Social capital in coach-athlete relationships: A longitudinal study on psychological commitment and persistence intention of junior tennis players

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Method A questionnaire survey was conducted on 215 competitive young tennis players aged 12–18 at three time points (baseline, 6 months, 12 months). We used structural equation modeling to examine the mediating role of social capital centered on relationship bonds, trust, and shared vision in the relationship between coach athlete relationships and psychological investment and persistence. Result Longitudinal analysis shows that: (1) the quality of coach athlete relationship at T1 time can significantly positively predict social capital at T2 time; (2) Social capital at T2 time can significantly positively predict psychological investment and persistence willingness at T3 time; (3) Social capital plays a fully mediating role between coach athlete relationships and psychological investment/persistence willingness. The influence of control variables (age, gender, training years) is not significant. Conclusion This study reveals that the coach athlete relationship is established through the key mechanism of building social capital to maintain the psychological investment and persistence willingness of adolescent athletes in the long term. This emphasizes that in youth sports training, coaches should consciously invest in elements related to social capital, rather than just technical and tactical guidance. Health sciences/Health care Biological sciences/Psychology Social science/Psychology Social capital Coach athlete relationship Psychological investment Persist in the will Longitudinal study Youth Tennis Figures Figure 1 Figure 2 Figure 3 Figure 4 1.Introduction The attrition of young athletes is a pervasive and severe challenge in the field of competitive sports. In individual sports like tennis, the combination of high-intensity training, fierce competition, and psychological pressure leads many promising young players to drop out prematurely [ 1 – 3 ]. Therefore, identifying key protective factors that promote long-term persistence among adolescent athletes is of paramount importance. Previous research has extensively confirmed that a positive coach-athlete relationship (CAR) is a core contextual factor in athlete development [ 4 – 6 ]. According to the tripartite model, closeness, commitment, and complementarity are the core dimensions constituting a high-quality CAR. Numerous cross-sectional studies have shown that this positive relationship is associated with higher athlete satisfaction, better performance, and lower dropout intentions [ 7 – 8 ]. However, the underlying mechanisms of its influence, particularly the dynamic processes within a longitudinal timeframe, remain underexplored. Specifically, it is still unclear how this relationship is "stored" and "transformed" into athletes' enduring internal motivation. To address this research gap, the present study introduces "social capital" theory as an integrative theoretical framework. Social capital refers to the sum of the actual and potential resources embedded within a social network, characterized by trust, norms of reciprocity, and shared goals [ 9 – 10 ]. Within the coach-athlete dyad, this capital manifests as strong relational bonds (emotional connections beyond formal roles), deep mutual trust (confidence in the coach's competence and benevolence), and a clear shared vision (a common understanding of developmental paths and objectives) [ 11 – 12 ]. We hypothesize that a high-quality coach-athlete relationship acts not merely as simple interaction, but as an "investment" that jointly constructs valuable social capital [ 13 – 15 ]. This capital, in turn, becomes the "dividend" that motivates athletes to sustain their engagement and willingness to persevere through challenges. Specifically, when athletes feel a strong connection with their coach, trust their coach's decisions, and identify with mutually set goals, they are more likely to internalize the value of training (i.e., psychological engagement) and develop a strong intention to continue their athletic careers [ 16 ]. Psychological engagement is a positive, fulfilling, sport-related state of mind characterized by vigor, dedication, and absorption [ 17 – 19 ], while persistence intention refers to a steadfast psychological tendency to continue sport participation until long-term goals are achieved [ 20 – 22 ]. Based on this rationale, this study employs a three-wave longitudinal design to test the core model: Coach-Athlete Relationship → Social Capital → Psychological Engagement and Persistence Intention. By uncovering this mediating pathway, we aim not only to elucidate the internal mechanism through which the coach-athlete relationship yields long-term benefits but also to provide more timely and targeted theoretical guidance for coaching practice, ultimately helping to reduce attrition and foster the sustainable development of adolescent athletes. 2. Methods 2.1 Participants and Sampling Procedure This study employed a longitudinal design. Participants were recruited via a convenience sampling method from six provincial-level tennis training centers located in Eastern, Central, and Western China. These centers are professional institutions dedicated to cultivating competitive adolescent tennis players, making their trainees representative of the competitive level in this age group across China. The initial sample consisted of 245 adolescent athletes. Over the 12-month longitudinal tracking period, 30 participants were lost to follow-up due to reasons such as athletic injuries, switching to other sports, or failure to complete all three waves of questionnaires. The final valid sample comprised 215 participants, yielding a longitudinal retention rate of 87.8%. The final sample included 112 males (52.1%) and 103 females (47.9%). Participants' ages ranged from 12 to 18 years, with a mean age of 14.8 years (SD = 1.7). Their mean duration of specialized tennis training was 5.2 years (SD = 2.4), indicating that the sample primarily consisted of adolescent athletes with considerable training experience, who were at a critical stage of specialized development. The flow of participants through each stage of the longitudinal study, including the recruitment at baseline (T1) and the attrition at subsequent follow-ups (T2 and T3), is presented in Fig. 1 . 2.2 Research Design and Procedure A three-wave time-lagged longitudinal design was adopted to test the hypothesized causal relationships. Data were collected at three time points, with a 6-month interval between each wave, resulting in a total duration of 12 months. The specific procedure was as follows: T1 (Baseline) : At the first time point, participants completed paper-and-pencil questionnaires on-site at their training centers, administered by the research team. Measures included the core independent variable, Coach-Athlete Relationship , and demographic information (age, gender, training years) as control variables. T2 (Second Wave, 6-month follow-up) : Six months after the baseline assessment, the same cohort of participants completed the second wave of questionnaires. This wave measured the mediating variable, Social Capital . T3 (Third Wave, 12-month follow-up) : Twelve months after the baseline, the third and final wave of questionnaires was administered. This wave measured the dependent variables, Psychological Engagement and Persistence Intention . Prior to the commencement of the study, written informed consent was obtained from all participants and their parents or legal guardians. The consent form detailed the study's purpose, procedures, potential risks, confidentiality, and the right to voluntary participation/withdrawal. All procedures performed in this study were in accordance with the ethical standards of the Declaration of Helsinki and were approved by the Institutional Review Board of University. Figure 2 illustrates the three-wave, time-lagged longitudinal design and the hypothesized theoretical model tested in this study. Data were collected across three time points, spanning a total period of 12 months. At Time 1 (Baseline) , participants completed measures assessing the independent variable, Coach-Athlete Relationship , along with demographic controls. Subsequently, at Time 2 (6-month follow-up) , the mediating variable, Social Capital , was measured. Finally, at Time 3 (12-month follow-up) , the two dependent variables, Psychological Engagement and Persistence Intention , were assessed. The hypothesized causal paths are indicated by arrows. As shown, Path H1 posits that the Coach-Athlete Relationship at T1 positively predicts the level of Social Capital at T2. Furthermore, Path H2 posits that Social Capital at T2, in turn, positively predicts both Psychological Engagement and Persistence Intention at T3. This model positions Social Capital as a critical mediating mechanism that transmits the influence of the initial Coach-Athlete Relationship onto the athletes' subsequent long-term psychological states and behavioral intentions. 2.3 Measures All constructs in this study were measured using validated scales with a 5-point Likert response format ranging from 1 ("Strongly Disagree") to 5 ("Strongly Agree"). The Coach-Athlete Relationship was assessed using the short form of the Coach-Athlete Relationship Questionnaire (CART-Q) developed by Jowett (2007), an 11-item instrument comprising three dimensions: Closeness (4 items, e.g., "I like my coach"), Commitment (3 items, e.g., "I feel loyal to my relationship with my coach"), and Complementarity (4 items, e.g., "When I am coached by my coach, I am responsive"), which demonstrated excellent internal consistency (α = .92) at T1. Social Capital was measured using a 9-item self-report scale developed based on Nahapiet & Ghoshal's (1998) theoretical framework, encompassing three core dimensions: Relational Bonds (3 items, e.g., "My coach and I often communicate outside of formal training sessions"), Trust (3 items, e.g., "I believe my coach always has my best interests at heart"), and Shared Vision (3 items, e.g., "My coach and I have a clear and aligned vision for my future goals"), with confirmatory factor analysis supporting the three-factor structure and showing good reliability (α = .89) at T2. Psychological Engagement was evaluated using the Athlete Engagement Questionnaire (Lonsdale et al., 2007), a 12-item scale measuring four dimensions: confidence, dedication, vigor, and enthusiasm (e.g., "I exert my full effort to my training"), which exhibited strong internal consistency (α = .91) at T3. Finally, Persistence Intention was measured using a brief 4-item scale adapted from Raedeke (2010) (e.g., "I intend to continue playing tennis for the next three years"), demonstrating good reliability (α = .86) at T3. 2.4 Data Analysis The data analysis proceeded in sequential phases using complementary statistical approaches [ 23 – 25 ]. Preliminary analyses were conducted using SPSS 26.0, which involved computing descriptive statistics (means and standard deviations) to summarize the data and Pearson product-moment correlations to examine the bivariate relationships among all study variables. Subsequently, the primary hypothesis concerning the mediating role of social capital was tested using Structural Equation Modeling (SEM) in Mplus version 8.3. The analytical procedure involved first establishing a confirmatory measurement model to validate the factor structure of the key latent constructs. Following this, the structural model illustrated in Fig. 2 was tested; this model specified that the T1 Coach-Athlete Relationship predicts T2 Social Capital, which in turn serves as a mediator by predicting both T3 Psychological Engagement and Persistence Intention, while controlling for the potential influences of age, gender, and training years. To rigorously evaluate the significance of the proposed indirect effects, the bias-corrected bootstrap resampling method with 5,000 iterations was employed to generate 95% confidence intervals for the estimates; an indirect effect is considered statistically significant at the p < .05 level if its confidence interval does not include zero. 3. Results 3.1 Common Method Bias and Confirmatory Factor Analysis To ensure data validity, we first examined potential common method bias. Harman's single-factor test was conducted by performing an unrotated exploratory factor analysis on all items of the key variables. The result showed that the first factor with an eigenvalue greater than one accounted for only 28.4% of the total variance, which is below the critical threshold of 40%, indicating that common method bias was not a serious concern in this study. Subsequently, a confirmatory factor analysis was conducted to assess the discriminant validity of the measurement model. A four-factor model was specified, comprising the latent variables of Coach-Athlete Relationship, Social Capital, Psychological Engagement, and Persistence Intention. The analysis indicated that the model fit the data well: χ²/df = 1.89, Comparative Fit Index (CFI) = .95, Tucker-Lewis Index (TLI) = .93, Root Mean Square Error of Approximation (RMSEA) = .06, with all indices meeting or exceeding recommended standards. To further establish discriminant validity, this four-factor model was compared against a series of nested models (e.g., a three-factor model merging Social Capital and Psychological Engagement). The four-factor model demonstrated a significantly better fit than all alternative models (all ΔCFI > 0.01), providing strong evidence for good discriminant validity among the four core constructs and justifying their treatment as distinct variables in subsequent analyses. 3.2 Descriptive Statistics and Correlational Analysis Table 1 presents the means, standard deviations, and intercorrelations for all study variables. Preliminary analysis showed that the mean scores for all key variables were at a relatively high level (all above 4.0), suggesting that participants generally reported positive coach-athlete relationships, high social capital, strong psychological engagement, and firm persistence intention. The correlation matrix provided strong preliminary support for our hypotheses. Specifically, the Coach-Athlete Relationship at T1 was significantly and positively correlated with Social Capital at T2 (r = .52, p < .001). Concurrently, the Coach-Athlete Relationship at T1 was significantly correlated with both Psychological Engagement (r = .41, p < .001) and Persistence Intention (r = .38, p < .001) at T3. More importantly, the hypothesized mediator, Social Capital at T2, also demonstrated strong and significant positive correlations with both outcome variables—Psychological Engagement at T3 (r = .58, p < .001) and Persistence Intention at T3 (r = .55, p < .001). This pattern of significant correlations among the variables met the preliminary conditions for testing mediation, laying a solid foundation for subsequently examining the mediating role of Social Capital using structural equation modeling. Table 1 presents the descriptive statistics and bivariate correlations for all study variables. The means for the core constructs were relatively high, ranging from 4.05 to 4.33 on a 5-point scale, indicating that participants generally reported positive levels of coach-athlete relationships, social capital, psychological engagement, and persistence intention. As expected, significant correlations were observed among the key variables. Specifically, the Coach-Athlete Relationship at T1 was positively correlated with Social Capital at T2 (r = .52, p < .001). Furthermore, Social Capital at T2 was positively correlated with both Psychological Engagement (r = .58, p < .001) and Persistence Intention (r = .55, p < .001) at T3. The correlation pattern also showed that the T1 Coach-Athlete Relationship was directly correlated with T3 Psychological Engagement (r = .41, p < .001) and Persistence Intention (r = .38, p < .001). Age and training years were highly correlated with each other (r = .67, p < .001) but were not significantly associated with any of the primary study variables, justifying their treatment as control variables. This correlational pattern provides preliminary support for the proposed mediation model, as the relationships between the predictor, mediator, and outcome variables are all significant and in the hypothesized directions. Table 1 Descriptive Statistics and Correlations among Study Variables (N = 215) Variable Mean SD 1 2 3 4 5 6 1. Age 14.8 1.7 1 2. Training Years 5.2 2.4 .67*** 1 3. T1 CAR 4.12 0.58 − .08 − .05 1 4. T2 Social Capital 4.05 0.61 − .11 − .09 .52*** 1 5. T3 Psychological Engagement 4.21 0.55 − .07 − .04 .41*** .58*** 1 6. T3 Persistence Intention 4.33 0.62 − .10 − .12 .38*** .55*** .49*** 1 Note CAR = Coach-Athlete Relationship. p < .05, ** p < .01, *** p < .001. 3.3 Structural Equation Modeling and Mediation Effect Analysis To test the core hypothesis of this study—that social capital mediates the relationship between the coach-athlete relationship and subsequent outcomes—a longitudinal structural equation model was constructed. The model was specified as follows: the Time 1 Coach-Athlete Relationship served as the exogenous variable predicting Time 2 Social Capital; subsequently, Time 2 Social Capital concurrently predicted both of the endogenous outcome variables at Time 3: Psychological Engagement and Persistence Intention. Furthermore, age, gender, and training years were included in the model as control variables to account for their potential confounding effects on the primary variable relationships. The results indicated that the path coefficients from all control variables to the main study variables were statistically non-significant (all *p* > .05), suggesting that age, gender, and training years did not exert a significant influence on the core variable relationships within the specified model. The overall model fit indices for the structural equation model were acceptable to good: χ²/df = 1.92, Comparative Fit Index (CFI) = .94, Tucker-Lewis Index (TLI) = .92, Root Mean Square Error of Approximation (RMSEA) = .065. These indices all met or exceeded conventional thresholds for acceptable model fit, indicating that the theoretical model was well-represented by the sample data. The standardized coefficients for all hypothesized paths in the model, all of which were statistically significant. To rigorously test the mediating effects of Social Capital, the bootstrap resampling method with 5,000 iterations was employed to generate bias-corrected estimates for the indirect effects and their 95% confidence intervals (CIs). The analysis revealed that the indirect effect of the Coach-Athlete Relationship on Psychological Engagement via Social Capital was 0.33, with a 95% CI of [0.21, 0.47]. The indirect effect on Persistence Intention was 0.32, with a 95% CI of [0.19, 0.45]. As neither confidence interval contained zero, both indirect paths were statistically significant. Moreover, after accounting for the mediating role of Social Capital, the direct effects of the Coach-Athlete Relationship on both Psychological Engagement (β = 0.08, *p* > .05) and Persistence Intention (β = 0.07, *p* > .05) became non-significant. This pattern of results indicates that Social Capital functioned as a complete mediator in the relationships between the Coach-Athlete Relationship and the two outcome variables. Figure 3 presents the results of the structural equation model testing the hypothesized relationships. The model demonstrates excellent fit to the data (χ²/df = 1.92, CFI = .94, TLI = .92, RMSEA = .065). All hypothesized paths are statistically significant at ** p < .001 . The path coefficients are standardized estimates. The model shows that the Coach-Athlete Relationship at T1 significantly predicts Social Capital at T2 (β = .54), which in turn significantly predicts both Psychological Engagement (β = .62) and Persistence Intention (β = .59) at T3. Control variables (age, gender, training years) were included in the model but their paths to the main variables were non-significant and are omitted from the figure for clarity. To rigorously test the mediating role of social capital, a bootstrap resampling method with 5,000 iterations was employed to assess the significance of the indirect effects. The analysis revealed that the indirect effect of the coach-athlete relationship on psychological engagement via social capital was 0.33, with a 95% bias-corrected confidence interval of [0.21, 0.47] . Simultaneously, the indirect effect on persistence intention through social capital was 0.32, with a 95% bias-corrected confidence interval of [0.19, 0.45] . Since both confidence intervals did not include zero, these results indicate that the two indirect paths were statistically significant at the *p* < .05 level, providing support for hypotheses H1 and H2. Furthermore, the direct effects were examined. After including social capital as the mediator in the structural equation model, the direct effect of the coach-athlete relationship on psychological engagement became non-significant ( β = .08, *p* > .05), and its direct effect on persistence intention was also non-significant ( β = .07, *p* > .05). This pattern of results—significant indirect effects alongside non-significant direct effects—suggests that social capital serves as a complete mediator in the relationships between the coach-athlete relationship and both psychological engagement and persistence intention. In other words, the positive influence of the coach-athlete relationship on the long-term development of adolescent athletes is entirely transmitted through the key psychological mechanism of building social capital within this relationship. Table 2 Results of Bootstrap Analysis for Mediating Effects Indirect Path Indirect Effect SE 95% Confidence Interval Conclusion CAR → Social Capital → Psychological Engagement 0.33 0.06 [0.21, 0.47] Significant CAR → Social Capital → Persistence Intention 0.32 0.07 [0.19, 0.45] Significant Note : N = 215. Bootstrap sample size = 5000. CAR = Coach-Athlete Relationship. SE = Standard Error. The indirect effect is significant at the *p* < .05 level if the 95% bias-corrected confidence interval does not contain zero. 3.4 Growth Trajectory Analysis of Social Capital To further elucidate the dynamic process underlying the mediation model, we conducted a growth trajectory analysis on social capital. Participants were divided into two groups based on a median split of their T1 Coach-Athlete Relationship (CAR) scores. As depicted in Fig. 4 , the group with higher initial CAR levels demonstrated a steeper and more positive growth trajectory in social capital from T1 to T3 compared to the group with lower initial CAR. This finding visually reinforces the first part of our mediation hypothesis, indicating that a strong coach-athlete relationship not only predicts higher social capital but also fosters its sustained growth over time. 4. Discussion This study, through a three-wave longitudinal design spanning 12 months, provides robust evidence that social capital serves as a key psychological mechanism through which the coach-athlete relationship influences psychological engagement and persistence intention among adolescent tennis players. This finding illuminates the intrinsic process through which relational dynamics translate into long-term developmental outcomes, offering a novel perspective for understanding and intervening in the sustained development of young athletes. First, the study found that a positive coach-athlete relationship established at the initial stage (T1) is a crucial prerequisite for the subsequent formation (T2) of high-quality social capital. This finding aligns with relational investment theories, suggesting that coaches, by consistently demonstrating care, fulfilling commitments, and establishing effective collaboration in daily interactions, are essentially making a productive "social investment." This investment is not a one-sided effort but co-constructs valuable relational resources, embodied as deep mutual trust, strong emotional bonds, and a clear, shared vision, thereby laying a solid psychosocial foundation for the athlete's subsequent development. Second, and most centrally, social capital was found to play the role of a complete mediator between the coach-athlete relationship and the distal outcomes. This implies that the positive influence of the coach-athlete relationship is not directly "radiated" onto the athletes' engagement and persistence behaviors; rather, it is entirely transmitted through the crucial link of building and accumulating social capital. A merely "good relationship" itself is insufficient to directly sustain long-term investment and perseverance; precisely, it is the profound trust (allowing athletes to feel safe and willing to accept challenges), strong bonds (providing emotional support and a sense of belonging), and shared vision (giving meaning to training and striving) incubated by this high-quality relationship that collectively constitute the internal wellspring of motivation. This enables athletes to maintain high levels of psychological engagement and the willingness to persevere even when confronted with high-intensity training, fierce competition, and psychological fatigue. This mechanism strongly resonates with Self-Determination Theory (SDT); the interactive environment fostered by social capital systematically satisfies the athletes' basic psychological needs for relatedness , competence , and autonomy , thereby effectively nurturing their internal motivation, which ultimately manifests as enduring persistence intention. 4.1 Theoretical Contributions This study made three key theoretical contributions: firstly, it introduced and validated social capital as a key intermediary mechanism, revealing the intrinsic process by which coach athlete relationships affect long-term outcomes, thus opening up the "black box" of this relationship; Secondly, a strict longitudinal design was adopted in the research methodology, which demonstrated the lagged predictive effects between variables and provided stronger evidence for quasi causal relationships between variables than cross-sectional studies; Finally, by integrating the core theory of sociology - social capital theory - with the study of coach athlete relationships in sports psychology, the research provides an explanatory interdisciplinary perspective and enriches the theoretical toolbox in this field. 4.2 Practical Implications This study carries clear and profound practical implications for coaches, sports organizations, and parents of adolescent athletes. The practical implications of these findings advocate for a fundamental evolution in the coaching role, necessitating a shift from being primarily a "technical instructor" to becoming a holistic "relational coach." This transformation is predicated on the recognition that proactively investing in high-quality relationships—through building genuine trust, engaging in deep communication, and co-creating shared goals—is of paramount importance, equaling the significance of designing and executing technical-tactical training plans. Specifically, coaching practices must be deliberately organized around the core dimensions of social capital: cultivating trust diligently by maintaining consistency and fairness; strengthening relational bonds conscientiously by showing genuine concern for the athlete's life beyond sport; and clarifying a shared vision collaboratively by ensuring mutually aligned goals and developmental pathways. 4.3 Limitations and Future Research Directions This study has several limitations, which point to fruitful avenues for future research. First, the sample was drawn from training centers within the Chinese context; the generalizability of the findings needs to be examined across broader cultural settings (e.g., Western individualistic cultures) and different sports. Second, although the longitudinal design strengthens causal inference, it remains correlational in nature. Future research could employ more causal methods such as experimental interventions —for instance, designing and implementing "Social Capital Building Training Programs for Coaches" and testing their efficacy through randomized controlled trials. Finally, future models could explore other potential mediating variables (e.g., mental toughness, athletic identity) or important moderating variables (e.g., parental support, peer climate, athlete personality) to build a more comprehensive and nuanced model of athlete development. 5. Conclusion This study, through a 12-month longitudinal empirical investigation, systematically uncovers and validates the underlying mechanism through which the coach-athlete relationship influences adolescent tennis players' psychological engagement and persistence intention. The central conclusion demonstrates that within youth tennis, the high-quality relationship established between coaches and athletes does not directly impact the outcome variables. Instead, its positive effect is indirectly yet powerfully facilitated through the systematic construction and accumulation of social capital —a process profoundly embodied as deep trust , strong relational bonds , and a clear shared vision . Social capital serves as an indispensable complete mediator, acting as a "converter" that transforms positive relational interactions into athletes' enduring internal motivation and commitment. Consequently, the findings of this study strongly advocate that fostering coaches' capacity to recognize, build, and maintain social capital should no longer be viewed as a soft or supplementary coaching skill. Rather, it must be formally recognized as a crucial strategic investment within the talent development systems for youth elite sports . This necessitates that sports organizations, in their processes of coach selection, training, and performance evaluation, look beyond traditional technical and tactical competencies and integrate the ability to build high-quality relationships and foster social capital into the core assessment framework. By empowering coaches to become "relationship architects" and "social capital cultivators," we can more effectively cultivate a new generation of athletes who are not only technically proficient but also psychologically resilient and capable of sustainable long-term development. Declarations Ethical Approval: This study was reviewed and approved by the Institutional Review Board of Pu’er University. All procedures performed in this study involving human participants were in accordance with the ethical standards of the Declaration of Helsinki. Written informed consent was obtained from all individual participants and their parents or legal guardians prior to the study. Competing Interests: The authors have no relevant financial or non-financial interests to disclose. Funding : No funding support Author Contribution C. wrote the main manuscript text and contributed to the study conception and design. Y. prepared figures and critically revised the manuscript and helped to realize the final draft. C.Y. performed investigation, data extraction and validated the analytical methods.All authors reviewed the manuscript Data Availability The questionnaire data that support the findings of this study are available from the corresponding author, Zhaoyuan Chen, upon reasonable request. However, restrictions apply to the availability of these data, which were collected under ethical approval and participant consent agreements that protect the privacy of the minor athletes involved. 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Development of a Webinar for Sport Coaches: Suggested Best Practices for Supporting Athletes[J]. Journal of Sport Psychology in Action, 2020, 12(2):1-14. Martin K, Jonas S, Markus G. Pay attention! The influence of coach-, content-, and player-related factors on focus of attention statements during tennis training.[J]. European journal of sport science, 2022, 23(6):11-17. Higinio G G, Guillaume M. Relationships between perceived coach leadership, athletes’ use of coping and emotions among competitive table tennis players[J]. European Journal of Sport Science, 2020, 20(8):1113-1123. Additional Declarations No competing interests reported. Supplementary Files TennisCoachAthleteStudyData.xlsx Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 10 May, 2026 Reviewers agreed at journal 23 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviewers invited by journal 20 Apr, 2026 Editor assigned by journal 20 Apr, 2026 Editor invited by journal 15 Dec, 2025 Submission checks completed at journal 08 Dec, 2025 First submitted to journal 08 Dec, 2025 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. 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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-8150403","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":628337431,"identity":"9bbd0b96-d1b3-4695-8af5-d278973821ea","order_by":0,"name":"Zhaoyuan Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVRIie3QsWrDMBCA4TMB2YOCtnBBpX6FC4YkQ4dOeQ5nT0tLFk9NIODJkFUmL+GO3VQEnZQ9kMWQF9CYsenYSRoL1T/fx3EHEIv9wcQWUucINyI3WrtrAEENLFHVvBwrtvxsmwBCj8AGma1KUrwwGQshwk4vSY3PJBtngEMuRtpDwM6K1xrXs7tjZ17mMGkPpYckDcm2xuRj+9QZxaGks48MOMnhjXR61RvOQsiCTyW3uOxOKwgjaNl6oiosxs0X3Z6M/lvE3rz3jt7uRbq7OHd9yIX0EICMfm31jf+U9iFTsVgs9p/7BsxXSEOjYCU3AAAAAElFTkSuQmCC","orcid":"","institution":"Kangwon National University","correspondingAuthor":true,"prefix":"","firstName":"Zhaoyuan","middleName":"","lastName":"Chen","suffix":""},{"id":628337432,"identity":"d01b2fa9-beea-4374-a1e3-69b3e73971cc","order_by":1,"name":"Sangmoon Yoon","email":"","orcid":"","institution":"Kangwon National University","correspondingAuthor":false,"prefix":"","firstName":"Sangmoon","middleName":"","lastName":"Yoon","suffix":""}],"badges":[],"createdAt":"2025-11-19 03:38:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8150403/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8150403/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108036554,"identity":"9d0b7bbe-1281-4a24-8db1-8678eb9465f9","added_by":"auto","created_at":"2026-04-28 16:59:31","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":76856,"visible":true,"origin":"","legend":"\u003cp\u003eLongitudinal Study Participation Process and Sample Dynamics Diagram\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8150403/v1/32c87ab9538f6c09d09c893e.png"},{"id":108181210,"identity":"94671eeb-0c84-4401-92c7-47d3ca6f3ecf","added_by":"auto","created_at":"2026-04-30 08:58:24","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":81313,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of longitudinal data collection and theoretical model\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8150403/v1/74961efd09a4231a29c8f00f.png"},{"id":108036555,"identity":"971d4b91-3398-4f7e-8557-f7553cd08a34","added_by":"auto","created_at":"2026-04-28 16:59:31","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":91551,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStructural equation model with standardized path coefficients.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8150403/v1/47782e4020495a1b94e85234.png"},{"id":108803913,"identity":"b7b04c95-2fb6-4b1e-9c34-995d161a5e20","added_by":"auto","created_at":"2026-05-08 15:10:43","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":440090,"visible":true,"origin":"","legend":"\u003cp\u003eThe impact of the initial level of coach athlete relationship on the trajectory of social capital growth\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8150403/v1/a7539f0ea7074ebca89d1706.png"},{"id":108979270,"identity":"2ef2da33-f512-474d-9999-d62a48a67420","added_by":"auto","created_at":"2026-05-11 11:56:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":819725,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8150403/v1/2674f120-2775-4de7-ab19-8d85232989a8.pdf"},{"id":108976592,"identity":"22ad7ed7-ec37-4230-a5ac-e5e24722a915","added_by":"auto","created_at":"2026-05-11 11:25:28","extension":"xlsx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":13536,"visible":true,"origin":"","legend":"","description":"","filename":"TennisCoachAthleteStudyData.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-8150403/v1/634e152de2aa2ece7af53557.xlsx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Social capital in coach-athlete relationships: A longitudinal study on psychological commitment and persistence intention of junior tennis players","fulltext":[{"header":"1.Introduction","content":"\u003cp\u003eThe attrition of young athletes is a pervasive and severe challenge in the field of competitive sports. In individual sports like tennis, the combination of high-intensity training, fierce competition, and psychological pressure leads many promising young players to drop out prematurely [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Therefore, identifying key protective factors that promote long-term persistence among adolescent athletes is of paramount importance.\u003c/p\u003e \u003cp\u003ePrevious research has extensively confirmed that a positive coach-athlete relationship (CAR) is a core contextual factor in athlete development [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. According to the tripartite model, closeness, commitment, and complementarity are the core dimensions constituting a high-quality CAR. Numerous cross-sectional studies have shown that this positive relationship is associated with higher athlete satisfaction, better performance, and lower dropout intentions [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. However, the underlying mechanisms of its influence, particularly the dynamic processes within a longitudinal timeframe, remain underexplored. Specifically, it is still unclear how this relationship is \"stored\" and \"transformed\" into athletes' enduring internal motivation.\u003c/p\u003e \u003cp\u003eTo address this research gap, the present study introduces \"social capital\" theory as an integrative theoretical framework. Social capital refers to the sum of the actual and potential resources embedded within a social network, characterized by trust, norms of reciprocity, and shared goals [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Within the coach-athlete dyad, this capital manifests as strong relational bonds (emotional connections beyond formal roles), deep mutual trust (confidence in the coach's competence and benevolence), and a clear shared vision (a common understanding of developmental paths and objectives) [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWe hypothesize that a high-quality coach-athlete relationship acts not merely as simple interaction, but as an \"investment\" that jointly constructs valuable social capital [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. This capital, in turn, becomes the \"dividend\" that motivates athletes to sustain their engagement and willingness to persevere through challenges. Specifically, when athletes feel a strong connection with their coach, trust their coach's decisions, and identify with mutually set goals, they are more likely to internalize the value of training (i.e., psychological engagement) and develop a strong intention to continue their athletic careers [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Psychological engagement is a positive, fulfilling, sport-related state of mind characterized by vigor, dedication, and absorption [\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], while persistence intention refers to a steadfast psychological tendency to continue sport participation until long-term goals are achieved [\u003cspan additionalcitationids=\"CR21\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBased on this rationale, this study employs a three-wave longitudinal design to test the core model: Coach-Athlete Relationship \u0026rarr; Social Capital \u0026rarr; Psychological Engagement and Persistence Intention. By uncovering this mediating pathway, we aim not only to elucidate the internal mechanism through which the coach-athlete relationship yields long-term benefits but also to provide more timely and targeted theoretical guidance for coaching practice, ultimately helping to reduce attrition and foster the sustainable development of adolescent athletes.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Participants and Sampling Procedure\u003c/h2\u003e \u003cp\u003eThis study employed a longitudinal design. Participants were recruited via a convenience sampling method from six provincial-level tennis training centers located in Eastern, Central, and Western China. These centers are professional institutions dedicated to cultivating competitive adolescent tennis players, making their trainees representative of the competitive level in this age group across China.\u003c/p\u003e \u003cp\u003eThe initial sample consisted of 245 adolescent athletes. Over the 12-month longitudinal tracking period, 30 participants were lost to follow-up due to reasons such as athletic injuries, switching to other sports, or failure to complete all three waves of questionnaires. The final valid sample comprised 215 participants, yielding a longitudinal retention rate of 87.8%.\u003c/p\u003e \u003cp\u003eThe final sample included 112 males (52.1%) and 103 females (47.9%). Participants' ages ranged from 12 to 18 years, with a mean age of 14.8 years (SD\u0026thinsp;=\u0026thinsp;1.7). Their mean duration of specialized tennis training was 5.2 years (SD\u0026thinsp;=\u0026thinsp;2.4), indicating that the sample primarily consisted of adolescent athletes with considerable training experience, who were at a critical stage of specialized development. The flow of participants through each stage of the longitudinal study, including the recruitment at baseline (T1) and the attrition at subsequent follow-ups (T2 and T3), is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Research Design and Procedure\u003c/h2\u003e \u003cp\u003eA three-wave time-lagged longitudinal design was adopted to test the hypothesized causal relationships. Data were collected at three time points, with a 6-month interval between each wave, resulting in a total duration of 12 months. The specific procedure was as follows: \u003cb\u003eT1 (Baseline)\u003c/b\u003e: At the first time point, participants completed paper-and-pencil questionnaires on-site at their training centers, administered by the research team. Measures included the core independent variable, \u003cb\u003eCoach-Athlete Relationship\u003c/b\u003e, and \u003cb\u003edemographic information\u003c/b\u003e (age, gender, training years) as control variables. \u003cb\u003eT2 (Second Wave, 6-month follow-up)\u003c/b\u003e: Six months after the baseline assessment, the same cohort of participants completed the second wave of questionnaires. This wave measured the mediating variable, \u003cb\u003eSocial Capital\u003c/b\u003e. \u003cb\u003eT3 (Third Wave, 12-month follow-up)\u003c/b\u003e: Twelve months after the baseline, the third and final wave of questionnaires was administered. This wave measured the dependent variables, \u003cb\u003ePsychological Engagement\u003c/b\u003e and \u003cb\u003ePersistence Intention\u003c/b\u003e.\u003c/p\u003e \u003cp\u003e Prior to the commencement of the study, written informed consent was obtained from all participants and their parents or legal guardians. The consent form detailed the study's purpose, procedures, potential risks, confidentiality, and the right to voluntary participation/withdrawal. All procedures performed in this study were in accordance with the ethical standards of the Declaration of Helsinki and were approved by the Institutional Review Board of University.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the three-wave, time-lagged longitudinal design and the hypothesized theoretical model tested in this study. Data were collected across three time points, spanning a total period of 12 months. At \u003cb\u003eTime 1 (Baseline)\u003c/b\u003e, participants completed measures assessing the independent variable, \u003cb\u003eCoach-Athlete Relationship\u003c/b\u003e, along with demographic controls. Subsequently, at \u003cb\u003eTime 2 (6-month follow-up)\u003c/b\u003e, the mediating variable, \u003cb\u003eSocial Capital\u003c/b\u003e, was measured. Finally, at \u003cb\u003eTime 3 (12-month follow-up)\u003c/b\u003e, the two dependent variables, \u003cb\u003ePsychological Engagement\u003c/b\u003e and \u003cb\u003ePersistence Intention\u003c/b\u003e, were assessed.\u003c/p\u003e \u003cp\u003eThe hypothesized causal paths are indicated by arrows. As shown, \u003cb\u003ePath H1\u003c/b\u003e posits that the Coach-Athlete Relationship at T1 positively predicts the level of Social Capital at T2. Furthermore, \u003cb\u003ePath H2\u003c/b\u003e posits that Social Capital at T2, in turn, positively predicts both Psychological Engagement and Persistence Intention at T3. This model positions Social Capital as a critical mediating mechanism that transmits the influence of the initial Coach-Athlete Relationship onto the athletes' subsequent long-term psychological states and behavioral intentions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Measures\u003c/h2\u003e \u003cp\u003eAll constructs in this study were measured using validated scales with a 5-point Likert response format ranging from 1 (\"Strongly Disagree\") to 5 (\"Strongly Agree\"). The Coach-Athlete Relationship was assessed using the short form of the Coach-Athlete Relationship Questionnaire (CART-Q) developed by Jowett (2007), an 11-item instrument comprising three dimensions: Closeness (4 items, e.g., \"I like my coach\"), Commitment (3 items, e.g., \"I feel loyal to my relationship with my coach\"), and Complementarity (4 items, e.g., \"When I am coached by my coach, I am responsive\"), which demonstrated excellent internal consistency (α\u0026thinsp;=\u0026thinsp;.92) at T1. Social Capital was measured using a 9-item self-report scale developed based on Nahapiet \u0026amp; Ghoshal's (1998) theoretical framework, encompassing three core dimensions: Relational Bonds (3 items, e.g., \"My coach and I often communicate outside of formal training sessions\"), Trust (3 items, e.g., \"I believe my coach always has my best interests at heart\"), and Shared Vision (3 items, e.g., \"My coach and I have a clear and aligned vision for my future goals\"), with confirmatory factor analysis supporting the three-factor structure and showing good reliability (α\u0026thinsp;=\u0026thinsp;.89) at T2. Psychological Engagement was evaluated using the Athlete Engagement Questionnaire (Lonsdale et al., 2007), a 12-item scale measuring four dimensions: confidence, dedication, vigor, and enthusiasm (e.g., \"I exert my full effort to my training\"), which exhibited strong internal consistency (α\u0026thinsp;=\u0026thinsp;.91) at T3. Finally, Persistence Intention was measured using a brief 4-item scale adapted from Raedeke (2010) (e.g., \"I intend to continue playing tennis for the next three years\"), demonstrating good reliability (α\u0026thinsp;=\u0026thinsp;.86) at T3.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Data Analysis\u003c/h2\u003e \u003cp\u003eThe data analysis proceeded in sequential phases using complementary statistical approaches [\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Preliminary analyses were conducted using SPSS 26.0, which involved computing descriptive statistics (means and standard deviations) to summarize the data and Pearson product-moment correlations to examine the bivariate relationships among all study variables. Subsequently, the primary hypothesis concerning the mediating role of social capital was tested using Structural Equation Modeling (SEM) in Mplus version 8.3. The analytical procedure involved first establishing a confirmatory measurement model to validate the factor structure of the key latent constructs. Following this, the structural model illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e was tested; this model specified that the T1 Coach-Athlete Relationship predicts T2 Social Capital, which in turn serves as a mediator by predicting both T3 Psychological Engagement and Persistence Intention, while controlling for the potential influences of age, gender, and training years. To rigorously evaluate the significance of the proposed indirect effects, the bias-corrected bootstrap resampling method with 5,000 iterations was employed to generate 95% confidence intervals for the estimates; an indirect effect is considered statistically significant at the p\u0026thinsp;\u0026lt;\u0026thinsp;.05 level if its confidence interval does not include zero.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Common Method Bias and Confirmatory Factor Analysis\u003c/h2\u003e \u003cp\u003eTo ensure data validity, we first examined potential common method bias. Harman's single-factor test was conducted by performing an unrotated exploratory factor analysis on all items of the key variables. The result showed that the first factor with an eigenvalue greater than one accounted for only 28.4% of the total variance, which is below the critical threshold of 40%, indicating that common method bias was not a serious concern in this study.\u003c/p\u003e \u003cp\u003eSubsequently, a confirmatory factor analysis was conducted to assess the discriminant validity of the measurement model. A four-factor model was specified, comprising the latent variables of Coach-Athlete Relationship, Social Capital, Psychological Engagement, and Persistence Intention. The analysis indicated that the model fit the data well: χ\u0026sup2;/df\u0026thinsp;=\u0026thinsp;1.89, Comparative Fit Index (CFI)\u0026thinsp;=\u0026thinsp;.95, Tucker-Lewis Index (TLI)\u0026thinsp;=\u0026thinsp;.93, Root Mean Square Error of Approximation (RMSEA)\u0026thinsp;=\u0026thinsp;.06, with all indices meeting or exceeding recommended standards. To further establish discriminant validity, this four-factor model was compared against a series of nested models (e.g., a three-factor model merging Social Capital and Psychological Engagement). The four-factor model demonstrated a significantly better fit than all alternative models (all ΔCFI\u0026thinsp;\u0026gt;\u0026thinsp;0.01), providing strong evidence for good discriminant validity among the four core constructs and justifying their treatment as distinct variables in subsequent analyses.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Descriptive Statistics and Correlational Analysis\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the means, standard deviations, and intercorrelations for all study variables. Preliminary analysis showed that the mean scores for all key variables were at a relatively high level (all above 4.0), suggesting that participants generally reported positive coach-athlete relationships, high social capital, strong psychological engagement, and firm persistence intention.\u003c/p\u003e \u003cp\u003eThe correlation matrix provided strong preliminary support for our hypotheses. Specifically, the Coach-Athlete Relationship at T1 was significantly and positively correlated with Social Capital at T2 (r\u0026thinsp;=\u0026thinsp;.52, p\u0026thinsp;\u0026lt;\u0026thinsp;.001). Concurrently, the Coach-Athlete Relationship at T1 was significantly correlated with both Psychological Engagement (r\u0026thinsp;=\u0026thinsp;.41, p\u0026thinsp;\u0026lt;\u0026thinsp;.001) and Persistence Intention (r\u0026thinsp;=\u0026thinsp;.38, p\u0026thinsp;\u0026lt;\u0026thinsp;.001) at T3. More importantly, the hypothesized mediator, Social Capital at T2, also demonstrated strong and significant positive correlations with both outcome variables\u0026mdash;Psychological Engagement at T3 (r\u0026thinsp;=\u0026thinsp;.58, p\u0026thinsp;\u0026lt;\u0026thinsp;.001) and Persistence Intention at T3 (r\u0026thinsp;=\u0026thinsp;.55, p\u0026thinsp;\u0026lt;\u0026thinsp;.001). This pattern of significant correlations among the variables met the preliminary conditions for testing mediation, laying a solid foundation for subsequently examining the mediating role of Social Capital using structural equation modeling.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the descriptive statistics and bivariate correlations for all study variables. The means for the core constructs were relatively high, ranging from 4.05 to 4.33 on a 5-point scale, indicating that participants generally reported positive levels of coach-athlete relationships, social capital, psychological engagement, and persistence intention. As expected, significant correlations were observed among the key variables. Specifically, the Coach-Athlete Relationship at T1 was positively correlated with Social Capital at T2 (r\u0026thinsp;=\u0026thinsp;.52, p\u0026thinsp;\u0026lt;\u0026thinsp;.001). Furthermore, Social Capital at T2 was positively correlated with both Psychological Engagement (r\u0026thinsp;=\u0026thinsp;.58, p\u0026thinsp;\u0026lt;\u0026thinsp;.001) and Persistence Intention (r\u0026thinsp;=\u0026thinsp;.55, p\u0026thinsp;\u0026lt;\u0026thinsp;.001) at T3. The correlation pattern also showed that the T1 Coach-Athlete Relationship was directly correlated with T3 Psychological Engagement (r\u0026thinsp;=\u0026thinsp;.41, p\u0026thinsp;\u0026lt;\u0026thinsp;.001) and Persistence Intention (r\u0026thinsp;=\u0026thinsp;.38, p\u0026thinsp;\u0026lt;\u0026thinsp;.001). Age and training years were highly correlated with each other (r\u0026thinsp;=\u0026thinsp;.67, p\u0026thinsp;\u0026lt;\u0026thinsp;.001) but were not significantly associated with any of the primary study variables, justifying their treatment as control variables. This correlational pattern provides preliminary support for the proposed mediation model, as the relationships between the predictor, mediator, and outcome variables are all significant and in the hypothesized directions.\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\u003eDescriptive Statistics and Correlations among Study Variables (N\u0026thinsp;=\u0026thinsp;215)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"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=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1. Age\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2. Training Years\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.67***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3. T1 CAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4. T2 Social Capital\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.52***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5. T3 Psychological Engagement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.41***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.58***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6. T3 Persistence Intention\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.38***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.55***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.49***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\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 \u003cstrong\u003eNote\u003c/strong\u003e \u003cp\u003eCAR\u0026thinsp;=\u0026thinsp;Coach-Athlete Relationship.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;.05, ** p\u0026thinsp;\u0026lt;\u0026thinsp;.01, *** p\u0026thinsp;\u0026lt;\u0026thinsp;.001.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Structural Equation Modeling and Mediation Effect Analysis\u003c/h2\u003e \u003cp\u003eTo test the core hypothesis of this study\u0026mdash;that social capital mediates the relationship between the coach-athlete relationship and subsequent outcomes\u0026mdash;a longitudinal structural equation model was constructed. The model was specified as follows: the Time 1 Coach-Athlete Relationship served as the exogenous variable predicting Time 2 Social Capital; subsequently, Time 2 Social Capital concurrently predicted both of the endogenous outcome variables at Time 3: Psychological Engagement and Persistence Intention. Furthermore, age, gender, and training years were included in the model as control variables to account for their potential confounding effects on the primary variable relationships.\u003c/p\u003e \u003cp\u003eThe results indicated that the path coefficients from all control variables to the main study variables were statistically non-significant (all *p* \u0026gt; .05), suggesting that age, gender, and training years did not exert a significant influence on the core variable relationships within the specified model.\u003c/p\u003e \u003cp\u003eThe overall model fit indices for the structural equation model were acceptable to good: χ\u0026sup2;/df\u0026thinsp;=\u0026thinsp;1.92, Comparative Fit Index (CFI)\u0026thinsp;=\u0026thinsp;.94, Tucker-Lewis Index (TLI)\u0026thinsp;=\u0026thinsp;.92, Root Mean Square Error of Approximation (RMSEA)\u0026thinsp;=\u0026thinsp;.065. These indices all met or exceeded conventional thresholds for acceptable model fit, indicating that the theoretical model was well-represented by the sample data. The standardized coefficients for all hypothesized paths in the model, all of which were statistically significant.\u003c/p\u003e \u003cp\u003eTo rigorously test the mediating effects of Social Capital, the bootstrap resampling method with 5,000 iterations was employed to generate bias-corrected estimates for the indirect effects and their 95% confidence intervals (CIs). The analysis revealed that the indirect effect of the Coach-Athlete Relationship on Psychological Engagement via Social Capital was 0.33, with a 95% CI of [0.21, 0.47]. The indirect effect on Persistence Intention was 0.32, with a 95% CI of [0.19, 0.45]. As neither confidence interval contained zero, both indirect paths were statistically significant. Moreover, after accounting for the mediating role of Social Capital, the direct effects of the Coach-Athlete Relationship on both Psychological Engagement (β\u0026thinsp;=\u0026thinsp;0.08, *p* \u0026gt; .05) and Persistence Intention (β\u0026thinsp;=\u0026thinsp;0.07, *p* \u0026gt; .05) became non-significant. This pattern of results indicates that Social Capital functioned as a \u003cb\u003ecomplete mediator\u003c/b\u003e in the relationships between the Coach-Athlete Relationship and the two outcome variables.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the results of the structural equation model testing the hypothesized relationships. The model demonstrates excellent fit to the data (χ\u0026sup2;/df\u0026thinsp;=\u0026thinsp;1.92, CFI\u0026thinsp;=\u0026thinsp;.94, TLI\u0026thinsp;=\u0026thinsp;.92, RMSEA\u0026thinsp;=\u0026thinsp;.065). All hypothesized paths are statistically significant at **\u003cem\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;.001\u003c/em\u003e. The path coefficients are standardized estimates. The model shows that the Coach-Athlete Relationship at T1 significantly predicts Social Capital at T2 (β\u0026thinsp;=\u0026thinsp;.54), which in turn significantly predicts both Psychological Engagement (β\u0026thinsp;=\u0026thinsp;.62) and Persistence Intention (β\u0026thinsp;=\u0026thinsp;.59) at T3. Control variables (age, gender, training years) were included in the model but their paths to the main variables were non-significant and are omitted from the figure for clarity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo rigorously test the mediating role of social capital, a bootstrap resampling method with 5,000 iterations was employed to assess the significance of the indirect effects. The analysis revealed that \u003cb\u003ethe indirect effect of the coach-athlete relationship on psychological engagement via social capital was 0.33, with a 95% bias-corrected confidence interval of [0.21, 0.47]\u003c/b\u003e. Simultaneously, \u003cb\u003ethe indirect effect on persistence intention through social capital was 0.32, with a 95% bias-corrected confidence interval of [0.19, 0.45]\u003c/b\u003e. Since both confidence intervals did not include zero, these results indicate that the two indirect paths were statistically significant at the *p* \u0026lt; .05 level, providing support for hypotheses H1 and H2.\u003c/p\u003e \u003cp\u003eFurthermore, the direct effects were examined. After including social capital as the mediator in the structural equation model, the direct effect of the coach-athlete relationship on psychological engagement became non-significant (\u003cem\u003eβ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.08, *p* \u0026gt; .05), and its direct effect on persistence intention was also non-significant (\u003cem\u003eβ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.07, *p* \u0026gt; .05). This pattern of results\u0026mdash;significant indirect effects alongside non-significant direct effects\u0026mdash;suggests that social capital serves as a \u003cb\u003ecomplete mediator\u003c/b\u003e in the relationships between the coach-athlete relationship and both psychological engagement and persistence intention. In other words, the positive influence of the coach-athlete relationship on the long-term development of adolescent athletes is entirely transmitted through the key psychological mechanism of building social capital within this relationship.\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\u003eResults of Bootstrap Analysis for Mediating Effects\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndirect Path\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIndirect Effect\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e95% Confidence Interval\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eConclusion\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCAR \u0026rarr; Social Capital \u0026rarr; Psychological Engagement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e[0.21, 0.47]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSignificant\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCAR \u0026rarr; Social Capital \u0026rarr; Persistence Intention\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e[0.19, 0.45]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSignificant\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003e\u003cem\u003eNote\u003c/em\u003e: N\u0026thinsp;=\u0026thinsp;215. Bootstrap sample size\u0026thinsp;=\u0026thinsp;5000. CAR\u0026thinsp;=\u0026thinsp;Coach-Athlete Relationship. SE\u0026thinsp;=\u0026thinsp;Standard Error. The indirect effect is significant at the *p* \u0026lt; .05 level if the 95% bias-corrected confidence interval does not contain zero.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Growth Trajectory Analysis of Social Capital\u003c/h2\u003e \u003cp\u003eTo further elucidate the dynamic process underlying the mediation model, we conducted a growth trajectory analysis on social capital. Participants were divided into two groups based on a median split of their T1 Coach-Athlete Relationship (CAR) scores. As depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the group with higher initial CAR levels demonstrated a steeper and more positive growth trajectory in social capital from T1 to T3 compared to the group with lower initial CAR. This finding visually reinforces the first part of our mediation hypothesis, indicating that a strong coach-athlete relationship not only predicts higher social capital but also fosters its sustained growth over time.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study, through a three-wave longitudinal design spanning 12 months, provides robust evidence that social capital serves as a key psychological mechanism through which the coach-athlete relationship influences psychological engagement and persistence intention among adolescent tennis players. This finding illuminates the intrinsic process through which relational dynamics translate into long-term developmental outcomes, offering a novel perspective for understanding and intervening in the sustained development of young athletes.\u003c/p\u003e \u003cp\u003eFirst, the study found that a positive coach-athlete relationship established at the initial stage (T1) is a crucial prerequisite for the subsequent formation (T2) of high-quality social capital. This finding aligns with relational investment theories, suggesting that coaches, by consistently demonstrating care, fulfilling commitments, and establishing effective collaboration in daily interactions, are essentially making a productive \"social investment.\" This investment is not a one-sided effort but co-constructs valuable relational resources, embodied as deep mutual trust, strong emotional bonds, and a clear, shared vision, thereby laying a solid psychosocial foundation for the athlete's subsequent development.\u003c/p\u003e \u003cp\u003eSecond, and most centrally, social capital was found to play the role of a \u003cb\u003ecomplete mediator\u003c/b\u003e between the coach-athlete relationship and the distal outcomes. This implies that the positive influence of the coach-athlete relationship is not directly \"radiated\" onto the athletes' engagement and persistence behaviors; rather, it is entirely transmitted through the crucial link of building and accumulating social capital. A merely \"good relationship\" itself is insufficient to directly sustain long-term investment and perseverance; precisely, it is the \u003cb\u003eprofound trust\u003c/b\u003e (allowing athletes to feel safe and willing to accept challenges), \u003cb\u003estrong bonds\u003c/b\u003e (providing emotional support and a sense of belonging), and \u003cb\u003eshared vision\u003c/b\u003e (giving meaning to training and striving) incubated by this high-quality relationship that collectively constitute the internal wellspring of motivation. This enables athletes to maintain high levels of psychological engagement and the willingness to persevere even when confronted with high-intensity training, fierce competition, and psychological fatigue. This mechanism strongly resonates with Self-Determination Theory (SDT); the interactive environment fostered by social capital systematically satisfies the athletes' basic psychological needs for \u003cb\u003erelatedness\u003c/b\u003e, \u003cb\u003ecompetence\u003c/b\u003e, and \u003cb\u003eautonomy\u003c/b\u003e, thereby effectively nurturing their internal motivation, which ultimately manifests as enduring persistence intention.\u003c/p\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Theoretical Contributions\u003c/h2\u003e \u003cp\u003eThis study made three key theoretical contributions: firstly, it introduced and validated social capital as a key intermediary mechanism, revealing the intrinsic process by which coach athlete relationships affect long-term outcomes, thus opening up the \"black box\" of this relationship; Secondly, a strict longitudinal design was adopted in the research methodology, which demonstrated the lagged predictive effects between variables and provided stronger evidence for quasi causal relationships between variables than cross-sectional studies; Finally, by integrating the core theory of sociology - social capital theory - with the study of coach athlete relationships in sports psychology, the research provides an explanatory interdisciplinary perspective and enriches the theoretical toolbox in this field.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Practical Implications\u003c/h2\u003e \u003cp\u003eThis study carries clear and profound practical implications for coaches, sports organizations, and parents of adolescent athletes.\u003c/p\u003e \u003cp\u003eThe practical implications of these findings advocate for a fundamental evolution in the coaching role, necessitating a shift from being primarily a \"technical instructor\" to becoming a holistic \"relational coach.\" This transformation is predicated on the recognition that proactively investing in high-quality relationships\u0026mdash;through building genuine trust, engaging in deep communication, and co-creating shared goals\u0026mdash;is of paramount importance, equaling the significance of designing and executing technical-tactical training plans. Specifically, coaching practices must be deliberately organized around the core dimensions of social capital: cultivating trust diligently by maintaining consistency and fairness; strengthening relational bonds conscientiously by showing genuine concern for the athlete's life beyond sport; and clarifying a shared vision collaboratively by ensuring mutually aligned goals and developmental pathways.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Limitations and Future Research Directions\u003c/h2\u003e \u003cp\u003eThis study has several limitations, which point to fruitful avenues for future research. First, the sample was drawn from training centers within the Chinese context; the generalizability of the findings needs to be examined across broader cultural settings (e.g., Western individualistic cultures) and different sports. Second, although the longitudinal design strengthens causal inference, it remains correlational in nature. Future research could employ more causal methods such as \u003cb\u003eexperimental interventions\u003c/b\u003e\u0026mdash;for instance, designing and implementing \"Social Capital Building Training Programs for Coaches\" and testing their efficacy through randomized controlled trials. Finally, future models could explore other potential mediating variables (e.g., mental toughness, athletic identity) or important moderating variables (e.g., parental support, peer climate, athlete personality) to build a more comprehensive and nuanced model of athlete development.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis study, through a 12-month longitudinal empirical investigation, systematically uncovers and validates the underlying mechanism through which the coach-athlete relationship influences adolescent tennis players' psychological engagement and persistence intention. The central conclusion demonstrates that within youth tennis, the high-quality relationship established between coaches and athletes does not directly impact the outcome variables. Instead, its positive effect is \u003cb\u003eindirectly yet powerfully facilitated through the systematic construction and accumulation of social capital\u003c/b\u003e\u0026mdash;a process profoundly embodied as \u003cb\u003edeep trust\u003c/b\u003e, \u003cb\u003estrong relational bonds\u003c/b\u003e, and a \u003cb\u003eclear shared vision\u003c/b\u003e. Social capital serves as an indispensable complete mediator, acting as a \"converter\" that transforms positive relational interactions into athletes' enduring internal motivation and commitment.\u003c/p\u003e \u003cp\u003eConsequently, the findings of this study strongly advocate that fostering coaches' capacity to recognize, build, and maintain social capital should no longer be viewed as a soft or supplementary coaching skill. Rather, it must be formally recognized as \u003cb\u003ea crucial strategic investment within the talent development systems for youth elite sports\u003c/b\u003e. This necessitates that sports organizations, in their processes of coach selection, training, and performance evaluation, look beyond traditional technical and tactical competencies and integrate the ability to build high-quality relationships and foster social capital into the core assessment framework. By empowering coaches to become \"relationship architects\" and \"social capital cultivators,\" we can more effectively cultivate a new generation of athletes who are not only technically proficient but also psychologically resilient and capable of sustainable long-term development.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eEthical Approval:\u003c/h2\u003e\n\u003cp\u003eThis study was reviewed and approved by the Institutional Review Board of Pu\u0026rsquo;er University. All procedures performed in this study involving human participants were in accordance with the ethical standards of the Declaration of Helsinki. Written informed consent was obtained from all individual participants and their parents or legal guardians prior to the study.\u003c/p\u003e\n\u003ch2\u003eCompeting Interests:\u003c/h2\u003e\n\u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003ch2\u003eFunding :\u003c/h2\u003e\n\u003cp\u003eNo funding support\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\n\u003cp\u003eC. wrote the main manuscript text and contributed to the study conception and design. Y. prepared figures and critically revised the manuscript and helped to realize the final draft. C.Y. performed investigation, data extraction and validated the analytical methods.All authors reviewed the manuscript\u003c/p\u003e\n\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eThe questionnaire data that support the findings of this study are available from the corresponding author, Zhaoyuan Chen, upon reasonable request. However, restrictions apply to the availability of these data, which were collected under ethical approval and participant consent agreements that protect the privacy of the minor athletes involved. Data are therefore not publicly available but can be accessed for verification or further analysis under conditions compliant with the original ethical approval and with the permission of the research team.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMartinent G, Louvet B, Decret J. Longitudinal trajectories of athlete burnout among young table tennis players: A 3-wave study[J]. Journal of Sport and Health Science, 2020, 9(4):367-375.\u003c/li\u003e\n\u003cli\u003eIchimura S, Kawakita H, Okada H, et al. A Review of the research in the coach-athlete psychological relationship:[J]. The Japan Journal of Coaching Studies, 2019, 33(1):13-20.\u003c/li\u003e\n\u003cli\u003eM M W, S B H, Jody L, et al. Coaches\u0026rsquo; impact on youth athletes\u0026rsquo; intentions to continue sport participation: The mediational influence of the coach\u0026ndash;athlete relationship[J]. International Journal of Sports Science \u0026amp; Coaching, 2021, 16(3):490-499.\u003c/li\u003e\n\u003cli\u003eScience - Social Science; Study Results from Kyonggi University Provide New Insights into Social Science (Coach-autonomy support and youth sport team efficacy mediated by coach-athlete relationship)[J]. Science Letter, 2020.\u003c/li\u003e\n\u003cli\u003eFenghui F, Jinyu C, Yunting C, et al. How relationship-maintenance strategies influence athlete burnout: Mediating roles of coach\u0026ndash;athlete relationship and basic psychological needs satisfaction [J]. Frontiers in Psychology, 2023, 13:1104143.\u003c/li\u003e\n\u003cli\u003ePreston J A, Rew L, Spees J. Social Determinants of Health and Psychological Capital Among Youth Experiencing Homelessness[J]. Western journal of nursing research, 2024, 1939459241253150.\u003c/li\u003e\n\u003cli\u003eChristine H, Stacy W, David W. The Impact of Athlete Culture and Coach Connections on Athlete Help-Seeking Intentions[J]. JOURNAL OF SPORT \u0026amp; EXERCISE PSYCHOLOGY, 2020, 42:S82.\u003c/li\u003e\n\u003cli\u003eFraser C, Mackenzie B, Steven J F, et al. Behaviors and Actions of the Strength and Conditioning Coach in Fostering a Positive Coach-Athlete Relationship[J]. Journal of Strength and Conditioning Research, 2021.\u003c/li\u003e\n\u003cli\u003eDario N, Filip S, Anđela E D. Connection between Social Capital and Sport Success of Young Tennis Players[J]. Social Sciences, 2020, 9(11):206.\u003c/li\u003e\n\u003cli\u003eAhmad M M I, Rizwan M S, Nadir H, et al. Social capital and social well-being among youth: Does self-efficacy moderate the relationship?[J]. Journal of Human Behavior in the Social Environment, 2024, 34(2):193-209.\u003c/li\u003e\n\u003cli\u003eSonja G, Alina S, Brit H, et al. Sexual Violence and the Coach\u0026ndash;Athlete Relationship\u0026mdash;a Scoping Review From Sport Sociological and Sport Psychological Perspectives [J]. Frontiers in Sports and Active Living, 2021, 3:643707.\u003c/li\u003e\n\u003cli\u003eJingfei W, Carlos M C, Jonathan B O. Examining the psychometric properties of the Coach-Athlete Relationship Questionnaire (CART-Q) with basketball players in China and Spain [J]. Frontiers in Psychology, 2023, 14:1273606.\u003c/li\u003e\n\u003cli\u003eA. S S, M. C H, A. C A. Congruence of efficacy beliefs on the coach-athlete relationship and athlete anxiety: Athlete self-efficacy and coach estimation of athlete self-efficacy[J]. Psychology of Sport \u0026amp; Exercise, 2022, 58.\u003c/li\u003e\n\u003cli\u003eMichał L. Clash of sports organization cultures: Differences in table tennis training and coach\u0026ndash;athlete relationships between China and Poland[J]. International Journal of Sports Science \u0026amp; Coaching, 2023, 18(1):46-56.\u003c/li\u003e\n\u003cli\u003eJie L, Beibei C, Yu Z. Adopting Evaluative Conditioning to Improve Coach\u0026ndash;Athlete Relationships [J]. Frontiers in Psychology, 2021, 12:751990.\u003c/li\u003e\n\u003cli\u003eKorkeila H, Hamari J. Avatar capital: The relationships between player orientation and their avatar\u0026apos;s social, symbolic, economic and cultural capital[J]. Computers in Human Behavior, 2020, 102:214-21.\u003c/li\u003e\n\u003cli\u003eMikaela P, A. G B, Cathrin L D. Building Successful Coach-Athlete Relationships Using Interpersonal Skills and Emotional Intelligence[J]. JOURNAL OF SPORT \u0026amp; EXERCISE PSYCHOLOGY, 2021, 43:S83.\u003c/li\u003e\n\u003cli\u003eJ. L O, Valentina M. Transnational peer relationships as social capital: mobile migrant youth between Ghana and Germany[J]. Journal of Youth Studies, 2022, 25(3):344-361.\u003c/li\u003e\n\u003cli\u003ePeter K, Kerstin S, Stefan B, et al. Acute Tennis Injuries in the Recreational Tennis Player[J]. Orthopaedic Journal of Sports Medicine, 2021, 9(1):2325967120973672.\u003c/li\u003e\n\u003cli\u003eSarah L, Matthew V, J. L M. Coach perceptions of the social environment in recreational youth sport[J]. INTERNATIONAL JOURNAL OF SPORT PSYCHOLOGY, 2020, 51(3):197-220.\u003c/li\u003e\n\u003cli\u003ePreston C, Allan V, Wolman L, et al. The Coach\u0026ndash;Parent Relationship and Athlete Development in Elite Youth Hockey: Lessons Learned for Conflict Management[J]. The Sport Psychologist, 2020, 34(2):143-152.\u003c/li\u003e\n\u003cli\u003eGabana T N, Wong J Y, D\u0026rsquo;Addario A, et al. The Athlete Gratitude Group (TAGG): Effects of coach participation in a positive psychology intervention with youth athletes[J]. Journal of Applied Sport Psychology, 2020, 34(2):1-34.\u003c/li\u003e\n\u003cli\u003ePoucher A Z, Bissett E J, Tamminen A K. Development of a Webinar for Sport Coaches: Suggested Best Practices for Supporting Athletes[J]. Journal of Sport Psychology in Action, 2020, 12(2):1-14.\u003c/li\u003e\n\u003cli\u003eMartin K, Jonas S, Markus G. Pay attention! The influence of coach-, content-, and player-related factors on focus of attention statements during tennis training.[J]. European journal of sport science, 2022, 23(6):11-17.\u003c/li\u003e\n\u003cli\u003eHiginio G G, Guillaume M. Relationships between perceived coach leadership, athletes\u0026rsquo; use of coping and emotions among competitive table tennis players[J]. European Journal of Sport Science, 2020, 20(8):1113-1123.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Social capital, Coach athlete relationship, Psychological investment, Persist in the will, Longitudinal study, Youth Tennis","lastPublishedDoi":"10.21203/rs.3.rs-8150403/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8150403/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eObjective\u003c/h2\u003e \u003cp\u003eThis study aims to explore how social capital formed in coach athlete relationships (CAR) affects the psychological investment and long-term persistence willingness of adolescent tennis players through a 12-month longitudinal study.\u003c/p\u003e\u003ch2\u003eMethod\u003c/h2\u003e \u003cp\u003eA questionnaire survey was conducted on 215 competitive young tennis players aged 12\u0026ndash;18 at three time points (baseline, 6 months, 12 months). We used structural equation modeling to examine the mediating role of social capital centered on relationship bonds, trust, and shared vision in the relationship between coach athlete relationships and psychological investment and persistence.\u003c/p\u003e\u003ch2\u003eResult\u003c/h2\u003e \u003cp\u003eLongitudinal analysis shows that: (1) the quality of coach athlete relationship at T1 time can significantly positively predict social capital at T2 time; (2) Social capital at T2 time can significantly positively predict psychological investment and persistence willingness at T3 time; (3) Social capital plays a fully mediating role between coach athlete relationships and psychological investment/persistence willingness. The influence of control variables (age, gender, training years) is not significant.\u003c/p\u003e\u003ch2\u003eConclusion\u003c/h2\u003e \u003cp\u003eThis study reveals that the coach athlete relationship is established through the key mechanism of building social capital to maintain the psychological investment and persistence willingness of adolescent athletes in the long term. This emphasizes that in youth sports training, coaches should consciously invest in elements related to social capital, rather than just technical and tactical guidance.\u003c/p\u003e","manuscriptTitle":"Social capital in coach-athlete relationships: A longitudinal study on psychological commitment and persistence intention of junior tennis players","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-28 16:59:27","doi":"10.21203/rs.3.rs-8150403/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-05-10T18:09:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"122488588153171508313040216236023045835","date":"2026-04-23T11:13:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"202223573352605804885359756982689747389","date":"2026-04-20T10:36:25+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-20T08:55:55+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-20T08:53:53+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-12-15T06:31:30+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-08T07:13:33+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-12-08T07:05:57+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"18c07324-1875-40f6-aa48-9c86f0e93b9d","owner":[],"postedDate":"April 28th, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-10T18:09:41+00:00","index":98,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":66877454,"name":"Health sciences/Health care"},{"id":66877455,"name":"Biological sciences/Psychology"},{"id":66877456,"name":"Social science/Psychology"}],"tags":[],"updatedAt":"2026-04-28T16:59:27+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-28 16:59:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8150403","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8150403","identity":"rs-8150403","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}