs) have been used ( 29 ). CNNs automatically extract spatial patterns from RGB-based video frames by convolving filters across images, enabling the model to learn visual representations related to performance quality. However, despite their predictive capability, their interpretability in identifying key contributing factors remains limited. Therefore, simpler models are preferred for practical applications, as they enable skaters and coaches to identify which kinematic features should be adjusted during training. Additionally, because this study focused only on the short program of a single competition, it remains unclear whether this trend applies to different competitions. This study aimed to determine whether the GOE assigned by judges to double Axel jumps performed by female skaters could be robustly predicted based on kinematic features across different World Championships, thereby extending previous single-competition findings and providing the first examination of the robustness of subjective evaluation of jump execution quality across multiple competitions. 3 Methods 3.1 Dataset This study examined double Axel jumps in the women's single event at the 2019 and 2023 World Championships, both held in Saitama, Japan. All jumps received a GOE of zero or higher from nine judges. In addition, combination jumps consisting of multiple consecutive jumps were excluded. The target GOE values were obtained from the official competition website ( 30 , 31 ). In this study, the target variable GOE was calculated as the trimmed mean of the 11-point scores assigned by nine judges, considering only positive evaluations; therefore, its theoretical range was 0–5. Furthermore, in the official competition results, this GOE value is converted into the final score by multiplying it by the element’s base value and dividing by 10. However, this study did not use this converted score. The features comprised three kinematic variables obtained from the Ice Scope system: VH, HD, and skating speed after landing (landing speed). This system was introduced by Fuji Television Network, a Japanese broadcasting company, as a media-oriented tracking system and was not used for competition scoring. The data obtained from this system are displayed in replay footage after a skater’s performance, making some of them publicly available. The system utilizes two 4 K cameras (3840 × 2160 pixels) recording at 30 fps, positioned to cover the entire 60 m × 30 m skating rink. The real-world scale of each pixel was calculated using the rink layout data. Based on reference materials (Fig. 2 , 3 ), each feature was measured using the two-dimensional Direct Linear Transformation method. In this study, the landing speed was recalculated as the landing distance (LD) to improve the interpretability ( 13 , 15 , 16 ). VH (m): The maximum vertical height measured from the frame where the toe-pick leaves the ice at takeoff to the frame where it contacts the ice upon landing. This parameter was calculated based on the position of the skater’s toe-pick. HD (m): The horizontal distance measured from the frame where the toe-pick leaves the ice at takeoff to the frame where it contacts the ice upon landing. This parameter was calculated based on the position of the skater’s toe-pick. LD (m/s): The skating distance over five frames starting from the frame where the heel edge fully contacts the ice upon landing. As the system operates at 30 fps, each frame corresponds to approximately 0.033 s. As this system was designed for real-time use in broadcast footage as a broadcast-oriented tracking tool, it does not achieve the precision of motion capture systems used in controlled laboratory environments. According to the development company, measurement errors of approximately 3 cm have been reported, depending on the camera placement ( 32 ). The system operators, employees of Qoncept Inc., visually determined all take-off and landing frames. In addition to the original three kinematic features obtained from Ice Scope, this study performed feature engineering by incorporating derived features based on previous studies ( 13 , 16 ). The derived features included the following ratios: (HD + LD) / VH, LD/HD, and HD/VH. The dataset comprised 66 jumps (2019 WC: 40 jumps by 31 skaters; 2023 WC: 26 jumps by 19 skaters). Table 3 summarizes the descriptive statistics of the dataset. Table 3 Summary Statistics of the Dataset for Double Axel Jumps Variables Mean ± SD Range Age 19.28 ± 2.56 16–25 Vertical Height, VH [m] 0.40 ± 0.05 0.31–0.51 Horizontal Distance, HD [m] 2.33 ± 0.42 1.16–3.74 Landing Distance, LD [m] 0.61 ± 0.17 0.27–0.97 (HD + LD) / VH 7.41 ± 1.41 4.03–11.56 LD / HD 0.27 ± 0.06 0.14–0.44 HD / VH 5.85 ± 1.07 2.97–8.89 GOE 2.12 ± 0.93 0.14–4.43 Table 4 presents the variance inflation factor (VIF) results used to evaluate multicollinearity among the kinematic features. The VIF results indicate a high degree of correlation between variables. Table 4 Evaluation of Multicollinearity Among Kinematic Features Kinematic Features Variance Inflation Factor Vertical Height, VH [m] 535 Horizontal Distance, HD [m] 4076 Landing Distance, LD [m] 2867 (HD + LD) / VH 47050 LD / HD 550 HD / VH 46199 3.2 Machine Learning model To address the high correlation among features and to identify the variables that influence GOE from similar features, an Elastic Net model was employed. Owing to the small sample size, leave-one-out cross-validation was used for parameter tuning and performance evaluation. Tuning was performed using a grid search within the following search ranges: the regularization parameter (λ) values logarithmically spaced across 20 points from 10⁻² to 10², and the L1 ratio values were divided into nine intervals from 0.1 to 0.9. The accuracy of the model was compared with that of a standard multiple regression model to assess the effectiveness of regularization. The adjusted R², MAE, and root mean squared error (RMSE) were used as evaluation metrics. Adjusted R² represents the proportion of variance explained by the model, and MAE indicates the average prediction error. It is less sensitive to outliers, and RMSE penalizes larger errors more heavily, reflecting the overall predictive accuracy of the model. Together, these metrics provide a comprehensive assessment of the model’s performance. All analyses were performed using scikit-learn (version 1.6.1; Python Software Foundation, Delaware, USA) implemented in Python (version 3.12.11). 4 Results Table 5 lists the accuracies of the models. The Elastic Net outperformed multiple regression across all evaluation metrics. Table 5 Results of Model Accuracy Comparison Models Adjusted R 2 MAE RMSE Elastic Net 0.429 0.528 0.666 Multiple Regression 0.342 0.568 0.715 Table 6 lists the regression coefficients for the Elastic Net model. The coefficients were − 0.068, 0.549, and 0.145 for VH, HD, and LD, respectively. All ratio-based derived features had coefficients of 0.00, indicating that they were excluded through variable selection. Table 6 Regression Coefficients of Each Feature for GOE in the Elastic Net Features Coefficient Vertical Height(VH) -0.068 Horizontal Distance(HD) 0.549 Landing Distance (LD) 0.145 (HD + LD) / VH 0.000 LD / HD 0.000 HD / VH 0.000 Figure 4 shows a line graph illustrating the error between the actual and predicted GOE for each sample. The blue and orange lines represent the actual and predicted GOE values, respectively. The overall mean error was 0.528 ± 0.405. The largest error was observed at Jump Index 55, with a value of 1.689, where the actual GOE was 3.429 and the predicted value was 1.740. The smallest error occurred at Jump Index 34, with a value of 0.005, where the actual GOE was 1.143 and the predicted value was 1.148. This figure visualizes the predictive accuracy of the model across all samples, highlighting the jumps with the largest and smallest errors 5 Discussion As expected, the dataset used in this study exhibited high correlations among the variables, with correspondingly high VIF values (Table 4 ). Additionally, because the Elastic Net outperformed multiple regression across all evaluation metrics, including the Adjusted R², MAE, and RMSE (Table 5 ), it can be considered that the Elastic Net effectively performed appropriate variable selection through regularization, resulting in a simpler and more interpretable model. As summarized in Table 1 , GOE is a complex evaluation metric based on six subjective criteria. However, the Adjusted R² value suggests that only three simple kinematic features could explain approximately 43% of the variance. A previous study that focused solely on the short program at the 2019 World Championships reported an adjusted R² of 0.504 ( 16 ). Because this dataset included data from both the short program and free skating events at the 2019 and 2023 World Championships, the adjusted R² value was lower than that of the previous study. Nevertheless, given the complexity of the GOE evaluation criteria, the model still captured a substantial portion of the variance. In terms of prediction, despite incorporating data from different programs and competition years, the MAE remained 0.528 ± 0.405, indicating that the model provides a useful estimate of GOE. This level of accuracy can help skaters develop a more objective understanding of their performances. Table 4 lists the regression coefficients for GOE using the Elastic Net. Ratio-based derived features that were previously relevant ( 16 ) were excluded through regularization, suggesting that their influence on GOE was specific to the 2019 Women’s Short Program and was not robust across competitions. Examining the regression coefficients, HD (0.549) and LD (0.145) positively influenced GOE, whereas VH (-0.068) had a negative impact. Although the GOE evaluation criteria mention "very good height and very good length," the results suggest that jump height has little effect, whereas a greater jump distance is associated with a higher GOE. One possible explanation for the negative coefficient of vertical height is that jumps emphasizing vertical height may lose horizontal momentum, resulting in reduced flow upon landing, which is also an important criterion for GOE. This finding aligns with a previous study on the 2019 Women’s Short Program, which reported that skaters with a higher GOE achieved significantly greater jump distances than those with lower GOE. Thus, for double Axel jumps performed by female skaters, HD has a stronger influence on GOE than VH, and this trend appears consistent across programs and competitions. Although LD has a smaller effect than HD, it still contributes positively to GOE. Therefore, to achieve a higher GOE in competitions, female skaters should aim for jumps with greater distance and smoother flow upon landing. Figure 4 shows the actual GOE and Elastic Net predictions for each jump. Figure 5 presents a sequence of images for Jump Index 55, which had the largest prediction error. The kinematics-based prediction used in this study underestimated the actual GOE by 3.429, yielding a value of 1.740. This discrepancy may have occurred because the skater’s jump entry, which was not captured by the kinematic features used in this study, played a crucial role in the performance. The skater approached the jump by skating backward in a spiral position (Images 1–5) and then executed a counter turn—a difficult transition from a left backward outside edge to a forward outside edge (Images 6–9)—directly into the Axel takeoff. Executing such a complex movement into the jump in synchronization with the music corresponds to the GOE evaluation criteria for “steps before the jump, unexpected or creative entry” and “element matches the music.” However, as these aspects were not captured by the kinematic features, the model likely underestimation the GOE. This example highlights the limitation of the model: relying solely on three kinematic features cannot capture the subjective aspects of GOE, such as creativity and musicality. This figure illustrates a jump with a large prediction error, demonstrating how movements not captured by kinematic features can affect prediction accuracy. Conversely, Jump Index 34 (Fig. 6 ), which had the highest prediction accuracy (actual: 1.143, predicted: 1.148), showed no distinctive movements before takeoff. The skater executed the takeoff following the standard preparation for an Axel jump—transitioning from backward outside edge skating through turns or edge changes, then stepping forward into the takeoff from a forward outside edge. Jumps performed with such standard preparations and postures tend to be accurately predicted based on kinematic features. In addition, while most skaters rotate counterclockwise relative to their body’s longitudinal axis, this skater rotates clockwise. In the dataset used for this study, only six out of 66 jumps were clockwise rotations. Because relatively few skaters perform clockwise jumps, evaluating the quality of these jumps may be challenging for judges without extensive experience. Based on this case, the model appears to generalize to jumps with different rotation directions; however, further research with a larger dataset of clockwise jumps is needed to confirm this robustness. Such findings could provide valuable feedback to coaches, skaters, and less experienced judges. This figure illustrates a jump accurately predicted by the model, showing that jumps with standard preparatory movements can be reliably captured through kinematic features. This study has several limitations. The first concerns the accuracy of data acquisition. The system used in this study operates at 30 fps, which is less precise than gold-standard motion capture systems or high-speed cameras commonly used by sports scientists for detailed analysis of rapid movements. Although obtaining data during competitions is challenging, the use of higher-precision equipment is preferable. Another limitation is that this study focused exclusively on the double Axel jumps performed by senior female skaters, making it unclear whether the findings are robust across different categories or jump types. The tracking system used in this study is limited to competitions for which Fuji Television Network, Inc. holds broadcasting rights. To better evaluate its robustness across different competitive settings, the system should be implemented in a wider range of categories and events. An additional concern is related to multicollinearity. In the context of machine learning, high multicollinearity often arises naturally when derived features are included. Although the Elastic Net mitigates this issue, the extremely high VIF values observed here indicate that caution is required when interpreting the stability of regression coefficients, even though prediction performance remains robust. Furthermore, the subjectivity inherent in GOE scoring should be acknowledged. Although the trimmed mean of nine judges’ scores helps mitigate the influence of outliers, inter-judge variability may still affect the GOE. Recent research comparing competitions before and after the expansion of the GOE range from ± 3 to ± 5 (2018 vs. 2022) reported decreased scoring consistency in some men’s, women’s, and pairs segments ( 33 ). This finding suggests that even within the standardized IJS framework, differences in individual judging tendencies can influence the evaluation outcome, which may, in turn, affect model predictions based on such scores. Despite these limitations, this study is the first to examine the robustness of the relationship between the kinematic characteristics of figure skating jumps and GOE, which is subjectively evaluated by judges, using real-world data from two different competitions. As larger datasets become available, more robust prediction models can be developed to provide deeper insights into the subjectivity of judging in evaluated sports. 6 Conclusion This study examined whether the GOE assigned to double Axel jumps at two editions of the World Championships could be robustly predicted using kinematic features and identified key contributing factors. The results demonstrated that three simple kinematic features explained 42.9% of the GOE variance, with an MAE of 0.528, demonstrating sufficient accuracy for reference. Although the GOE criteria mention "very good height and length," the VH had little impact, whereas the HD and LD played a greater role, suggesting that jumps with greater flow received higher GOE scores. Ratio-based derived features, previously determined to be relevant, exhibited no significant relationship with GOE, indicating that their influence is competition-specific rather than generalizable. Future work should focus on constructing a larger dataset to develop a more generalizable model that accounts for differences in jump types and categories. Developing such models is expected to provide a more objective perspective on performance evaluation in judged sports, including figure skating, where scoring inherently involves subjectivity. Furthermore, the findings offer practical implications for coaches and skaters, helping them refine their training strategies based on data-driven insights. For example, rather than simply maximizing jump height, emphasizing smooth flow and sufficient horizontal distance upon landing may contribute to achieving higher GOE scores. These insights can support both performance improvement for skaters and optimization of coaching approaches. Abbreviations GOE: Grade of execution MAE: Mean absolute error RMSE: Root mean squared error VIF: Variance inflation factor FPS: Frames per second Declarations Ethics approval and consent to participate This study did not involve any experimental interventions on participants; therefore, it is not applicable. Consent for publication The data used in this study were provided by Qoncept Inc. with their consent, and permission was obtained for the research use and publication of the analysis results. Competing interests The authors declare that they have no competing interests. Funding This study was supported by a research grant from the Okawa Foundation for Information and Telecommunications. Author Contribution S.H. was responsible for the conceptualization, methodology, data collection, formal analysis, software implementation, validation, investigation, visualization, and writing of the original draft, as well as review and editing. 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1","display":"","copyAsset":false,"role":"figure","size":335627,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe Ice Scope tracking system was utilized as media content (Adapted from (15)).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6233774/v1/66911b56cd4bb7f4b3f7b063.png"},{"id":95655725,"identity":"fd1a5168-b185-428c-9b1a-ecd69440f6d1","added_by":"auto","created_at":"2025-11-11 16:16:48","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":651457,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eData calculation process for vertical height and horizontal distance using the Ice Scope system (Adapted from (15)).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6233774/v1/a4e31abaf2c56d6dc4ed4102.png"},{"id":95655449,"identity":"69de6841-0259-4490-8e61-80e9c85568ae","added_by":"auto","created_at":"2025-11-11 16:16:10","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":243394,"visible":true,"origin":"","legend":"\u003cp\u003eCalculation process of landing speed of the Ice Scope (Adapted from (15)).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6233774/v1/740df82aafdc61d6abf880ca.png"},{"id":95568085,"identity":"2884d62c-13a1-4369-b224-cab8fa0f779d","added_by":"auto","created_at":"2025-11-10 16:24:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":139182,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of True GOE and Elastic Net Predictions.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6233774/v1/0ce89993badae289a2fed095.png"},{"id":95655828,"identity":"83a0f13c-3747-4a57-8c0f-586f4bc28be5","added_by":"auto","created_at":"2025-11-11 16:17:01","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":133213,"visible":true,"origin":"","legend":"\u003cp\u003eEntry and Takeoff Sequence of a Double Axel Jump (Jump Index 55).\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6233774/v1/6fdd70d0e0547625ea51b181.png"},{"id":95655589,"identity":"73b6ed05-3835-4fa1-b472-2fd6f10b95f6","added_by":"auto","created_at":"2025-11-11 16:16:32","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":154213,"visible":true,"origin":"","legend":"\u003cp\u003eEntry and Takeoff Sequence of a Double Axel Jump (Jump Index 34).\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6233774/v1/3864b5f479cff25878bac823.png"},{"id":95798408,"identity":"37baf0fd-3c0e-4490-b448-24d254e54f49","added_by":"auto","created_at":"2025-11-13 08:16:44","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2580676,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6233774/v1/a2fb60a4-044c-4b15-8fb0-53c7853527ea.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Can Machine Learning Robustly Predict Grade of Execution in Figure Skating Jumps from Kinematic Features Across Competitions—A Case Study of Ladies' Double Axel at the World Championships","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eIn the current figure skating scoring system, the technical score is determined by summing the scores of the executed technical elements, including jumps, spins, and steps. The score for each element is the sum of the base value, which represents the difficulty, and the grade of execution (GOE), which reflects the execution quality. Previously, Technical Merit was scored on a scale of 0.0\u0026ndash;6.0 in 0.1-point increments for the entire performance. However, to ensure greater transparency in judgment, the system was changed to the current International Judging System (IJS), where each technical element is scored individually and summed to determine the final technical score. In the IJS, a jump's score is determined by its base value\u0026mdash;predefined based on the jump type and rotation count\u0026mdash;and adjusted by GOE-based bonuses or deductions reflecting execution quality.\u003c/p\u003e\u003cp\u003eIn recent years, more skaters have attempted high-difficulty triple and quadruple jumps in European and World Championships (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e). However, to win competitions, simply landing difficult jumps without falling is not sufficient; skaters must also perform jumps that judges recognize as high quality. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the positive, and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e the negative, criteria for jump GOE. Judges assess each jump in real time, assigning a score on an 11-point scale from \u0026minus;\u0026thinsp;5 to +\u0026thinsp;5. The scoring guidelines for positive GOE are based on the number of bullets (evaluation items officially listed in the ISU judging guidelines) fulfilled: +1 for one bullet, +\u0026thinsp;2 for two, +\u0026thinsp;3 for three, +\u0026thinsp;4 for four, and +\u0026thinsp;5 for five or more bullets. For GOE scores of +\u0026thinsp;4 and +\u0026thinsp;5, the first three bullets highlighted in bold in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e must be included. GOE is a complex evaluation criterion determined by multiple factors. Compared with the negative aspects shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the positive aspects in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e leave greater room for interpretation, as they include more qualitative and subjective elements. The evaluation criteria encompass not only kinematic characteristics of jumps, such as 'very good height and very good length' or 'good take-off and landing,' but also aspects related to creativity and musical expression, such as 'unexpected or creative entry' and 'element matches the music,' making the evaluation system highly complex. Additionally, even among criteria related to kinematic characteristics, the term \"good\" is used, leaving room for subjective judgment by the judge. As skating techniques continue to advance, current figure skaters refine even successfully landed jumps to ensure they are judged as high in quality. However, because the criteria for GOE remain ambiguous and clear coaching indicators are lacking, skaters may feel compelled to pursue excessive refinement of jumps that are already successful. This tendency appears to be related to the higher prevalence of overuse injuries reported in previous studies (\u003cspan additionalcitationids=\"CR3 CR4\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e), as the pursuit of aesthetic perfection is likely to increase physical strain.\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\u003e\u003cb\u003eGuidelines for the Positive Aspects of Grade of Execution (GOE)\u003c/b\u003e (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e)\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"1\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1. very good height and very good length (of all jumps in a combo or sequence)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2. \u003cb\u003egood take-off and landing\u003c/b\u003e\u003c/p\u003e\u003cp\u003e3. \u003cb\u003eeffortless throughout (including rhythm in Jump combination)\u003c/b\u003e\u003c/p\u003e\u003cp\u003e4. steps before the jump, unexpected or creative entry\u003c/p\u003e\u003cp\u003e5. very good body position from take-off to landing\u003c/p\u003e\u003cp\u003e6. element matches the music\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\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\u003e\u003cb\u003eGuidelines for Establishing GOE for Errors (Negative Aspects)\u003c/b\u003e (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e)\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=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003eReduction for errors (Jump Elements)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eJump element not according to requirements, final GOE must be\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDowngraded (sign \u0026lt;\u0026lt;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-3 to -4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFall\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUnder-rotated (sign \u0026lt;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-2 to -3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLanding on two feet in a jump\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-3 to -4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLanded on the quarter (sign q)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStepping out of landing in a jump\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-3 to -4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLess than quarter missing (no sign)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTwo three-turns in between (jump combo/sequence)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-2 to -3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eEuler executed as step over\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-1 to -2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eChange of edge in between jump combo\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-1 to -2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePoor speed, height, distance, or air position\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-1 to -3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWrong edge take-off Flip/Lutz (sign \u0026ldquo;e\u0026rdquo;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-2 to -4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTouch down with both hands in a jump\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-2 to -3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUnclear edge take-off Flip/Lutz (sign \u0026ldquo;!\u0026rdquo;)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-1 to -2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTouch down with one hand or free foot (including in between jumps)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-1 to -2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUnclear edge take-off Flip/Lutz (no sign)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLoss of flow/direction/rhythm between jumps (combo/seq.)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-1 to -3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePoor take-off\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-1 to -3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eWeak landing (bad position/wrong edge/scratching etc.)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-1 to -3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLong preparation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-1 to -3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eSince the 2018\u0026ndash;2019 season, a broadcast-oriented tracking system called \u0026ldquo;Ice Scope\u0026rdquo; has been utilized in figure skating competitions (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The system calculates jump height, horizontal distance, and landing speed. These kinematics metrics are provided for media presentation only and are not used in the official judging process. By integrating such biomechanical data with scoring outcomes, it becomes possible to examine whether quantitative features can explain or predict subjective evaluations such as GOE. Therefore, this study aimed to determine whether the GOE assigned by judges to jumps can be robustly predicted using kinematic features obtained from the Ice Scope tracking system and to identify the specific kinematic characteristics associated with higher-quality execution.\u003c/p\u003e\u003cp\u003eThe key contributions of this study are as follows:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eThree interpretable kinematic features explain a substantial portion of GOE variance across competitions, providing a basis for objectifying subjective evaluations.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eDespite GOE criteria emphasizing \u0026ldquo;height and length,\u0026rdquo; horizontal and landing distances are more critical than vertical height, offering a new perspective on jump quality.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eRatio-based features previously reported to be related to GOE did not show a consistent relationship in this study, suggesting that their importance may be competition-specific.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"2 Related work","content":"\u003cp\u003eRegarding the kinematic characteristics of figure skating jumps, previous research has primarily focused on increasing difficulty and examining how skaters can successfully land jumps with a higher number of rotations. Among the six types of jumps, the Axel jump has been the most extensively studied (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e). The Axel jump is the only jump that takes off in a forward direction. Additionally, skaters are required to perform an Axel jump in both the short program and free skating. According to the principles of mechanics, maximizing rotations in the air requires both sufficient jump height (vertical velocity) and a high rotational speed (angular velocity). Multiple biomechanical studies have reported that skaters maintain the same jump height, even when performing jumps with more rotations and skaters achieve more difficult jumps by increasing their rotational speed (\u003cspan additionalcitationids=\"CR9 CR10\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e). Some studies have proposed the use of weighted gloves to further increase rotational speed. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e). However, recent studies have reported that the only skater in the world to have successfully landed a quadruple Axel achieved a significantly greater maximum jump height compared with skaters performing triple Axel jumps at the World Championships. This suggests that skaters aim to increase their jump height to master new jumps (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e). This finding is consistent with case studies conducted when only a few skaters were capable of performing a triple Axel (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e), highlighting the ongoing debate on the relationship between jump height and the achievement of high-difficulty jumps.\u003c/p\u003e\u003cp\u003eWhile the debate on jump height and difficulty continues, an equally important aspect of competitive success is the quality of execution. From the perspective of GOE, an analysis based on kinematic features obtained from a tracking system named IceScope\u0026mdash;the Japanese media-oriented tracking system developed by Qoncept Inc. and used in selected competitions (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e)\u0026mdash;was performed on double Axel jumps in the women's short program at the 2019 World Championship. The results showed that greater horizontal distance and landing distance compared with vertical height, and greater horizontal distance compared with landing distance, contributed to higher GOE. However, since this study was limited to the short program of a single competition, it remains unclear whether these trends are consistent across different competitive contexts (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eBuilding on such efforts to link kinematics with subjective evaluation, research in the field of computer vision has explored figure skating as a subject for score prediction within the broader task of action quality assessment (AQA), which involves predicting a score from a video sequence of actions (\u003cspan additionalcitationids=\"CR18 CR19 CR20\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e). Most studies use broadcast videos as inputs and predict technical and program component scores using RGB-based image features or pose estimation-based features as inputs to deep learning models (\u003cspan additionalcitationids=\"CR23 CR24 CR25 CR26 CR27\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e). Among these models, deep learning approaches are commonly employed to automatically extract features from consecutive video frames. By learning hierarchical patterns related to body posture, motion dynamics, and visual appearance, deep learning models can map these features to performance scores assigned by judges. The evaluation of technical scores in figure skating has shifted from an overall performance-based assessment to the sum of individual technical elements. Therefore, using the entire performance as input may be suitable for predicting program component scores; however, its applicability to technical scores remains limited. Predicting an individual jump score could provide valuable feedback to skaters and coaches.\u003c/p\u003e\u003cp\u003eIn AQA-related research focusing on the prediction of GOE, deep learning models such as convolutional neural networks (CNNs) have been used (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e). CNNs automatically extract spatial patterns from RGB-based video frames by convolving filters across images, enabling the model to learn visual representations related to performance quality. However, despite their predictive capability, their interpretability in identifying key contributing factors remains limited. Therefore, simpler models are preferred for practical applications, as they enable skaters and coaches to identify which kinematic features should be adjusted during training. Additionally, because this study focused only on the short program of a single competition, it remains unclear whether this trend applies to different competitions.\u003c/p\u003e\u003cp\u003eThis study aimed to determine whether the GOE assigned by judges to double Axel jumps performed by female skaters could be robustly predicted based on kinematic features across different World Championships, thereby extending previous single-competition findings and providing the first examination of the robustness of subjective evaluation of jump execution quality across multiple competitions.\u003c/p\u003e"},{"header":"3 Methods","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Dataset\u003c/h2\u003e\u003cp\u003eThis study examined double Axel jumps in the women's single event at the 2019 and 2023 World Championships, both held in Saitama, Japan. All jumps received a GOE of zero or higher from nine judges. In addition, combination jumps consisting of multiple consecutive jumps were excluded. The target GOE values were obtained from the official competition website (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e). In this study, the target variable GOE was calculated as the trimmed mean of the 11-point scores assigned by nine judges, considering only positive evaluations; therefore, its theoretical range was 0\u0026ndash;5. Furthermore, in the official competition results, this GOE value is converted into the final score by multiplying it by the element\u0026rsquo;s base value and dividing by 10. However, this study did not use this converted score.\u003c/p\u003e\u003cp\u003eThe features comprised three kinematic variables obtained from the Ice Scope system: VH, HD, and skating speed after landing (landing speed). This system was introduced by Fuji Television Network, a Japanese broadcasting company, as a media-oriented tracking system and was not used for competition scoring. The data obtained from this system are displayed in replay footage after a skater\u0026rsquo;s performance, making some of them publicly available. The system utilizes two 4 K cameras (3840 \u0026times; 2160 pixels) recording at 30 fps, positioned to cover the entire 60 m \u0026times; 30 m skating rink. The real-world scale of each pixel was calculated using the rink layout data. Based on reference materials (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), each feature was measured using the two-dimensional Direct Linear Transformation method. In this study, the landing speed was recalculated as the landing distance (LD) to improve the interpretability (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eVH (m): The maximum vertical height measured from the frame where the toe-pick leaves the ice at takeoff to the frame where it contacts the ice upon landing. This parameter was calculated based on the position of the skater\u0026rsquo;s toe-pick.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eHD (m): The horizontal distance measured from the frame where the toe-pick leaves the ice at takeoff to the frame where it contacts the ice upon landing. This parameter was calculated based on the position of the skater\u0026rsquo;s toe-pick.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eLD (m/s): The skating distance over five frames starting from the frame where the heel edge fully contacts the ice upon landing. As the system operates at 30 fps, each frame corresponds to approximately 0.033 s.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs this system was designed for real-time use in broadcast footage as a broadcast-oriented tracking tool, it does not achieve the precision of motion capture systems used in controlled laboratory environments. According to the development company, measurement errors of approximately 3 cm have been reported, depending on the camera placement (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e). The system operators, employees of Qoncept Inc., visually determined all take-off and landing frames.\u003c/p\u003e\u003cp\u003eIn addition to the original three kinematic features obtained from Ice Scope, this study performed feature engineering by incorporating derived features based on previous studies (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e). The derived features included the following ratios: (HD\u0026thinsp;+\u0026thinsp;LD) / VH, LD/HD, and HD/VH. The dataset comprised 66 jumps (2019 WC: 40 jumps by 31 skaters; 2023 WC: 26 jumps by 19 skaters). Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e summarizes the descriptive statistics of the dataset.\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\u003eSummary Statistics of the Dataset for Double Axel Jumps\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=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariables\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRange\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAge\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e19.28\u0026thinsp;\u0026plusmn;\u0026thinsp;2.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e16\u0026ndash;25\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVertical Height, VH [m]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.40\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.31\u0026ndash;0.51\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHorizontal Distance, HD [m]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e2.33\u0026thinsp;\u0026plusmn;\u0026thinsp;0.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.16\u0026ndash;3.74\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLanding Distance, LD [m]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.61\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.27\u0026ndash;0.97\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(HD\u0026thinsp;+\u0026thinsp;LD) / VH\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e7.41\u0026thinsp;\u0026plusmn;\u0026thinsp;1.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4.03\u0026ndash;11.56\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLD / HD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.27\u0026thinsp;\u0026plusmn;\u0026thinsp;0.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.14\u0026ndash;0.44\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHD / VH\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e5.85\u0026thinsp;\u0026plusmn;\u0026thinsp;1.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.97\u0026ndash;8.89\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGOE\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e2.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.14\u0026ndash;4.43\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\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the variance inflation factor (VIF) results used to evaluate multicollinearity among the kinematic features. The VIF results indicate a high degree of correlation between variables.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eEvaluation of Multicollinearity Among Kinematic Features\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\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\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKinematic Features\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eVariance Inflation Factor\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVertical Height, VH [m]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e535\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHorizontal Distance, HD [m]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4076\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLanding Distance, LD [m]\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2867\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(HD\u0026thinsp;+\u0026thinsp;LD) / VH\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e47050\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLD / HD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e550\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHD / VH\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e46199\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=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Machine Learning model\u003c/h2\u003e\u003cp\u003eTo address the high correlation among features and to identify the variables that influence GOE from similar features, an Elastic Net model was employed. Owing to the small sample size, leave-one-out cross-validation was used for parameter tuning and performance evaluation. Tuning was performed using a grid search within the following search ranges: the regularization parameter (λ) values logarithmically spaced across 20 points from 10⁻\u0026sup2; to 10\u0026sup2;, and the L1 ratio values were divided into nine intervals from 0.1 to 0.9. The accuracy of the model was compared with that of a standard multiple regression model to assess the effectiveness of regularization. The adjusted R\u0026sup2;, MAE, and root mean squared error (RMSE) were used as evaluation metrics. Adjusted R\u0026sup2; represents the proportion of variance explained by the model, and MAE indicates the average prediction error. It is less sensitive to outliers, and RMSE penalizes larger errors more heavily, reflecting the overall predictive accuracy of the model. Together, these metrics provide a comprehensive assessment of the model\u0026rsquo;s performance.\u003c/p\u003e\u003cp\u003eAll analyses were performed using scikit-learn (version 1.6.1; Python Software Foundation, Delaware, USA) implemented in Python (version 3.12.11).\u003c/p\u003e\u003c/div\u003e"},{"header":"4 Results","content":"\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e lists the accuracies of the models. The Elastic Net outperformed multiple regression across all evaluation metrics.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults of Model Accuracy Comparison\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\u003cp\u003eModels\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAdjusted R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMAE\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRMSE\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eElastic Net\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e0.429\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e0.528\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e0.666\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMultiple Regression\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.342\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.568\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.715\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\u003eTable\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e lists the regression coefficients for the Elastic Net model. The coefficients were \u0026minus;\u0026thinsp;0.068, 0.549, and 0.145 for VH, HD, and LD, respectively. All ratio-based derived features had coefficients of 0.00, indicating that they were excluded through variable selection.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eRegression Coefficients of Each Feature for GOE in the Elastic Net\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\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\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFeatures\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCoefficient\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVertical Height(VH)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-0.068\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHorizontal Distance(HD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.549\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLanding Distance (LD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.145\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e(HD\u0026thinsp;+\u0026thinsp;LD) / VH\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLD / HD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHD / VH\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.000\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\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows a line graph illustrating the error between the actual and predicted GOE for each sample. The blue and orange lines represent the actual and predicted GOE values, respectively. The overall mean error was 0.528\u0026thinsp;\u0026plusmn;\u0026thinsp;0.405. The largest error was observed at Jump Index 55, with a value of 1.689, where the actual GOE was 3.429 and the predicted value was 1.740. The smallest error occurred at Jump Index 34, with a value of 0.005, where the actual GOE was 1.143 and the predicted value was 1.148.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThis figure visualizes the predictive accuracy of the model across all samples, highlighting the jumps with the largest and smallest errors\u003c/p\u003e"},{"header":"5 Discussion","content":"\u003cp\u003eAs expected, the dataset used in this study exhibited high correlations among the variables, with correspondingly high VIF values (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Additionally, because the Elastic Net outperformed multiple regression across all evaluation metrics, including the Adjusted R\u0026sup2;, MAE, and RMSE (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), it can be considered that the Elastic Net effectively performed appropriate variable selection through regularization, resulting in a simpler and more interpretable model.\u003c/p\u003e\u003cp\u003eAs summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, GOE is a complex evaluation metric based on six subjective criteria.\u003c/p\u003e\u003cp\u003eHowever, the Adjusted R\u0026sup2; value suggests that only three simple kinematic features could explain approximately 43% of the variance. A previous study that focused solely on the short program at the 2019 World Championships reported an adjusted R\u0026sup2; of 0.504 (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e). Because this dataset included data from both the short program and free skating events at the 2019 and 2023 World Championships, the adjusted R\u0026sup2; value was lower than that of the previous study. Nevertheless, given the complexity of the GOE evaluation criteria, the model still captured a substantial portion of the variance. In terms of prediction, despite incorporating data from different programs and competition years, the MAE remained 0.528\u0026thinsp;\u0026plusmn;\u0026thinsp;0.405, indicating that the model provides a useful estimate of GOE. This level of accuracy can help skaters develop a more objective understanding of their performances.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e lists the regression coefficients for GOE using the Elastic Net. Ratio-based derived features that were previously relevant (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e) were excluded through regularization, suggesting that their influence on GOE was specific to the 2019 Women\u0026rsquo;s Short Program and was not robust across competitions. Examining the regression coefficients, HD (0.549) and LD (0.145) positively influenced GOE, whereas VH (-0.068) had a negative impact. Although the GOE evaluation criteria mention \"very good height and very good length,\" the results suggest that jump height has little effect, whereas a greater jump distance is associated with a higher GOE. One possible explanation for the negative coefficient of vertical height is that jumps emphasizing vertical height may lose horizontal momentum, resulting in reduced flow upon landing, which is also an important criterion for GOE.\u003c/p\u003e\u003cp\u003eThis finding aligns with a previous study on the 2019 Women\u0026rsquo;s Short Program, which reported that skaters with a higher GOE achieved significantly greater jump distances than those with lower GOE. Thus, for double Axel jumps performed by female skaters, HD has a stronger influence on GOE than VH, and this trend appears consistent across programs and competitions. Although LD has a smaller effect than HD, it still contributes positively to GOE. Therefore, to achieve a higher GOE in competitions, female skaters should aim for jumps with greater distance and smoother flow upon landing.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the actual GOE and Elastic Net predictions for each jump. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents a sequence of images for Jump Index 55, which had the largest prediction error. The kinematics-based prediction used in this study underestimated the actual GOE by 3.429, yielding a value of 1.740. This discrepancy may have occurred because the skater\u0026rsquo;s jump entry, which was not captured by the kinematic features used in this study, played a crucial role in the performance. The skater approached the jump by skating backward in a spiral position (Images 1\u0026ndash;5) and then executed a counter turn\u0026mdash;a difficult transition from a left backward outside edge to a forward outside edge (Images 6\u0026ndash;9)\u0026mdash;directly into the Axel takeoff. Executing such a complex movement into the jump in synchronization with the music corresponds to the GOE evaluation criteria for \u0026ldquo;steps before the jump, unexpected or creative entry\u0026rdquo; and \u0026ldquo;element matches the music.\u0026rdquo; However, as these aspects were not captured by the kinematic features, the model likely underestimation the GOE. This example highlights the limitation of the model: relying solely on three kinematic features cannot capture the subjective aspects of GOE, such as creativity and musicality.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThis figure illustrates a jump with a large prediction error, demonstrating how movements not captured by kinematic features can affect prediction accuracy.\u003c/p\u003e\u003cp\u003eConversely, Jump Index 34 (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), which had the highest prediction accuracy (actual: 1.143, predicted: 1.148), showed no distinctive movements before takeoff. The skater executed the takeoff following the standard preparation for an Axel jump\u0026mdash;transitioning from backward outside edge skating through turns or edge changes, then stepping forward into the takeoff from a forward outside edge. Jumps performed with such standard preparations and postures tend to be accurately predicted based on kinematic features. In addition, while most skaters rotate counterclockwise relative to their body\u0026rsquo;s longitudinal axis, this skater rotates clockwise. In the dataset used for this study, only six out of 66 jumps were clockwise rotations. Because relatively few skaters perform clockwise jumps, evaluating the quality of these jumps may be challenging for judges without extensive experience. Based on this case, the model appears to generalize to jumps with different rotation directions; however, further research with a larger dataset of clockwise jumps is needed to confirm this robustness. Such findings could provide valuable feedback to coaches, skaters, and less experienced judges.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThis figure illustrates a jump accurately predicted by the model, showing that jumps with standard preparatory movements can be reliably captured through kinematic features.\u003c/p\u003e\u003cp\u003eThis study has several limitations. The first concerns the accuracy of data acquisition. The system used in this study operates at 30 fps, which is less precise than gold-standard motion capture systems or high-speed cameras commonly used by sports scientists for detailed analysis of rapid movements. Although obtaining data during competitions is challenging, the use of higher-precision equipment is preferable.\u003c/p\u003e\u003cp\u003eAnother limitation is that this study focused exclusively on the double Axel jumps performed by senior female skaters, making it unclear whether the findings are robust across different categories or jump types. The tracking system used in this study is limited to competitions for which Fuji Television Network, Inc. holds broadcasting rights. To better evaluate its robustness across different competitive settings, the system should be implemented in a wider range of categories and events.\u003c/p\u003e\u003cp\u003eAn additional concern is related to multicollinearity. In the context of machine learning, high multicollinearity often arises naturally when derived features are included. Although the Elastic Net mitigates this issue, the extremely high VIF values observed here indicate that caution is required when interpreting the stability of regression coefficients, even though prediction performance remains robust.\u003c/p\u003e\u003cp\u003eFurthermore, the subjectivity inherent in GOE scoring should be acknowledged. Although the trimmed mean of nine judges\u0026rsquo; scores helps mitigate the influence of outliers, inter-judge variability may still affect the GOE. Recent research comparing competitions before and after the expansion of the GOE range from \u0026plusmn;\u0026thinsp;3 to \u0026plusmn;\u0026thinsp;5 (2018 vs. 2022) reported decreased scoring consistency in some men\u0026rsquo;s, women\u0026rsquo;s, and pairs segments (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e). This finding suggests that even within the standardized IJS framework, differences in individual judging tendencies can influence the evaluation outcome, which may, in turn, affect model predictions based on such scores.\u003c/p\u003e\u003cp\u003eDespite these limitations, this study is the first to examine the robustness of the relationship between the kinematic characteristics of figure skating jumps and GOE, which is subjectively evaluated by judges, using real-world data from two different competitions. As larger datasets become available, more robust prediction models can be developed to provide deeper insights into the subjectivity of judging in evaluated sports.\u003c/p\u003e"},{"header":"6 Conclusion","content":"\u003cp\u003eThis study examined whether the GOE assigned to double Axel jumps at two editions of the World Championships could be robustly predicted using kinematic features and identified key contributing factors. The results demonstrated that three simple kinematic features explained 42.9% of the GOE variance, with an MAE of 0.528, demonstrating sufficient accuracy for reference. Although the GOE criteria mention \"very good height and length,\" the VH had little impact, whereas the HD and LD played a greater role, suggesting that jumps with greater flow received higher GOE scores.\u003c/p\u003e\u003cp\u003eRatio-based derived features, previously determined to be relevant, exhibited no significant relationship with GOE, indicating that their influence is competition-specific rather than generalizable. Future work should focus on constructing a larger dataset to develop a more generalizable model that accounts for differences in jump types and categories. Developing such models is expected to provide a more objective perspective on performance evaluation in judged sports, including figure skating, where scoring inherently involves subjectivity.\u003c/p\u003e\u003cp\u003eFurthermore, the findings offer practical implications for coaches and skaters, helping them refine their training strategies based on data-driven insights. For example, rather than simply maximizing jump height, emphasizing smooth flow and sufficient horizontal distance upon landing may contribute to achieving higher GOE scores. These insights can support both performance improvement for skaters and optimization of coaching approaches.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003eGOE: Grade of execution\u003c/p\u003e\n\u003cp\u003eMAE: Mean absolute error\u003c/p\u003e\n\u003cp\u003eRMSE: Root mean squared error\u003c/p\u003e\n\u003cp\u003eVIF: Variance inflation factor\u003c/p\u003e\n\u003cp\u003eFPS: Frames per second\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study did not involve any experimental interventions on participants; therefore, it is not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data used in this study were provided by Qoncept Inc. with their consent, and permission was obtained for the research use and publication of the analysis results.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was supported by a research grant from the Okawa Foundation for Information and Telecommunications.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eS.H. was responsible for the conceptualization, methodology, data collection, formal analysis, software implementation, validation, investigation, visualization, and writing of the original draft, as well as review and editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eQoncept Inc. is sincerely acknowledged for providing the kinematic data from the tracking system.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data are not available.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eRauer T, Pape H-C, Knobe M, Pohlemann T, Ganse B. 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Available from: http://dx.doi.org/10.1007/978-3-030-93954-0_28-1\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"journal-of-big-data","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bigd","sideBox":"Learn more about [Journal of Big Data](http://journalofbigdata.springeropen.com)","snPcode":"40537","submissionUrl":"https://submission.nature.com/new-submission/40537/3","title":"Journal of Big Data","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Judged sports, Performance evaluation, Sports biomechanics, Sports analytics, Kinematic analysis, Scoring prediction, Application of machine learning in sports, Elastic Net regression","lastPublishedDoi":"10.21203/rs.3.rs-6233774/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6233774/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn the current figure skating scoring system, a jump's score is determined by the sum of its base value, which represents difficulty, and the grade of execution (GOE), which reflects execution quality. The criteria for evaluating the GOE allow for subjective judgment by the judges. Consequently, skaters may train without concrete guidelines for maximizing their scores. If execution quality could be robustly predicted based on kinematic characteristics, it could contribute to improving the performance of skaters.\u003c/p\u003e\u003cp\u003eThis study examined whether the GOE assigned by judges to double Axel jumps performed by female skaters at the 2019 and 2023 World Championships could be robustly predicted based on kinematic features and explored the features that contribute to these predictions. The results demonstrated that three simple kinematic features\u0026mdash;vertical height (VH), horizontal distance (HD), and landing distance\u0026mdash;explained 42.9% of the variance in GOE, even in a dataset that included different competitions. The mean absolute error of the prediction was 0.528. Although the GOE evaluation criteria mentioned \"very good height and length,\" the VH had little impact in practice. Instead, jumps with a greater HD and good flow on landing resulted in higher GOE. However, in this study, ratio-based derived features, previously shown to be relevant, were not significantly related to GOE, suggesting that their influence was competition-specific rather than consistent across different competitions. This study contributes to an objective understanding of performance evaluation in judged sports from a kinematic perspective, in which scoring is inherently subjective and based on complex criteria.\u003c/p\u003e","manuscriptTitle":"Can Machine Learning Robustly Predict Grade of Execution in Figure Skating Jumps from Kinematic Features Across Competitions—A Case Study of Ladies' Double Axel at the World Championships","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-10 16:23:56","doi":"10.21203/rs.3.rs-6233774/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-19T15:30:39+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-19T15:23:58+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-17T23:22:07+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-12T13:19:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"34279026083115973621795970885565597769","date":"2025-11-14T06:34:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"309200258776771804937715528114423705719","date":"2025-11-14T02:29:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"5745834931566810533493831064710515013","date":"2025-11-10T00:57:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"269429871383653986790652638819298581754","date":"2025-11-09T23:38:33+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-09T00:12:13+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-13T04:57:24+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Big Data","date":"2025-10-12T10:50:12+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-big-data","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bigd","sideBox":"Learn more about [Journal of Big Data](http://journalofbigdata.springeropen.com)","snPcode":"40537","submissionUrl":"https://submission.nature.com/new-submission/40537/3","title":"Journal of Big Data","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e51c5f77-af7d-49d0-a04a-af42c7226f65","owner":[],"postedDate":"November 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-02T22:53:42+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-10 16:23:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6233774","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6233774","identity":"rs-6233774","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}