Using neural network interpretability to understand outcomes in women’s 3 x 3 basketball

Using neural network interpretability to understand outcomes in women’s 3 x 3 basketball | 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 Using neural network interpretability to understand outcomes in women’s 3 x 3 basketball Li Dong, Mingyi Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4547091/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Despite the inclusion of 3x3 basketball in the Olympic Games, research on this topic remains sparse, especially concerning women's 3x3 basketball. This study aimed to understand game outcomes in the FIBA 3x3 women's professional circuit. Data was sourced from the official FIBA 3x3 website, encompassing 15 indicators and 2 contextual variables from 987 matches across four seasons. All games were classified into balanced and unbalanced categories. The Multilayer Perceptron neural network outperformed discriminant analysis in both balanced and unbalanced games, achieving classification accuracy exceeding 85%. To interpret the neural network's predictions, we calculated SHAP values, revealing that one-point field goal made and defensive rebounds were the key performance indicators. In balanced games, free-throw made and ball possession contributed significantly to the classification of winning and losing teams, while team fouls and turnovers were instrumental in distinguishing outcomes in unbalanced games. This study provides valuable insights into game outcomes in women's 3x3 basketball. basketball match outcome sports prediction women 3x3 basketball SHAP value Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction In 2007, FIBA formally adopted 3x3 basketball as an official discipline by establishing a standardised rule set and launching the 3x3 World Tour and World Championships. Since then, the sport has rapidly gained global prominence, marked by its inclusion in the Tokyo 2020 Olympics. Distinct from traditional 5x5 basketball, 3x3 games are played on a half-court with a single basket, reflecting its streetball roots where court size was often limited. Teams consist of three players and one substitute, facilitating a fast-paced game. A coin toss starts the game, with the winner choosing to start with possession. Matches last 10 minutes, and the first team to reach 21 points within this time or have the higher score wins. Several researchers assert that 3x3 basketball should be viewed as an independent sport despite its origins as a variation of 5x5 basketball. The smaller court size in 3x3 demands greater physical exertion, aligning with findings in small-sided soccer games ( 1 ). A recent study that monitored the load parameters of 3x3 players identifies 3x3 basketball as a high-intensity sport characterised by faster speed and transitions, making it more exhausting than traditional basketball ( 2 ). Additional research emphasises the importance of agility-based training for 3x3 players and highlights different movement patterns such as the high work-to-rest ratio ( 3 – 5 ). Further focusing on physical demands by gender, the importance of jumping ability for male players and ball-handling sprints for female players was emphasized ( 6 , 7 ). The application of sports performance analysis (SPA) in 5x5 basketball has become standard practice, providing coaches with crucial insights into player performance, game strategies, and other competitive aspects ( 8 ). Research in this area mainly utilized notational analysis and biomechanics, emphasizing statistical assessment, talent identification, match analysis, and injury risk ( 9 ). Notational analysis focuses on identifying key events in the game and draws conclusions based on quantitative and qualitative feedback ( 10 ). This approach enables analysts and coaches to gain deeper insights into tactical techniques and movement patterns( 11 ), which helps coaches monitor players' development. Apparently, professional 5x5 basketball clubs recognize the benefits of notational analysis ( 12 ), but similar research was largely overlooked in 3x3 basketball. Some studies analysed 3x3 basketball through notational analysis, identifying performance indicators that significantly affect game outcomes. These include two-point scoring efficiency, quick scoring after a successful defence, the percentage of two- and one-point shots, turnovers, rebounds, and fouls ( 6 , 13 – 16 ). However, previous research primarily focused on men's games, with women's games being underreported. Artificial neural networks (ANNs) represent innovative tools for analyzing sports performance and hold significant potential in the sports context ( 17 ). In notational analysis, ANNs were primarily used for predictive tasks, including talent identification, performance forecasting, match outcome prediction, and more. Various adaptations of ANNs have also been widely employed to predict 5x5 basketball match outcomes with high accuracy ( 18 ). Previous study accurately predicted basketball match outcomes using a feed-forward neural network with an accuracy exceeding 80% ( 19 ). They identified several key performance indicators, including two-point and three-point attempts, steals, turnovers, offensive rebounds, blocks, and assists. Similarly, in a study comparing various machine learning models for predicting college basketball game outcomes, the multilayer perceptron neural network outperformed the others, with each model validated using separate training and test sets ( 20 ). Despite their predictive power, artificial neural networks are often considered as a 'black box,' as their internal workings can be challenging to interpret. This opacity can present difficulties for coaching staff when understanding their output. Recently, SHapley Additive exPlanations (SHAP) provided a method to explain the classifications of neural networks. By aggregating Shapley values, SHAP offers global explanations for a model's predictions, enhancing the transparency and interpretability of neural networks' decision-making processes ( 21 ). However, this approach failed to be applied in 3x3 basketball performance analysis so far. Given the anthropometric differences between men and women, studying professional women's 3x3 basketball games is essential. To gain deeper insights into game outcomes, we utilized artificial neural networks for their robust ability to handle non-linear datasets. We also applied discriminant analysis, which is widely used in basketball performance analysis, to compare the analytical ability between models. In this pathway, we can extract valuable insights from historical game experiences and offer different methodological perspectives for future research on 3x3 basketball performance analysis. 2. Methods 2.1 Data sample This study utilized a retrospective analysis, collecting data from the women's professional 3x3 basketball circuit between 2019 and 2023 (excluding 2020 due to lockdowns). The dataset comprised 987 matches, sourced from the official FIBA website ( https://womens-series.fiba3x3.com/ ). It included 15 performance indicators: one-point field goals (1PT_made and 1PT_missed), two-point field goals (2PT_made and 2PT_missed), free throws (FT_made and FT_missed), offensive rebounds (OREB), defensive rebounds (DREB), key assists (KAS), drives (DRV), blocked shots (BS), turnovers (TO), team fouls (TF), team fouls against (TFA), ball possession (POS), and offensive quality (OQ). To minimize the potential effects of game pace, all performance indicators were normalized by ball possession and multiplied by 100 ( 22 ). Situational variables, like match type and opponent quality, were also considered. Specifically, Team quality was reflected by the difference in points between teams at the end of the season (Team A's points - Team B's points). We used K-means algorithm to categorize matches into balanced (7 points or fewer) and unbalanced (8 points or more). The data for each game was recorded in Excel. 2.2 Data analysis As the initial exploration step, we performed descriptive statistics, such as calculating the mean and standard deviation, to compare winning and losing teams in both balanced and unbalanced games. This initial exploration helps in understanding the basic trends and differences between groups. Next, to comprehend the pattern and significant difference between winning and losing teams, the independent samples t-tests were conducted. The significance was set at p ≤ 0.05. A discriminant analysis was conducted to identify the variables that most effectively distinguish between the groups ( 23 ). Discriminant analysis has been widely used in basketball performance analysis and is considered robust ( 24 ). To interpret the results, we focused on structure coefficients above ∣0.30∣ ( 25 ). These coefficients indicate which variables have the most substantial impact on discriminating between the groups. We validated the discriminant models using the leave-one-out cross-validation method, which involves dividing the data into subsets for training and testing. This approach assesses the models' ability to classify new data effectively, providing a realistic measure of model performance. The outcomes of basketball matches are influenced by many factors that exhibit non-linear relationships. Neural Networks are suitable for capturing such complex patterns, so we trained a basic Multilayer Perceptron (MLP) neural network using gradient-based optimization algorithms. Our model consisted of one hidden layer with eleven neurons, the constant learning rate of 0.001 and momentum set at 0.969. The MLP model aims to classify game outcomes based on input features, learning the relationships from historical data. To assess the model's performance and ensure its generalizability, we employed k-fold cross-validation. This method allowed us to evaluate the model's predictive power across multiple data subsets, providing a more robust measure of its accuracy. Additionally, we used the AUC metric to quantify the model's ability to differentiate between the positive and negative classes over all possible classification thresholds. To make the neural network's predictions more interpretable, we utilized SHAP (SHapley Additive exPlanations) values, which reveal how each feature impacts the model's predictions. A SHAP summary plot offers a comprehensive view of feature contributions across all data points, ranking them by their average impact on the model’s predictions. A dependence plot helps us understand the relationship between a specific feature and the model's predictions while considering another interacting feature. Given that exact Shapley values are computationally expensive to compute in real-world scenarios, we used the KernelSHAP explainer with 120 weighted k-medians to approximate the Shapley values. All data analysis work was done using Python software (3.7, Wilmington, DE, USA), using the Scikit-Learn machine learning library and SHAP library for the KernelExplainer. This study did not involve human participants and the data was collected from the public resource so ethical approval is not needed. 3. Results Table 1 presents the descriptive analysis and t-test results, providing insight into how winning and losing teams perform in balanced and unbalanced games. In balanced games, where the competition is closely matched, winning teams exhibit differences compared to losing teams across nearly all metrics, except for 1PT_missed. The superiority of the winning teams is evident in scoring metrics such as 1PT_made, 2PT_made, and FT_made, emphasizing the importance of converting scoring opportunities in close matches. Similarly, controlling rebounds, both offensive (ORB) and defensive (DRB), plays a critical role in maintaining possession and limiting opponents' chances. Defensive metrics like turnovers (TO) and total fouls (TF) also highlight the significance of disciplined play, as winning teams minimize mistakes and play with greater defensive discipline. On the other hand, all metrics show significant differences between winning and losing teams in unbalanced games. Winning teams dominate in scoring efficiency, demonstrated by higher 1PT_made and 2PT_made scores. They also exert control over the game's flow through superior rebounding (ORB and DRB) and effective ball distribution, indicated by higher assists (KAS). These teams' superior defensive play is evident through metrics like turnovers (TO) and fouls (TF). Table 1 The mean value and standard deviation of each performance indicator in balanced and unbalanced games Performance indicators Balanced game Unbalanced game Wining Losing Wining Losing 1PT_made a** b** 27.13 ± 7.78 21.81 ± 7.59 31.76 ± 8.51 17.08 ± 7.66 1PT_missed b** 25.43 ± 8.34 25.96 ± 8.67 19.84 ± 8.11 26.89 ± 9.26 2PT_made a* b** 6.51 ± 4.55 6.02 ± 4.22 9.77 ± 6.30 4.07 ± 3.51 2PT_ missed a** b** 18.25 ± 7.74 22.31 ± 8.77 18.51 ± 7.72 24.42 ± 9.77 FT_ made a** b** 7.09 ± 5.35 4.85 ± 4.59 7.37 ± 5.68 2.92 ± 3.21 FT_ missed a** b** 3.20 ± 3.20 2.60 ± 3.24 3.05 ± 3.19 2.39 ± 2.92 BLK a* b** 3.69 ± 3.60 3.20 ± 3.25 4.75 ± 4.25 2.11 ± 2.67 ORB a** b** 15.42 ± 6.68 13.72 ± 5.95 16.77 ± 6.78 12.07 ± 6.48 DRB a** b** 33.96 ± 8.59 30.01 ± 8.29 36.61 ± 8.87 25.05 ± 8.54 TO a** b** 15.07 ± 6.63 18.16 ± 7.54 12.17 ± 5.87 23.17 ± 8.91 TF a** b** 16.28 ± 5.27 18.83 ± 5.66 13.52 ± 5.85 19.45 ± 6.74 TFA a** b** 18.21 ± 5.21 16.72 ± 5.22 17.98 ± 6.03 14.48 ± 6.22 BP a* b** 37.45 ± 4.15 36.35 ± 3.83 35.67 ± 5.13 33.12 ± 5.05 KAS a** b** 9.30 ± 5.58 6.85 ± 4.74 13.17 ± 6.99 4.81 ± 3.91 DRV a** b** 7.55 ± 5.38 6.27 ± 4.96 7.86 ± 5.51 4.70 ± 4.20 Legend: a Significance determined by t-test in balanced games; b Significance determined by t-test in unbalanced games; * p < 0.05; **p < 0.001 The discriminant function derived from our analysis was statistically significant (P < 0.01) and demonstrated a high level of predictive accuracy, correctly classifying 82.4% of the cases in balanced games and 99.6% in unbalanced games. The structural coefficients (SCs) resulting from the discriminant analysis, presented in Tables 2 and 3 , effectively distinguish between the best and worst-performing teams in both balanced and unbalanced games. In balanced games, the key discriminative features included 1PT_made (SC = 0.48), free throws made (FT_made, SC = 0.32), and offensive efficiency (OQ, SC = 0.42). These metrics highlight the importance of scoring efficiency and maintaining offensive control in closely contested matches. Assists (KAS, SC = 0.34) and defensive rebounds (DREB, SC = 0.33) also emerged as significant discriminators, showing that teamwork in offence and controlling defensive rebounds are crucial for winning balanced games. Negative structural coefficients for turnovers (TO, SC = -0.31) and total fouls (TF, SC = -0.33) emphasize the need for reducing mistakes and maintaining disciplined play. In unbalanced games, the discriminant analysis results (Table 3 ) showed that winning teams significantly outperformed losing teams across all game metrics. The discriminant function highlighted 1PT_made (SC = 0.73), 2PT_made (SC = 0.53), and assists (KAS, SC = 0.64) as major contributors to success in these matches, underlining the importance of shooting efficiency and offensive collaboration. Rebounding, both offensive (OREB, SC = 0.36) and defensive (DREB, SC = 0.60), also played a substantial role in differentiating winning and losing teams. In contrast, turnovers (TO, SC = -0.64) and total fouls (TF, SC = -0.46) had strong negative correlations with winning, indicating the importance of disciplined play and ball control. Table 2 The structure coefficients and tests of statistical significance in balanced games Statistic SC 1PT_made 0.48 1PT_missed -0.05 2PT_made 0.08 2PT_missed -0.35 FT_made 0.32 FT_missed 0.14 OQ 0.42 POS 0.20 KAS 0.34 DRV 0.18 BS 0.10 OREB 0.20 DREB 0.33 TO -0.31 TF -0.33 TFA 0.21 Eigenvalue 1.12 Wilks’ lambda 0.47 Canonical correlation 0.73 Chi-squared 78.52 Significance < 0.001 Reclassification 80.54% Table 3 The structure coefficients and tests of statistical significance in unbalanced games Statistic SC 1PT_made 0.73 1PT_missed -0.41 2PT_made 0.53 2PT_missed -0.34 FT_made 0.47 FT_missed 0.12 OQ 0.66 POS 0.26 KAS 0.64 DRV 0.33 BS 0.38 OREB 0.36 DREB 0.60 TO -0.64 TF -0.46 TFA 0.30 Eigenvalue 1.08 Wilks’ lambda 0.46 Canonical correlation 0.73 Chi-squared 99.87 Significance < 0.001 Reclassification 99.52% The Multilayer Perceptron (MLP) neural network outperformed discriminant analysis, achieving 85.38% accuracy and AUC 0.89 in balanced games and 99.8% accuracy and AUC 0.99 in unbalanced games. The model's superior performance demonstrates its ability to discern between winning and losing teams by leveraging complex, non-linear patterns in basketball data. The SHAP analysis (visualized in the attached plots) reveals the relative importance of various features influencing the prediction of basketball game outcomes. In balanced games, positive correlations with winning probabilities include 1PT_made, 2PT_made, FT_made, and defensive rebounds, while negative correlations are observed for 1PT_missed and 2PT_missed. The SHAP value of 1PT_made shows a clear positive correlation, indicating that as the number of 1PT_made increases, the SHAP value predicted by the model increases, thereby positively impacting the prediction. Higher FT_made values, represented by the red color, are typically associated with higher 1PT_made SHAP values. In contrast, there is a clear negative correlation between 1PT_missed and its SHAP value, as higher missed free throw values lead to more negative SHAP values, reducing the team's probability of winning.The dominance of red dots in the upper right corner and blue dots in the lower-left corner suggests that teams with more missed free throws and lower drive values are significantly less likely to win. Conversely, teams with good free throw conversions and high drive values are more likely to win. In unbalanced games, the SHAP value plot shows a positive correlation between 1PT_made, 2PT_made, and winning probabilities, while 1PT_missed and 2PT_missed are negatively correlated. Defensive rebounds (DREB) and offensive rebounds (OREB) also show positive correlations, while turnovers (TO) negatively impact predictions. Other features like FT_made, KAS, and DRV have varying impacts on model predictions. This plot demonstrates a positive correlation between 1PT_made and the model's predictions. As the number of 1-pointers made increases, the SHAP value predicted by the model also increases, positively impacting the prediction. The colour gradient (OQ) adds additional context, showing that teams with higher offensive quality tend to make more 1-pointers. This plot illustrates the positive correlation between 2PT_made and its SHAP value. As the number of 2-pointers made increases, the SHAP value increases, positively impacting the prediction. The colour gradient (1PT_made) shows a positive association between making both 1-pointers and 2-pointers. 4. Discussion To the best of the researcher’s knowledge, no study previously utilized SHAP values to understand game outcomes and performance indicators in 3x3 professional women's basketball. This investigation aimed to enhance comprehension surrounding game outcomes within this young basketball discipline. By analyzing the collected data using discriminant analysis and neural networks, the study achieved over 80% accuracy in classifying both balanced and unbalanced games. In addition, we explored model-agnostic methods to explain classification algorithms. The SHAP method enabled us to gain insights into how basic neural networks classify data, which is crucial for understanding predictive models that often lack clear guidance due to ambiguities in defining and classifying performance indicators ( 26 ). By using SHAP values, we could unpack the inner workings of the models, providing actionable insights into which features most influence game outcomes, thereby helping players, coaches, and analysts make more informed decisions. Previous research on men's 3x3 basketball has highlighted the significance of two-point shots, as they yield twice the points of one-point shots ( 6 , 14 ). However, our analysis reveals a different trend in women's 3x3 basketball, where the accuracy of one-point shots (both made and missed) emerges as a more crucial key performance indicator (KPI). This difference also underscores the importance of studying men's and women's 3x3 basketball separately. The findings from our study align with previous shooting analyses, which found that women tend to attempt more one-point shots than men in 3x3 games but do not have the same shooting efficiency ( 27 ). We consider two factors contributing to this situation. Firstly, the reduced number of players in 3x3 basketball creates more opportunities for drives and cuts to the basket. Additionally, the ball used in 3x3 basketball, while being the same size as the one used in women's 5x5 basketball, has the same weight as the ball used in men's 5x5 games. This difference could explain why female players tend to take more inside shots in 3x3 basketball. In the realm of rebounds, defensive rebounds stand out as one of the key performance indicators, more than offensive rebounds. This pattern aligns with trends observed in 5x5 basketball ( 28 ), emphasizing the importance of securing defensive rebounds. A widely recognized concept in basketball strategy is that teams with more defensive rebounds often find themselves in a better position to win championships ( 29 ). This advantage arises because defensive rebounds effectively end the opponent's offensive possession, denying them the chance to score and granting the defending team a new possession. Securing defensive rebounds not only prevents the opposite team from scoring but also allows the team to transition quickly into offense, potentially catching their opponents off-guard and creating fast-break opportunities. In 3x3 basketball, where the game is even faster-paced than in 5x5, controlling defensive rebounds is crucial for maintaining momentum and keeping the pressure on the opposition. In addition to traditional performance indicators, we found that contextual variables, such as team quality, also significantly impact game outcomes and act as key predictive indicators. We also examined another contextual variable, such as game type, and discovered distinct patterns depending on whether the games were balanced or unbalanced. In balanced games, where the teams are more evenly matched, FT_made and POS emerged as important differentiators in determining the outcome. In unbalanced games, where one team dominates, TF and TO became more critical in distinguishing the outcome. This finding suggests that in games with a clear disparity in team quality, legal fouls behaviours and reducing turnovers are key to maintaining control and achieving decisive victories. These findings underline the importance of considering contextual variables in 3x3 basketball performance analysis. Different game contexts require distinct strategies and KPIs, emphasizing the need for tailored approaches to game analysis to better understand and predict game outcomes. From a technical analysis perspective, we compared different analytical pipelines, including neural networks and discriminant analysis, to achieve higher accuracy. The neural networks, in particular, demonstrated superior performance in complex contexts like balanced games, highlighting their ability to recognize intricate non-linear relationships. Traditionally viewed as a black-box model, neural networks have often been challenging to interpret. However, the use of SHAP values has shed light on the inner workings of these networks, helping us understand how they process complex variables and their relationship with predictive outcomes. Our innovative introduction of SHAP values into the realm of 3x3 basketball emphasizes the importance of understanding the relationships between intricate variables and predictive outcomes. This method has seen extensive application in sports analytics, and by adopting it, we provide actionable insights into how neural networks process and predict game outcomes. This approach offers a new level of transparency, enabling practitioners to translate these insights into practical strategies and better decision-making. This study aims to extract valuable insights into the relationship between performance indicators and game outcomes in 3x3 women's basketball series. While we achieved satisfactory accuracy and identified key performance indicators, the investigation has certain limitations that need to be addressed. Firstly, even though we gathered all available data from the FIBA official website, the sample size still needs to be expanded. The limited sample size can introduce bias into the results, affecting the reliability of the conclusions. Additionally, due to the small sample size, we couldn't include additional contextual variables, such as the competition stage, which could influence performance. Insufficient data can reduce the reliability of analytical results, especially when accounting for multiple contextual variables ( 30 ). 5. Conclusion The current work applied the neural network to reveal the key performance indicators that can significantly influence the game outcome in 3 x 3 women’s basketball series. The SHAP value can help us understand better the ANNs work and it outperforms the traditional discriminant analysis. We identified the one-points made, defensive rebounds and the key assists as the key performance indicators that can discriminate the winning and losing teams. Expanding the dataset and including a broader range of variables would help improve the reliability of future analyses and enable a more comprehensive understanding of the relationship between performance indicators and game outcomes in 3x3 women's basketball. In the future, researchers should expand the dataset and incorporate a broader range of contextual variables to improve the reliability of analyses. Declarations Data availability statement The data that support the findings of this study are available at 10.6084/m9.figshare.25827631. Disclosure of interest The authors declare that there are no conflicts of interest to disclose. Funding No funding was received. Ethics Approval and Consent to Participate are not applicable due to no human participants being involved. Author Contribution L.D wroted the main manuscript text and MY.Z collected the dataset. References Kelly DM, Drust B. 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Mackenzie R, Cushion C. Performance analysis in football: A critical review and implications for future research. J Sports Sci [Internet]. 2013;31(6):639–76. https://doi.org/10.1080/02640414.2012.746720 . Erčulj F, Vidic M, Leskošek B. Shooting efficiency and structure of shooting in 3 × 3 basketball compared to 5v5 basketball. Int J Sports Sci Coach [Internet]. 2020;15(1):91–8. https://doi.org/10.1177/1747954119887722 . Puente C, Coso J, Del, Salinero JJ, Abián-Vicén. J. Basketball performance indicators during the ACB regular season from 2003 to 2013. Int J Perform Anal Sport [Internet]. 2015;15(3):935–48. https://doi.org/10.1080/24748668.2015.11868842 . Oliver D. Basketball on Paper: Rules and Tools for Performance Analysis [Internet]. U of Nebraska Press; 2011. 393 p. https://books.google.de/books?id=uLeHDwAAQBAJ . McGarry Tim O’Donoghue, Peter, Sampaio AJ, de Eira. Routledge handbook of sports performance analysis [Internet]. Routledge; 2013 [cited 2024 May 16]. https://www.routledge.com/Routledge-Handbook-of-Sports-Performance-Analysis/McGarry-ODonoghue-Sampaio/p/book/9781138908208 . Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4547091","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":315812885,"identity":"83508e6a-e77a-4145-b8a6-ad70da8c2428","order_by":0,"name":"Li Dong","email":"","orcid":"","institution":"Yangtze Normal University","correspondingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Dong","suffix":""},{"id":315812890,"identity":"ee58d4b5-b834-4c01-83e4-e306302d4b53","order_by":1,"name":"Mingyi Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzUlEQVRIiWNgGAWjYBACfmb+Dwc+GPyzY2xvIFKLZHuD4cEZFQeSmXsOEKnF4MwB48M8Zw4wts9IINaWGQkJB3jb7jDzzny88QZDjU00QS38EgkHDki2PeOTnJ1WbMFwLC23gbAtiQ0HDNuYmQ1n55hJMDYcJqzF4EYyw4HENmbG/TfPEKvlzDGGAwfOHGZsnMFDpBbJ9h6Ggw0VacmMPUC/JBDjF35mHubPfwxsgFF5eOONDzU2hLWgOFIigRTlEC2k6hgFo2AUjIKRAQD/00fhu/+zvQAAAABJRU5ErkJggg==","orcid":"","institution":"Guangxi Normal University","correspondingAuthor":true,"prefix":"","firstName":"Mingyi","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2024-06-07 15:44:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4547091/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4547091/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":59285518,"identity":"6bbadb7e-cf0c-43e6-a957-f2935978e8c4","added_by":"auto","created_at":"2024-06-28 16:23:32","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":128812,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe SHAP summary plot with all performance indicators in balanced games\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4547091/v1/652dcc9b07615970d1e5acfa.png"},{"id":59285517,"identity":"cbf7b8f3-c403-4cbf-9829-01d95077eebc","added_by":"auto","created_at":"2024-06-28 16:23:32","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":131359,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe SHAP dependence plot for 1PT_made and 1PT_missedin balanced games\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4547091/v1/504c388cdb32c7691dafdaa2.png"},{"id":59284956,"identity":"be18ba9a-8f70-495c-9325-c1275176d13a","added_by":"auto","created_at":"2024-06-28 16:15:32","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":135178,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe SHAP summary plot with all performance indicators in unbalanced games\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4547091/v1/6a2134f731221fa8cc68e4ea.png"},{"id":59284953,"identity":"bda1fefc-ec9a-45f1-b295-6476a79bc8bb","added_by":"auto","created_at":"2024-06-28 16:15:32","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":154667,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe SHAP dependence plot for 1PT_made and 2PT_made in unbalanced games\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4547091/v1/ecd3a0dbe0f63590ffc27e80.png"},{"id":60501338,"identity":"897c86c6-6511-4bb5-9205-6eab433e2226","added_by":"auto","created_at":"2024-07-17 12:44:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":930870,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4547091/v1/8c4cd61d-aa98-4a33-b538-90846011e3a6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Using neural network interpretability to understand outcomes in women’s 3 x 3 basketball","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn 2007, FIBA formally adopted 3x3 basketball as an official discipline by establishing a standardised rule set and launching the 3x3 World Tour and World Championships. Since then, the sport has rapidly gained global prominence, marked by its inclusion in the Tokyo 2020 Olympics. Distinct from traditional 5x5 basketball, 3x3 games are played on a half-court with a single basket, reflecting its streetball roots where court size was often limited. Teams consist of three players and one substitute, facilitating a fast-paced game. A coin toss starts the game, with the winner choosing to start with possession. Matches last 10 minutes, and the first team to reach 21 points within this time or have the higher score wins.\u003c/p\u003e \u003cp\u003eSeveral researchers assert that 3x3 basketball should be viewed as an independent sport despite its origins as a variation of 5x5 basketball. The smaller court size in 3x3 demands greater physical exertion, aligning with findings in small-sided soccer games (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e). A recent study that monitored the load parameters of 3x3 players identifies 3x3 basketball as a high-intensity sport characterised by faster speed and transitions, making it more exhausting than traditional basketball (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e). Additional research emphasises the importance of agility-based training for 3x3 players and highlights different movement patterns such as the high work-to-rest ratio (\u003cspan additionalcitationids=\"CR4\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e). Further focusing on physical demands by gender, the importance of jumping ability for male players and ball-handling sprints for female players was emphasized (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe application of sports performance analysis (SPA) in 5x5 basketball has become standard practice, providing coaches with crucial insights into player performance, game strategies, and other competitive aspects (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e). Research in this area mainly utilized notational analysis and biomechanics, emphasizing statistical assessment, talent identification, match analysis, and injury risk (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e). Notational analysis focuses on identifying key events in the game and draws conclusions based on quantitative and qualitative feedback (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e). This approach enables analysts and coaches to gain deeper insights into tactical techniques and movement patterns(\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e), which helps coaches monitor players' development. Apparently, professional 5x5 basketball clubs recognize the benefits of notational analysis (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e), but similar research was largely overlooked in 3x3 basketball. Some studies analysed 3x3 basketball through notational analysis, identifying performance indicators that significantly affect game outcomes. These include two-point scoring efficiency, quick scoring after a successful defence, the percentage of two- and one-point shots, turnovers, rebounds, and fouls (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan additionalcitationids=\"CR14 CR15\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e). However, previous research primarily focused on men's games, with women's games being underreported.\u003c/p\u003e \u003cp\u003eArtificial neural networks (ANNs) represent innovative tools for analyzing sports performance and hold significant potential in the sports context (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e). In notational analysis, ANNs were primarily used for predictive tasks, including talent identification, performance forecasting, match outcome prediction, and more. Various adaptations of ANNs have also been widely employed to predict 5x5 basketball match outcomes with high accuracy (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e). Previous study accurately predicted basketball match outcomes using a feed-forward neural network with an accuracy exceeding 80% (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e). They identified several key performance indicators, including two-point and three-point attempts, steals, turnovers, offensive rebounds, blocks, and assists. Similarly, in a study comparing various machine learning models for predicting college basketball game outcomes, the multilayer perceptron neural network outperformed the others, with each model validated using separate training and test sets (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e). Despite their predictive power, artificial neural networks are often considered as a 'black box,' as their internal workings can be challenging to interpret. This opacity can present difficulties for coaching staff when understanding their output. Recently, SHapley Additive exPlanations (SHAP) provided a method to explain the classifications of neural networks. By aggregating Shapley values, SHAP offers global explanations for a model's predictions, enhancing the transparency and interpretability of neural networks' decision-making processes (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e). However, this approach failed to be applied in 3x3 basketball performance analysis so far.\u003c/p\u003e \u003cp\u003eGiven the anthropometric differences between men and women, studying professional women's 3x3 basketball games is essential. To gain deeper insights into game outcomes, we utilized artificial neural networks for their robust ability to handle non-linear datasets. We also applied discriminant analysis, which is widely used in basketball performance analysis, to compare the analytical ability between models. In this pathway, we can extract valuable insights from historical game experiences and offer different methodological perspectives for future research on 3x3 basketball performance analysis.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Data sample\u003c/h2\u003e \u003cp\u003eThis study utilized a retrospective analysis, collecting data from the women's professional 3x3 basketball circuit between 2019 and 2023 (excluding 2020 due to lockdowns). The dataset comprised 987 matches, sourced from the official FIBA website (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://womens-series.fiba3x3.com/\u003c/span\u003e\u003cspan address=\"https://womens-series.fiba3x3.com/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). It included 15 performance indicators: one-point field goals (1PT_made and 1PT_missed), two-point field goals (2PT_made and 2PT_missed), free throws (FT_made and FT_missed), offensive rebounds (OREB), defensive rebounds (DREB), key assists (KAS), drives (DRV), blocked shots (BS), turnovers (TO), team fouls (TF), team fouls against (TFA), ball possession (POS), and offensive quality (OQ). To minimize the potential effects of game pace, all performance indicators were normalized by ball possession and multiplied by 100 (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e). Situational variables, like match type and opponent quality, were also considered. Specifically, Team quality was reflected by the difference in points between teams at the end of the season (Team A's points - Team B's points). We used K-means algorithm to categorize matches into balanced (7 points or fewer) and unbalanced (8 points or more). The data for each game was recorded in Excel.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Data analysis\u003c/h2\u003e \u003cp\u003eAs the initial exploration step, we performed descriptive statistics, such as calculating the mean and standard deviation, to compare winning and losing teams in both balanced and unbalanced games. This initial exploration helps in understanding the basic trends and differences between groups. Next, to comprehend the pattern and significant difference between winning and losing teams, the independent samples t-tests were conducted. The significance was set at p\u0026thinsp;\u0026le;\u0026thinsp;0.05.\u003c/p\u003e \u003cp\u003eA discriminant analysis was conducted to identify the variables that most effectively distinguish between the groups (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e). Discriminant analysis has been widely used in basketball performance analysis and is considered robust (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e). To interpret the results, we focused on structure coefficients above ∣0.30∣ (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). These coefficients indicate which variables have the most substantial impact on discriminating between the groups. We validated the discriminant models using the leave-one-out cross-validation method, which involves dividing the data into subsets for training and testing. This approach assesses the models' ability to classify new data effectively, providing a realistic measure of model performance.\u003c/p\u003e \u003cp\u003eThe outcomes of basketball matches are influenced by many factors that exhibit non-linear relationships. Neural Networks are suitable for capturing such complex patterns, so we trained a basic Multilayer Perceptron (MLP) neural network using gradient-based optimization algorithms. Our model consisted of one hidden layer with eleven neurons, the constant learning rate of 0.001 and momentum set at 0.969. The MLP model aims to classify game outcomes based on input features, learning the relationships from historical data. To assess the model's performance and ensure its generalizability, we employed k-fold cross-validation. This method allowed us to evaluate the model's predictive power across multiple data subsets, providing a more robust measure of its accuracy. Additionally, we used the AUC metric to quantify the model's ability to differentiate between the positive and negative classes over all possible classification thresholds. To make the neural network's predictions more interpretable, we utilized SHAP (SHapley Additive exPlanations) values, which reveal how each feature impacts the model's predictions. A SHAP summary plot offers a comprehensive view of feature contributions across all data points, ranking them by their average impact on the model\u0026rsquo;s predictions. A dependence plot helps us understand the relationship between a specific feature and the model's predictions while considering another interacting feature. Given that exact Shapley values are computationally expensive to compute in real-world scenarios, we used the KernelSHAP explainer with 120 weighted k-medians to approximate the Shapley values.\u003c/p\u003e \u003cp\u003eAll data analysis work was done using Python software (3.7, Wilmington, DE, USA), using the Scikit-Learn machine learning library and SHAP library for the KernelExplainer. This study did not involve human participants and the data was collected from the public resource so ethical approval is not needed.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the descriptive analysis and t-test results, providing insight into how winning and losing teams perform in balanced and unbalanced games. In balanced games, where the competition is closely matched, winning teams exhibit differences compared to losing teams across nearly all metrics, except for 1PT_missed. The superiority of the winning teams is evident in scoring metrics such as 1PT_made, 2PT_made, and FT_made, emphasizing the importance of converting scoring opportunities in close matches. Similarly, controlling rebounds, both offensive (ORB) and defensive (DRB), plays a critical role in maintaining possession and limiting opponents' chances. Defensive metrics like turnovers (TO) and total fouls (TF) also highlight the significance of disciplined play, as winning teams minimize mistakes and play with greater defensive discipline. On the other hand, all metrics show significant differences between winning and losing teams in unbalanced games. Winning teams dominate in scoring efficiency, demonstrated by higher 1PT_made and 2PT_made scores. They also exert control over the game's flow through superior rebounding (ORB and DRB) and effective ball distribution, indicated by higher assists (KAS). These teams' superior defensive play is evident through metrics like turnovers (TO) and fouls (TF).\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\u003eThe mean value and standard deviation of each performance indicator in balanced and unbalanced games\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"14\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePerformance indicators\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003eBalanced game\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c12\" namest=\"c9\"\u003e \u003cp\u003eUnbalanced game\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eWining\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eLosing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003eWining\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003eLosing\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1PT_made\u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e27.13 \u0026plusmn; 7.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e21.81 \u0026plusmn; 7.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e31.76 \u0026plusmn; 8.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e17.08 \u0026plusmn; 7.66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1PT_missed\u003csup\u003eb**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e25.43 \u0026plusmn; 8.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e25.96 \u0026plusmn; 8.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e19.84 \u0026plusmn; 8.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e26.89 \u0026plusmn; 9.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2PT_made\u003csup\u003ea* b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e6.51 \u0026plusmn; 4.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e6.02 \u0026plusmn; 4.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e9.77 \u0026plusmn; 6.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e4.07 \u0026plusmn; 3.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2PT_ missed \u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e18.25 \u0026plusmn; 7.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e22.31 \u0026plusmn; 8.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e18.51 \u0026plusmn; 7.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e24.42 \u0026plusmn; 9.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFT_ made\u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e7.09 \u0026plusmn; 5.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e4.85 \u0026plusmn; 4.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e7.37 \u0026plusmn; 5.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e2.92 \u0026plusmn; 3.21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFT_ missed\u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e3.20 \u0026plusmn; 3.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e2.60 \u0026plusmn; 3.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e3.05 \u0026plusmn; 3.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e2.39 \u0026plusmn; 2.92\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBLK \u003csup\u003ea* b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e3.69 \u0026plusmn; 3.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e3.20 \u0026plusmn; 3.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e4.75 \u0026plusmn; 4.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e2.11 \u0026plusmn; 2.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eORB \u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e15.42 \u0026plusmn; 6.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e13.72 \u0026plusmn; 5.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e16.77 \u0026plusmn; 6.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e12.07 \u0026plusmn; 6.48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDRB \u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e33.96 \u0026plusmn; 8.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e30.01 \u0026plusmn; 8.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e36.61 \u0026plusmn; 8.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e25.05 \u0026plusmn; 8.54\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTO \u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e15.07 \u0026plusmn; 6.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e18.16 \u0026plusmn; 7.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e12.17 \u0026plusmn; 5.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e23.17 \u0026plusmn; 8.91\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTF \u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e16.28 \u0026plusmn; 5.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e18.83 \u0026plusmn; 5.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e13.52 \u0026plusmn; 5.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e19.45 \u0026plusmn; 6.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTFA \u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e18.21 \u0026plusmn; 5.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e16.72 \u0026plusmn; 5.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e17.98 \u0026plusmn; 6.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e14.48 \u0026plusmn; 6.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBP \u003csup\u003ea* b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e37.45 \u0026plusmn; 4.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e36.35 \u0026plusmn; 3.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e35.67 \u0026plusmn; 5.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e33.12 \u0026plusmn; 5.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKAS \u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e9.30 \u0026plusmn; 5.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e6.85 \u0026plusmn; 4.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e13.17 \u0026plusmn; 6.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c14\" namest=\"c12\"\u003e \u003cp\u003e4.81 \u0026plusmn; 3.91\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDRV \u003csup\u003ea** b**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e7.55 \u0026plusmn; 5.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e6.27 \u0026plusmn; 4.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e7.86 \u0026plusmn; 5.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003e4.70 \u0026plusmn; 4.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c14\" namest=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"14\"\u003eLegend: \u003csup\u003ea\u003c/sup\u003e Significance determined by t-test in balanced games; \u003csup\u003eb\u003c/sup\u003e Significance determined by t-test in unbalanced games; * p\u0026thinsp;\u0026lt;\u0026thinsp;0.05; **p\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe discriminant function derived from our analysis was statistically significant (P \u0026lt; 0.01) and demonstrated a high level of predictive accuracy, correctly classifying 82.4% of the cases in balanced games and 99.6% in unbalanced games. The structural coefficients (SCs) resulting from the discriminant analysis, presented in Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, effectively distinguish between the best and worst-performing teams in both balanced and unbalanced games.\u003c/p\u003e \u003cp\u003eIn balanced games, the key discriminative features included 1PT_made (SC\u0026thinsp;=\u0026thinsp;0.48), free throws made (FT_made, SC\u0026thinsp;=\u0026thinsp;0.32), and offensive efficiency (OQ, SC\u0026thinsp;=\u0026thinsp;0.42). These metrics highlight the importance of scoring efficiency and maintaining offensive control in closely contested matches. Assists (KAS, SC\u0026thinsp;=\u0026thinsp;0.34) and defensive rebounds (DREB, SC\u0026thinsp;=\u0026thinsp;0.33) also emerged as significant discriminators, showing that teamwork in offence and controlling defensive rebounds are crucial for winning balanced games. Negative structural coefficients for turnovers (TO, SC = -0.31) and total fouls (TF, SC = -0.33) emphasize the need for reducing mistakes and maintaining disciplined play.\u003c/p\u003e \u003cp\u003eIn unbalanced games, the discriminant analysis results (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) showed that winning teams significantly outperformed losing teams across all game metrics. The discriminant function highlighted 1PT_made (SC\u0026thinsp;=\u0026thinsp;0.73), 2PT_made (SC\u0026thinsp;=\u0026thinsp;0.53), and assists (KAS, SC\u0026thinsp;=\u0026thinsp;0.64) as major contributors to success in these matches, underlining the importance of shooting efficiency and offensive collaboration. Rebounding, both offensive (OREB, SC\u0026thinsp;=\u0026thinsp;0.36) and defensive (DREB, SC\u0026thinsp;=\u0026thinsp;0.60), also played a substantial role in differentiating winning and losing teams. In contrast, turnovers (TO, SC = -0.64) and total fouls (TF, SC = -0.46) had strong negative correlations with winning, indicating the importance of disciplined play and ball control.\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\u003eThe structure coefficients and tests of statistical significance in balanced games\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=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStatistic\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1PT_made\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1PT_missed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2PT_made\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2PT_missed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFT_made\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFT_missed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOQ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePOS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKAS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDRV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOREB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDREB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTFA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEigenvalue\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWilks\u0026rsquo; lambda\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCanonical correlation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChi-squared\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e78.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSignificance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReclassification\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e80.54%\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=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe structure coefficients and tests of statistical significance in unbalanced games\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=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStatistic\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1PT_made\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1PT_missed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.41\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2PT_made\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2PT_missed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFT_made\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFT_missed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOQ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePOS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKAS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.64\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDRV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOREB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDREB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.64\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTFA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEigenvalue\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWilks\u0026rsquo; lambda\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCanonical correlation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChi-squared\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e99.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSignificance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReclassification\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e99.52%\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\u003eThe Multilayer Perceptron (MLP) neural network outperformed discriminant analysis, achieving 85.38% accuracy and AUC 0.89 in balanced games and 99.8% accuracy and AUC 0.99 in unbalanced games. The model's superior performance demonstrates its ability to discern between winning and losing teams by leveraging complex, non-linear patterns in basketball data. The SHAP analysis (visualized in the attached plots) reveals the relative importance of various features influencing the prediction of basketball game outcomes. In balanced games, positive correlations with winning probabilities include 1PT_made, 2PT_made, FT_made, and defensive rebounds, while negative correlations are observed for 1PT_missed and 2PT_missed. The SHAP value of 1PT_made shows a clear positive correlation, indicating that as the number of 1PT_made increases, the SHAP value predicted by the model increases, thereby positively impacting the prediction. Higher FT_made values, represented by the red color, are typically associated with higher 1PT_made SHAP values. In contrast, there is a clear negative correlation between 1PT_missed and its SHAP value, as higher missed free throw values lead to more negative SHAP values, reducing the team's probability of winning.The dominance of red dots in the upper right corner and blue dots in the lower-left corner suggests that teams with more missed free throws and lower drive values are significantly less likely to win. Conversely, teams with good free throw conversions and high drive values are more likely to win.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn unbalanced games, the SHAP value plot shows a positive correlation between 1PT_made, 2PT_made, and winning probabilities, while 1PT_missed and 2PT_missed are negatively correlated. Defensive rebounds (DREB) and offensive rebounds (OREB) also show positive correlations, while turnovers (TO) negatively impact predictions. Other features like FT_made, KAS, and DRV have varying impacts on model predictions. This plot demonstrates a positive correlation between 1PT_made and the model's predictions. As the number of 1-pointers made increases, the SHAP value predicted by the model also increases, positively impacting the prediction. The colour gradient (OQ) adds additional context, showing that teams with higher offensive quality tend to make more 1-pointers. This plot illustrates the positive correlation between 2PT_made and its SHAP value. As the number of 2-pointers made increases, the SHAP value increases, positively impacting the prediction. The colour gradient (1PT_made) shows a positive association between making both 1-pointers and 2-pointers.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eTo the best of the researcher\u0026rsquo;s knowledge, no study previously utilized SHAP values to understand game outcomes and performance indicators in 3x3 professional women's basketball. This investigation aimed to enhance comprehension surrounding game outcomes within this young basketball discipline. By analyzing the collected data using discriminant analysis and neural networks, the study achieved over 80% accuracy in classifying both balanced and unbalanced games. In addition, we explored model-agnostic methods to explain classification algorithms. The SHAP method enabled us to gain insights into how basic neural networks classify data, which is crucial for understanding predictive models that often lack clear guidance due to ambiguities in defining and classifying performance indicators (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e). By using SHAP values, we could unpack the inner workings of the models, providing actionable insights into which features most influence game outcomes, thereby helping players, coaches, and analysts make more informed decisions.\u003c/p\u003e \u003cp\u003ePrevious research on men's 3x3 basketball has highlighted the significance of two-point shots, as they yield twice the points of one-point shots (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e). However, our analysis reveals a different trend in women's 3x3 basketball, where the accuracy of one-point shots (both made and missed) emerges as a more crucial key performance indicator (KPI). This difference also underscores the importance of studying men's and women's 3x3 basketball separately. The findings from our study align with previous shooting analyses, which found that women tend to attempt more one-point shots than men in 3x3 games but do not have the same shooting efficiency (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e). We consider two factors contributing to this situation. Firstly, the reduced number of players in 3x3 basketball creates more opportunities for drives and cuts to the basket. Additionally, the ball used in 3x3 basketball, while being the same size as the one used in women's 5x5 basketball, has the same weight as the ball used in men's 5x5 games. This difference could explain why female players tend to take more inside shots in 3x3 basketball.\u003c/p\u003e \u003cp\u003eIn the realm of rebounds, defensive rebounds stand out as one of the key performance indicators, more than offensive rebounds. This pattern aligns with trends observed in 5x5 basketball (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e), emphasizing the importance of securing defensive rebounds. A widely recognized concept in basketball strategy is that teams with more defensive rebounds often find themselves in a better position to win championships (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e). This advantage arises because defensive rebounds effectively end the opponent's offensive possession, denying them the chance to score and granting the defending team a new possession. Securing defensive rebounds not only prevents the opposite team from scoring but also allows the team to transition quickly into offense, potentially catching their opponents off-guard and creating fast-break opportunities. In 3x3 basketball, where the game is even faster-paced than in 5x5, controlling defensive rebounds is crucial for maintaining momentum and keeping the pressure on the opposition.\u003c/p\u003e \u003cp\u003eIn addition to traditional performance indicators, we found that contextual variables, such as team quality, also significantly impact game outcomes and act as key predictive indicators. We also examined another contextual variable, such as game type, and discovered distinct patterns depending on whether the games were balanced or unbalanced. In balanced games, where the teams are more evenly matched, FT_made and POS emerged as important differentiators in determining the outcome. In unbalanced games, where one team dominates, TF and TO became more critical in distinguishing the outcome. This finding suggests that in games with a clear disparity in team quality, legal fouls behaviours and reducing turnovers are key to maintaining control and achieving decisive victories. These findings underline the importance of considering contextual variables in 3x3 basketball performance analysis. Different game contexts require distinct strategies and KPIs, emphasizing the need for tailored approaches to game analysis to better understand and predict game outcomes.\u003c/p\u003e \u003cp\u003eFrom a technical analysis perspective, we compared different analytical pipelines, including neural networks and discriminant analysis, to achieve higher accuracy. The neural networks, in particular, demonstrated superior performance in complex contexts like balanced games, highlighting their ability to recognize intricate non-linear relationships. Traditionally viewed as a black-box model, neural networks have often been challenging to interpret. However, the use of SHAP values has shed light on the inner workings of these networks, helping us understand how they process complex variables and their relationship with predictive outcomes. Our innovative introduction of SHAP values into the realm of 3x3 basketball emphasizes the importance of understanding the relationships between intricate variables and predictive outcomes. This method has seen extensive application in sports analytics, and by adopting it, we provide actionable insights into how neural networks process and predict game outcomes. This approach offers a new level of transparency, enabling practitioners to translate these insights into practical strategies and better decision-making.\u003c/p\u003e \u003cp\u003eThis study aims to extract valuable insights into the relationship between performance indicators and game outcomes in 3x3 women's basketball series. While we achieved satisfactory accuracy and identified key performance indicators, the investigation has certain limitations that need to be addressed. Firstly, even though we gathered all available data from the FIBA official website, the sample size still needs to be expanded. The limited sample size can introduce bias into the results, affecting the reliability of the conclusions. Additionally, due to the small sample size, we couldn't include additional contextual variables, such as the competition stage, which could influence performance. Insufficient data can reduce the reliability of analytical results, especially when accounting for multiple contextual variables (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e).\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThe current work applied the neural network to reveal the key performance indicators that can significantly influence the game outcome in 3 x 3 women\u0026rsquo;s basketball series. The SHAP value can help us understand better the ANNs work and it outperforms the traditional discriminant analysis. We identified the one-points made, defensive rebounds and the key assists as the key performance indicators that can discriminate the winning and losing teams. Expanding the dataset and including a broader range of variables would help improve the reliability of future analyses and enable a more comprehensive understanding of the relationship between performance indicators and game outcomes in 3x3 women's basketball. In the future, researchers should expand the dataset and incorporate a broader range of contextual variables to improve the reliability of analyses.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available at 10.6084/m9.figshare.25827631.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDisclosure of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that there are no conflicts of interest to disclose.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo funding was received.\u003c/p\u003e\n\u003cp\u003eEthics Approval and Consent to Participate are not applicable due to no human participants being involved.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eL.D wroted the main manuscript text and MY.Z collected the dataset.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eKelly DM, Drust B. 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Routledge; 2013 [cited 2024 May 16]. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.routledge.com/Routledge-Handbook-of-Sports-Performance-Analysis/McGarry-ODonoghue-Sampaio/p/book/9781138908208\u003c/span\u003e\u003cspan address=\"https://www.routledge.com/Routledge-Handbook-of-Sports-Performance-Analysis/McGarry-ODonoghue-Sampaio/p/book/9781138908208\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"basketball match outcome, sports prediction, women 3x3 basketball, SHAP value","lastPublishedDoi":"10.21203/rs.3.rs-4547091/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4547091/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDespite the inclusion of 3x3 basketball in the Olympic Games, research on this topic remains sparse, especially concerning women's 3x3 basketball. This study aimed to understand game outcomes in the FIBA 3x3 women's professional circuit. Data was sourced from the official FIBA 3x3 website, encompassing 15 indicators and 2 contextual variables from 987 matches across four seasons. All games were classified into balanced and unbalanced categories. The Multilayer Perceptron neural network outperformed discriminant analysis in both balanced and unbalanced games, achieving classification accuracy exceeding 85%. To interpret the neural network's predictions, we calculated SHAP values, revealing that one-point field goal made and defensive rebounds were the key performance indicators. In balanced games, free-throw made and ball possession contributed significantly to the classification of winning and losing teams, while team fouls and turnovers were instrumental in distinguishing outcomes in unbalanced games. This study provides valuable insights into game outcomes in women's 3x3 basketball.\u003c/p\u003e","manuscriptTitle":"Using neural network interpretability to understand outcomes in women’s 3 x 3 basketball","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-28 16:15:27","doi":"10.21203/rs.3.rs-4547091/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c0c27dfd-dd2d-4b6c-a278-5c0746b9318a","owner":[],"postedDate":"June 28th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-08-12T13:08:55+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-28 16:15:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4547091","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4547091","identity":"rs-4547091","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}