The Effect of Social Support on Adolescent Athletes Engagement: Self-Efficacy and Mental Toughness of the Chain Mediated Effects

The Effect of Social Support on Adolescent Athletes Engagement: Self-Efficacy and Mental Toughness of the Chain Mediated Effects | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article The Effect of Social Support on Adolescent Athletes Engagement: Self-Efficacy and Mental Toughness of the Chain Mediated Effects Pukui Wang, Chenge Shi, Jun Chen, Zewen Wang, Xiang Gao, Yongzhao Fan, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3839312/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Feb, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract To explore the relationship between social support and adolescent athlete engagement and the role of self-efficacy and mental toughness in this relationship. A convenience sampling method was used to administer the athletes' received social support questionnaire, general self-efficacy scale, mental toughness inventory, and athletic engagement questionnaire to adolescent athletes in seven youth sports schools in China, and 513 valid questionnaires were collected. 1) After controlling for the effects of adolescent athlete age and sport level, regression analyses revealed that social support positively predicted adolescent athlete engagement; 2) Self-efficacy and mental toughness mediated the relationship between social support and adolescent athlete engagement, and this mediation consisted of three pathways: parallel mediation of both self-efficacy and mental toughness, and chain mediation of both self-efficacy and mental toughness. The mediating effects model constructed in this study can inform the promotion of youth athlete engagement levels, which can be crucial for improving youth athlete engagement in the future by enriching youth athletes' social support networks, enhancing self-efficacy, and developing mental toughness levels. Health sciences/Health care/Occupational health Biological sciences/Psychology/Human behaviour adolescent athletes social support athlete engagement self-efficacy mental toughness Figures Figure 1 Figure 2 Introduction Engagement is one of the core concepts in the field of positive psychology. It refers to the sustained mental state of an individual filled with positive emotions. It is an essential factor in influencing an individual's behavioral performance and the direction of behavioral development 1 . Lonsdale et al. 2 , 3 first introduced the concept of athlete engagement in the field of competitive sport, which is characterized by self-confidence (belief in one's ability to achieve a high level of performance and desired goals), dedication (desire to invest energy and time in the achievement of personally important goals), vitality (a state of feeling of being physically and psychologically energized), and enthusiasm (the experience of a strong sense of arousal and pleasure). Athlete engagement is an important indicator of athletes' positive psychology, which can reflect athletes' positive and healthy psychological state, and is conducive to stimulating athletes' positive qualities such as optimism, perseverance, creativity, etc., so as to effectively promote the development and maturity of athletes, and to lay a solid foundation for them to enhance their athletic ability and to improve their athletic performance 4 . Comprehensively exploring the factors affecting athlete engagement helps to scientifically and systematically grasp the changes and developmental laws of athlete engagement. It provides theoretical references for stimulating athletes' potential and improving sports performance. External factors such as group cohesion 4 , motivational climate 5 , and coach-athlete relationship 6 and internal factors such as perfectionism 7 , basic psychological needs 8 , and self-concept 9 are essential factors influencing athlete engagement. In addition, work and learning engagement studies have demonstrated that social support is a significant predictor of individual engagement 10 . Adolescent athletes are an important reserve resource for the sustainable development of a country's sports. At the same time, young athletes are a particular group. On the one hand, adolescent athletes are in a high-intensity training environment for a long time and must withstand many external pressures, such as coaches' harshness and external expectations. On the other hand, young athletes are in a sensitive period of sports level and physical and mental development, which is a critical stage to improve sports performance and become elite athletes 11 . Therefore, this study explores the effects of social support on adolescent athletes' engagement with adolescent athletes as subjects. Based on this, it explores the internal mechanism of action of athlete engagement, aiming to provide a valuable reference basis for adolescent athletes' engagement intervention practice. Social support refers to the moral and material comfort, care, respect, and help given to an individual by various social parties such as family, relatives, and friends 10 . Athletes, as a high-pressure group, are constantly exposed to stressors such as training, competition, injuries, etc. They experience a higher sense of belonging and security when they have more social support. They can receive adequate advice and guidance from others to improve their athletic skills, competence, and confidence 4 . A study of Olympic athletes shows that high levels of social support are necessary for athletes on the road to success 12 . Athletes' perceived social support can be categorized in terms of type into emotional support (meaning that others accompany and care for the individual to enhance his or her sense of security and comfort), respectful support (which is when others help the individual to enhance his sense of competence and self-esteem), informational support (which means that others provide the individual with advice and guidance on relevant issues), and tangible support (which refers to substantial help such as money, services, and sharing of responsibilities) 12 . Social support can be categorized as coaching, parental, and peer support 13 . Coaches are recognized as the primary providers of social support for athletes, and their social support is critical to their growth and development 12 . Improving the support provided by coaches may help create a harmonious sporting environment, allowing for quicker allocation of resources and an improved sporting experience for athletes 14 . Parental encouragement and the level of emotional and respectful support shown to adolescent athletes can effectively mitigate the negative effects of stressors present in the athletic environment on self-confidence and athletic performance 15 . Peer support promotes positive emotions, reduces mental fatigue, and enhances athlete engagement during athletic training and competition 16 . Based on this, this research proposes hypothesis H1: Social support can positively predicts adolescent athlete engagement. Self-efficacy refers to an individual's assumptions and judgments about their ability to perform a behavior 17 . Typically, the more robust an individual's sense of self-efficacy and outcome expectations, the more likely they are to start and persist in a particular activity 18 . Self-efficacy is a crucial psychological factor for athletes. Athletes encounter a variety of pressures at any time during training and competition, and how to properly understand each other and master effective solutions depends on the level of individual self-efficacy 19 . From the self-efficacy perspective, a positive subjective assessment of an individual can impact the level of interest and commitment to engage in a specific activity, which can play a decisive role in determining an individual's behavioral choices 20 . During exercise, individuals with higher self-efficacy make a subjective assessment of their effectiveness in accomplishing the activity prior to the action, and this pre-estimation has a significant impact on regulating the athlete's mood and facilitating commitment to the game 21 . In addition, obtaining more social support can promote adolescents' self-efficacy, and social support can positively and positively influence self-efficacy 22 . According to self-efficacy theory, social persuasion, vicarious experience, and emotional state are the main factors that affect an individual's self-efficacy 17 . Social support can help individuals experience more success and thus increase self-efficacy 23 . In the process of training or competition, coaches' encouragement and guidance to the athletes play a function of social persuasion to a certain extent. The training feelings, experience sharing, and communication among peers help form the athletes' alternative experiences, and parents' support and understanding of the athletes' participation in training can help enhance the athletes' emotional state of participation in training. In other words, a favorable social supportive environment can help individuals improve their confidence in training and competing and improve athletes' self-efficacy. Based on this, this research proposes hypothesis H2: Self-efficacy plays a mediation role between social support and athlete engagement. Psychological resilience is the ability or trait of an individual to cope with adverse life events such as stress, frustration, and trauma 24 . Athletes need mental toughness to achieve athletic excellence in training and competition 25 . Because of this, mental toughness is viewed by athletes, coaches, and researchers in athlete psychology as one of the most important psychological traits for athletes to be successful in competition 26 . On the one hand, mental toughness is significantly and positively correlated with an individual's athletic performance, with athletes high in mental toughness participating at higher levels of competition, having better performances in competitions, and achieving more success 27 . Athletes with high mental toughness have higher control beliefs about stressful situations, tend to evaluate stressors as challenges rather than threats, have higher coping efficacy, and adopt more coping strategies focused on solving realistic problems 28 . On the other hand, athletes with high mental toughness are less likely to experience negative emotions. A longitudinal follow-up study of adolescent athletes showed that mental toughness effectively reduced physiological and emotional exhaustion, reduced mental fatigue overall, and demonstrated sustained impact effects 29 . In addition to the protective effects in stressful situations, relevant studies have found that mental toughness has significant gainful functions, such as attentional control, goal orientation, and fluency states 30 . Athletes with high mental toughness make more positive and accurate cognitive evaluations of the individual and engage in a more proactive attitude toward training and competition 31 . At the same time, an individual's level of mental toughness is not static. In addition to innate genetic factors, enhancement through later life is equally important. Previous research has shown that social support is essential to mental toughness 32 . Comprehensive and diversified social support is of great relevance in improving athletes' mental toughness 33 , increasing athletes' problem-solving strategies, but also by decreasing athletes' risk appraisal of adversity 34 . Based on this, this research proposes hypothesis H3: Mental toughness mediates between social support and athlete engagement. Related research has confirmed that self-efficacy significantly predicts levels of mental toughness 35 . A high level of self-efficacy helps individuals cope with stress and frustration with good mental toughness, thus developing a sound personality and forming a healthy psychology 36 . A study of elite marathon runners showed that self-efficacy was closely related to mental toughness, with athletes with higher efficacy having better mental toughness 37 . According to the Goal-Expectation-Self-Control model, self-efficacy is considered an essential component of psychological resilience 38 , and many studies have demonstrated its contribution to psychological resilience 39 . An individual with a high sense of self-efficacy will inspire greater confidence and courage to face adversity or setbacks and face changes in the environment with a positive attitude. Because of this, individuals with a high sense of self-efficacy can further increase their level of mental toughness as they proactively cope with a variety of problems 40 . The relationship between self-efficacy and mental toughness is perhaps related to endogenous opioid activation 41 . Related studies have noted that endogenous opioids relieve pain, self-efficacy can cause endogenous opioid activation and mental toughness is associated with pain tolerance. Athletes may experience higher levels of mental toughness because they have a stronger sense of self-efficacy to relieve pain through the body's endocrine system 42 . Based on this, this research proposes hypothesis H4: Self-efficacy and mental toughness mediate between social support and athlete engagement. The hypothesized model of this study is shown in Fig. 1 . Methods Participants and procedure This study adopted a convenience sampling method, tested collectively on a group basis in schools, youth athletes from 7 sports schools (2 in Beijing, 2 in Guangdong Province, 1 in Fujian Province, 1 in Henan Province, and 1 in Hubei Province) were selected for the survey. A total of 541 questionnaires were distributed, and 537 questionnaires were collected. After excluding invalid questionnaires such as regular responses, incomplete demographic information, and missing options, 513 valid questionnaires remained, with a validity rate of 95.5%. The demographic information of the study population is shown in Table 1 . Table 1 Participants' demographic information(N = 513) Characteristics Category Sample Size Percentage Gender Male 264 51.46% Female 249 48.54% Age Sixteen years old 94 18.32% Seventeen years old 90 17.55% Eighteen years old 150 29.24% Nineteen years old 179 34.89% Sports Level National elite athletes 47 9.16% National first-level athletes 146 28.46% National second-level athletes 197 38.40% Others 123 23.98% Game Basketball 244 47.56% Football 121 23.59% Volleyball 96 18.71% Others 52 10.14% Research tools Athletes Received Social Support Questionnaire(ARSQ) Adopted the Athletes Received Social Support Questionnaire by Freeman et al., 43 , which consists of 22 items and includes 4 dimensions: emotional support, respectful support, informational support, and tangible support. Using a 5-point Likert scale, with 1 representing "completely non-compliant" and 5 representing "completely compliant", the higher the score, the higher the social support the adolescent athlete receives. In this study, the Cronbanch's α coefficient of the scale was 0.926. The Cronbanch's α coefficients of the three dimensions of family support, friend support, and other support were 0.869, 0.905, and 0.871, respectively, and the factor loadings of each item ranged from 0.771 to 0.878., Validated factor analysis fit index: χ 2 / df = 3.819, RMR = 0.024, RMSEA = 0.074, GFI = 0.940, TLI = 0.956, and the structural validity of the scale was favorable 44 . General Self-Efficacy Scale(GSES) They have adopted the General Self-Efficacy Scale developed by Schwarzer et al., 45 , which consists of 10 items and is scored on a 5-point Likert scale, with 1 being " completely non-compliant" and 5 being "completely compliant". The higher the score, the better the self-efficacy of the adolescent athletes. In this study, the Cronbanch's α coefficient of the scale was 0.890, the factor loadings of each item ranged from 0.715 to 0.899, and the fit indices of the validated factor analysis were χ 2 / df = 2.533, RMR = 0.016, RMSEA = 0.069, GFI = 0.964, TLI = 0.964, and TLI = 0.964, respectively., TLI = 0.966, the scale has favorable structural validity 44 . Mental Toughness Inventory(MTI) It adopted the Mental Toughness Inventory developed by Gucciardi et al., 46 , which consists of 8 items. It is scored on a 5-point Likert scale, with 1 being " complete non-compliance" and 5 being "complete compliance", with higher scores representing higher levels of mental toughness in adolescent athletes. In this study, the scale Cronbanch's α coefficient was 0.924, the factor loadings of each question item ranged from 0.827 to 0.896, and the fit indices of the validated factor analysis: χ 2 / df = 3.667, RMR = 0.020, RMSEA = 0.079, GFI = 0.943, TLI = 0.954, the scale has favorable structural validity 44 . Athlete Engagement Questionnaire(AEQ) Adopted was the Athlete Engagement Questionnaire developed by Lonsdale et al., 2 a 16-item questionnaire comprising four dimensions: confidence, commitment, energy, and enthusiasm. The questionnaire is scored on a 5-point Likert scale, with 1 being " completely non-compliant" and 5 being "completely compliant", with higher scores representing higher levels of engagement in adolescent athletes. In this study, the Cronbach's α coefficient of the scale was 0.934. The Cronbach's α coefficients of the three dimensions of family support, friend support, and other support were 0.871, 0.912, and 0.886, respectively, and the factor loadings of the items ranged from 0.800 to 0.893., Validated factor analysis fit index: χ 2 / df = 3.573, RMR = 0.022, RMSEA = 0.065, GFI = 0.932, TLI = 0.944, and the structural validity of the scale was favorable 44 . Research methods AMOS 26.0 software was used to calculate the model fitting index of the scale in the study, and SPSS 26.0 was used for common method bias testing, descriptive statistics, and Pearson correlation analysis. SPSS macro program PROCESS 4.2, developed by Hayes, was used for mediation and chain mediation effects analysis 47 . Model 6 of 92 typical models provided by Hayes was selected for analysis. The bootstrap method was used (repeated sampling 5000 times). P<0.05 was set to represent the statistical result with significance. Ethics statement The study was conduct in accordance with the Declaration of Helsinki and approved by the Human Research Ethics Committee of Capital university of Physical Education and Sports. All participants agreed to participate in this research voluntarily; they provided informed consent when they completed the suevey and were able to withdraw from the study freely at any time. In addition, our data were anonymizd to ensure the privacy of all participants. Result Common Method Bias Testing All questionnaires were filled in anonymously for the empirical procedure, while Harman's one-way test was used for testing. KMO test and Bartlett's test of sphericity were performed on the data, and the results showed KMO = 0.897 and Bartlett's test of sphericity χ 2 = 8526.193, df = 351, P 1 were extracted, and the explained variance of the first factor was 23.512%, which is less than the criterion of 40% critical value. Thus, this can indicate that there is no standard severe method bias in the data of this study 48 . Descriptive statistics and correlation analysis The results of the correlation analysis showed (Table 2 ) that there was no significant correlation between the demographic variables of gender and sports and the 4 research variables. Therefore, the 2 demographic variables of gender and sports were no longer considered in the mediation and chained mediation effect analyses. Instead, age and sport level were correlated with the research variables, so they were included as control variables in the model in the subsequent mediation and chained mediation effect analyses. Meanwhile, significant positive correlations existed between the 4 research variables of social support, athlete engagement, self-efficacy, and mental toughness. Table 2 Descriptive Statistics and Correlation Analysis of Variables Variables M ± SD 1 2 3 4 5 6 7 1. SS 4.10 ± 0.68 2. AE 4.18 ± 0.57 0.61 *** 3. S-E 3.76 ± 0.63 0.44 *** 0.52 *** 4. MT 3.55 ± 0.46 0.29 ** 0.40 *** 0.45 *** 5. Gender a 0.09 0.06 0.06 0.02 6. Age b 0.32 ** 0.37 ** 0.40 *** 0.26 ** 0.14 * 7. SL c 0.38 *** 0.25 ** 0.44 *** 0.31 ** 0.24 ** 0.20 ** 8. Game d 0.12 * 0.05 0.10 * 0.09 0.06 0.09 0.13 * Note: N = 513, SS: Social Support; AE: Athlete Engagement; S-E: Self-Efficacy; MT: Mental Toughness; SL: Sports Level; a: gender is a dummy variable, with 1 for boys and 2 for girls; b: age is a dummy variable, with 1 for sixteen years old, 2 for seventeen years old, 3 for eighteen years old and 4 for nineteen years old; c: sports level is a dummy variable, with 1 for national elite athletes, 2 for national first-level athletes, 3 for national second-level athletes and 4 for others. d: the game is a dummy variable, with 1 for Basketball, 2 for Football, 3 for Volleyball, and 4 for Others, * P < 0.05, * * P < 0.01, * * * P < 0.001; same below. Mediation and chain mediation effects analysis Social support was analyzed as the independent variable, athlete engagement as the dependent variable, and self-efficacy and mental toughness as the mediating variables for mediation and chain mediation effects. The results showed (Table 3 ): that social support had a positive predictive effect on athlete engagement ( β = 0.192, P < 0.001); social support had a positive predictive effect on self-efficacy ( β = 0.177, P < 0.001); social support had a positive predictive effect on mental toughness ( β = 0.146, P < 0.001); self-efficacy had a positive predictive effect on athlete engagement ( β = 0.423, P < 0.001); self-efficacy was a positive predictor of mental toughness ( β = 0.318, P < 0.001); and mental toughness was a positive predictor of athlete engagement ( β = 0.191, P < 0.001). Table 3 Regression Analysis of a Chain Mediated Model of the Relationship Between Social Support and Athlete Engagement Variable S-E MT AE β SE t β SE t β SE t Age b 0.047 0.443 1.005 -0.338 0.682 -0.491 -0.067 0.072 -1.010 SL c 0.345 0.078 9.488 *** 0.446 0.357 -2.997 1.336 0.618 5.256 *** SS 0.177 0.018 9.679 *** 0.146 0.014 7.707 *** 0.192 0.012 15.705 *** S-E 0.318 0.032 9.971 *** 0.423 0.044 9.192 *** MT 0.191 0.838 8.868 *** R 2 = 0.191 R 2 = 0.267 R 2 = 0.627 F = 93.689 *** F = 72.391 *** F = 222.556 *** Note: N = 513, SS: Social Support; AE: Athlete Engagement; S-E: Self-Efficacy; MT: Mental Toughness; SL: Sports Level; b: age is a dummy variable, with 1 for sixteen years old, 2 for seventeen years old, 3 for eighteen years old and 4 for nineteen years old; c: sports level is a dummy variable, with 1 for national elite athletes, 2 for national first-level athletes, 3 for national second-level athletes and 4 for others The mediated effects test showed that the direct effect size of social support on athlete engagement was 0.192 (95% CI=[0.168,0.216]), accounting for 62.75% of the total effect size. Therefore, hypothesis H1 was tested; social support affected athlete engagement through self-efficacy with a mediated effect size of 0.075 (95% CI=[0.377,0.745]), accounting for 24.51% of the total effect size. Therefore, hypothesis H2 was tested; social support influenced athlete engagement through mental toughness, with a mediated effect size of 0.028 (95% CI=[0.006,0.058]), accounting for 9.15% of the total effect size. Therefore, hypothesis H3 was tested; social support influenced athlete engagement through the chain mediation of self-efficacy and mental toughness, with a mediated effect size of 0.011 (95% CI=[0.003,0.101]), accounting for 3.59% of the total effect size. Therefore, hypothesis H4 was tested. Specific results are shown in Table 4 and Fig. 2 . Table 4 Chain Mediated Effect Test of Self-Efficacy and Mental Toughness on Social Support and Athlete Engagement Path Standardizedβ Boot SE 95%CI 下限 上限 SS→AE 0.192 0.012 0.168 0.216 SS→S-E→AE 0.075 0.009 0.377 0.745 SS→MT→AE 0.028 0.002 0.006 0.058 SS→S-E→MT→AE 0.011 0.003 0.003 0.101 Total Effect 0.306 0.013 0.229 0.279 Indirect Total Effect 0.114 0.018 0.045 0.080 Discussion The relationship between social support and athlete engagement Athletes' training engagement status is closely related to their skill level, competitive performance, mental health, personality traits, etc. Enhancing athletes' training engagement will lay a solid foundation for their professional sports career and life development 49 . The results of this study show that social support is positively related to adolescent athlete engagement and significantly and positively predicts athlete engagement after controlling for demographic variables. The results suggest that as an essential external resource, social support can significantly enhance athlete engagement and motivate them to devote themselves to training and competition with enthusiasm, vigor, confidence, and conviction, consistent with previous research findings 12 . The social environment is not only an essential source of stress but also provides resources that can be utilized for the survival and development of the individual. External support is critical for high-pressure groups such as athletes, and its abundance will directly impact the athlete's engagement and performance 50 . Coaches with solid professional knowledge and skills-rich experience in training and competition can effectively improve athletes' motivation to participate in training, promote athletes to train hard, and improve athletes' state of engagement 5 . Social cognitive theory indicates that peer role modeling helps to facilitate the acquisition and occurrence of individual behaviors 51 . Athletes enhance their affective performance in training by modeling their participation after their peers' excellent performance during the training process. At the same time, peer motivation and support can help athletes form a healthy and positive attitude toward sports training, enhance training effort and persistence, and promote the level of training engagement 16 . Related studies have found that parents or guardians are just as important in supporting, guiding, and supervising adolescent athletes as they are coaches 52 . Parents' sports beliefs, perceptions, and behaviors can affect adolescent athletes' training status and effectiveness. Therefore, enhancing the level of social support for adolescent athletes is one of the most important ways to promote the improvement of their engagement status. The mediation effect of self-efficacy and mental toughness This study found that self-efficacy mediated the relationship between social support and adolescent athlete engagement. First, in the first part of the mediation pathway, the present study found that social support positively predicted athletes' self-efficacy. This finding extends the primary effects model and resource conservation theory of social support. This is because social support, as an essential psychological resource for individuals, enhances athletes' sports experience, relieves training and competition anxiety, and helps individuals maintain positive emotions 23 . Individuals with high self-efficacy are usually oriented towards accomplishing the tasks they set out to do in their studies and work, and their perceived social support is mainly used to complete the task successfully 53 . Adolescent athletes feel support, encouragement, and understanding from coaches, peers, and parents in daily training and life. They become more confident in accomplishing their training tasks and goals, enhancing their sense of sports efficacy. Then, in the second half of the mediation pathway, this study found that self-efficacy significantly increased athletes' training engagement. This result is consistent with previous research 21 and supports the self-efficacy theory 17 . Self-efficacy influences an individual's level of effort, persistence, and resilience during behavior, which in turn influences the individual's level of engagement 53 . Athletes with higher self-efficacy who face adversity, frustration, and failure in sports and engage in challenging tasks will exert more significant effort and persevere until they reach their goals, promoting the level of engagement in behavioral activities. In addition, related studies have found that students' self-efficacy influences cognitive judgments of learning tasks and determines persistence and motivation in learning activities. The higher the student's efficacy to learn, the higher the level of engagement toward learning. Adolescent athletes with high self-efficacy make more accurate cognitive judgments about training and competition tasks, can cope with various pressures more flexibly, and have higher confidence in accomplishing the tasks, thus showing a higher state of engagement. This study found that social support positively predicts adolescent athlete engagement through mental toughness. Positive psychology suggests that genetic factors do not solely determine personality and remain static but constantly change due to the combined influence of physiological mechanisms, external behaviors, and the social environment 54 . Early developmental models state that mental toughness in individuals requires experiencing a severe traumatic event or natural disaster and recovering from adversity 55 . However, as researchers continue to explore, it has been found that personal abilities such as physical fitness, intelligence, and social skills, as well as protective factors such as interpersonal and self-control, also significantly influence an individual's mental toughness 56 . According to the positive emotion broadening construct theory, a favorable social network can help individuals better perceive and utilize supportive social resources 57 . Adolescent athletes can experience more respect, encouragement, and trust in a higher social support environment. These resources can help adolescent athletes cope with the pressure of training and competition, help them overcome difficulties and setbacks, and hone their will in the process, making athletes more determined to participate in sports training and competition and significantly improve their mental toughness. Athletes' mental toughness encompasses a variety of positive psychological qualities, such as perseverance, self-confidence, and self-control, which respectively reflect athletes' persistent pursuit of goals, total confidence in themselves, and effective control of emotions 58 . These adaptive psychological strengths help athletes form a positive mental cognitive model to transform and digest the adverse effects of negative events in training and life promptly 59 , for example, treating the stress encountered in training as an opportunity to identify and solve problems. This positive emotional cognition helps athletes suppress psychological fear, eliminate negative thinking, stimulate positive emotions, and enhance adaptive ability, which prompts young athletes to be more actively involved in sports training, and the level of sports engagement has been significantly increased. Social support positively predicts chain mediation of adolescent athlete engagement The present study found that social support can influence adolescent athlete engagement through the chain-mediated effects of self-efficacy and mental toughness. Based on previous theories and perspectives and following the process orientation concept, the study hypothesized that social support indirectly affects the engagement level of adolescent athletes through self-efficacy and mental toughness in a sequential manner, and the results of the present study confirmed the reasonableness of this hypothesis. Social cognitive theory suggests that individuals are subjective and increase their self-efficacy by actively seeking support and help from others 60 . Social support influences the internal mechanism of self-efficacy for adolescent athletes can be explained from the perspective of social cognitive theory, in which adolescent athletes receive support and assistance from coaches, peers, and parents, which helps to optimize the athlete's sense of competence, effort, and control, among others, and significantly enhances the adolescent athlete's sense of self-efficacy. The meta-theory of psychological resilience suggests that social stressors and protective factors interact to determine whether an individual can maintain internal homeostasis, that social practices may disrupt an individual's internal homeostasis, and that an individual needs to cope with the challenge by restructuring their mental state to develop a higher level of adaptation, namely resilience restructuring 61 . According to the goal-expectation-self-control model, self-efficacy is crucial for resilience reorganization 38 . The results of the present study confirm that self-efficacy is a good protective factor for mental toughness in adolescent athletes and contributes to the promotion of resilience reorganization in athletes. The results of the study further confirm the meta-theory of mental toughness. Prior research has confirmed that in addition to its protective effects in stressful scenarios, mental toughness also has significant gainful functions 30 . With the increase in mental toughness level, athletes have higher behavioral motivation, athletes' emotions can be effectively managed, the cognitive scope has been further expanded, and they can set up practical development goals for themselves, according to the reality of the conditions of the use of problem focusing, cognitive reconstruction, active help and other diversified coping methods to solve the difficulties faced by their own, so that the young athletes are fully engaged in their sports training. This will enable young athletes to devote themselves to individual sports training. Conclusion There was a positive correlation between social support, self-efficacy, mental toughness, and athlete engagement. Social support had a positive predictive effect on athlete engagement, which had both direct and indirect effects. Among the indirect effects, social support can positively influence athlete engagement either through the parallel mediation of self-efficacy and mental toughness or the chain mediation of self-efficacy and mental toughness. The mediation effect model constructed in this study has a specific reference value for improving adolescent athletes sports engagement. In the future, we may further enrich the social support network of adolescent athletes, enhance the level of self-efficacy and psychological toughness of adolescent athletes, and then improve the level of adolescent athlete's engagement. Research limitations and prospects This study reveals the intrinsic mechanism of social support affecting athlete engagement, which has specific theoretical and practical significance. However, there are some limitations in the study. First, this study used cross-sectional data to explore the relationships among variables, and future research could further use longitudinal studies to verify the longitudinal relationships among social support, self-efficacy, mental toughness, and athlete engagement. Second, all of the data in this study were measured based on adolescent athletes' perspectives, which is somewhat subjective. Future research could compensate for the lack of self-reported statements with objective comments from coaches, peers, and parents. Finally, this study verified the mediating role of self-efficacy and mental toughness between social support and adolescent athlete engagement. However, it does not rule out that there may still be other mediating and moderating variables, and future research could further explore the effects of variables such as self-control, psychological capital, and coping styles on athlete engagement. Declarations Data availability The data available from the corresponding author upon request. Author contributions P.W. and Y.M. designed the study and written the original manuscript. C.S. and J.C. revised the manuscript. Z.W. and X.G. collected and analyzed the data. Y.F. designed the study and revised the manuscript. All authors contributed to the article and approved the submitted version. Funding This study was supported by the National Education Sciences Planning of China (Grant No.CLA230300) and National Social Science Foundation of China (Grant No.20BTY066). Competing interests The authors declare no competing interests. Additional information Correspondence and requests for materials should be addressed to Y.M. 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Journal of Applied Sport Psychology 33, 627–643 (2021). Sabouripour, F., Roslan, S., Ghiami, Z. & Memon, M. A. Mediating role of self-efficacy in the relationship between optimism, psychological well-being, and resilience among Iranian students. Frontiers in psychology 12, 675645 (2021). Chen, K., Liu, F., Mou, L., Zhao, P. & Guo, L. How physical exercise impacts academic burnout in college students: The mediating effects of self-efficacy and resilience. Frontiers in Psychology 13, 964169 (2022). Bandura, A., O'Leary, A., Taylor, C. B., Gauthier, J. & Gossard, D. Perceived self-efficacy and pain control: opioid and nonopioid mechanisms. Journal of personality and social psychology 53, 563 (1987). Birrer, D. & Morgan, G. Psychological skills training as a way to enhance an athlete's performance in high-intensity sports. Scandinavian journal of medicine & science in sports 20, 78–87 (2010). Freeman, P., Coffee, P., Moll, T., Rees, T. & Sammy, N. The ARSQ: the athletes’ received support questionnaire. Journal of Sport and Exercise Psychology 36, 189–202 (2014). Hu, L.-t. & Bentler, P. M. Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological methods 3, 424 (1998). Schwarzer, R. & Jerusalem, M. Generalized self-efficacy scale. J. Weinman, S. Wright, & M. Johnston, Measures in health psychology: A user’s portfolio. Causal and control beliefs 35, 37 (1995). Gucciardi, D. F., Hanton, S., Gordon, S., Mallett, C. J. & Temby, P. The concept of mental toughness: Tests of dimensionality, nomological network, and traitness. Journal of personality 83, 26–44 (2015). Hayes, A. F. Introduction to mediation, moderation, and conditional process analysis: A regression-based approach . Vol. 20–21 20–21 (Guilford publications, 2017). Podsakoff, P. M., MacKenzie, S. B., Lee, J.-Y. & Podsakoff, N. P. Common method biases in behavioral research: a critical review of the literature and recommended remedies. Journal of applied psychology 88, 879 (2003). Hodge, K., Lonsdale, C. & Jackson, S. A. Athlete engagement in elite sport: An exploratory investigation of antecedents and consequences. The Sport Psychologist 23, 186–202 (2009). Ye, L., Wang, B., Wu, M., Liu, Z. & Dong, L. Effect of social support on athlete engagement: serial mediation of mental toughness and coping style. J. Bei Jing Sport Unniv 7, 75–82 (2016). Benight, C. C. & Bandura, A. Social cognitive theory of posttraumatic recovery: The role of perceived self-efficacy. Behaviour research and therapy 42, 1129–1148 (2004). Smoll, F. L., Cumming, S. P. & Smith, R. E. Enhancing Coach-Parent Relationships in Youth Sports: Increasing Harmony and Minimizing Hassle. International Journal of Sports Science & Coaching 6, 13–26, doi: 10.1260/1747-9541.6.1.13 (2011). Atkinson, F. & Martin, J. Gritty, hardy, resilient, and socially supported: A replication study. Disability and Health Journal 13, 100839 (2020). Endler, N. S. & Magnusson, D. Toward an interactional psychology of personality. Psychological bulletin 83, 956 (1976). Masten, A. S. & Coatsworth, J. D. The development of competence in favorable and unfavorable environments: Lessons from research on successful children. American psychologist 53, 205 (1998). Olsson, C. A., Bond, L., Burns, J. M., Vella-Brodrick, D. A. & Sawyer, S. M. Adolescent resilience: A concept analysis. Journal of adolescence 26, 1–11 (2003). Kalaitzaki, A., Tsouvelas, G. & Koukouli, S. Social capital, social support and perceived stress in college students: The role of resilience and life satisfaction. Stress and Health 37, 454–465 (2021). Sheard, M., Golby, J. & Van Wersch, A. Progress toward construct validation of the Sports Mental Toughness Questionnaire (SMTQ). European Journal of Psychological Assessment 25, 186–193 (2009). Weber, M. C., Pavlacic, J. M., Gawlik, E. A., Schulenberg, S. E. & Buchanan, E. M. Modeling resilience, meaning in life, posttraumatic growth, and disaster preparedness with two samples of tornado survivors. Traumatology 26, 266 (2020). Bandura, A. Social cognitive theory of self-regulation. Organizational behavior and human decision processes 50, 248–287 (1991). Richardson, G. E. The metatheory of resilience and resiliency. Journal of clinical psychology 58, 307–321 (2002). Additional Declarations No competing interests reported. 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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-3839312","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":266060439,"identity":"abc4bf70-5216-4377-90c7-1fb8e59c04fb","order_by":0,"name":"Pukui 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Technology","correspondingAuthor":false,"prefix":"","firstName":"Chenge","middleName":"","lastName":"Shi","suffix":""},{"id":266060441,"identity":"f5731dc7-1ddb-4123-9336-defd6c89a918","order_by":2,"name":"Jun Chen","email":"","orcid":"","institution":"Capital University of Physical Education and Sports","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Chen","suffix":""},{"id":266060442,"identity":"edc82920-f171-4c37-a9b3-58c1f74d5670","order_by":3,"name":"Zewen Wang","email":"","orcid":"","institution":"Capital University of Physical Education and Sports","correspondingAuthor":false,"prefix":"","firstName":"Zewen","middleName":"","lastName":"Wang","suffix":""},{"id":266060443,"identity":"6519c088-84a7-42ba-af2e-afaed46f78cd","order_by":4,"name":"Xiang Gao","email":"","orcid":"","institution":"Guangzhou Sport 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08:59:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3839312/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3839312/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-92110-9","type":"published","date":"2025-02-27T15:57:33+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":49427468,"identity":"f347e8d7-01e0-4671-a56a-620f5f374c7c","added_by":"auto","created_at":"2024-01-10 16:03:15","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":31465,"visible":true,"origin":"","legend":"\u003cp\u003eChain mediation effect model of self-efficacy and mental toughness\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3839312/v1/a44a4af39cb699d2cd188655.png"},{"id":49427467,"identity":"ff95389d-d30d-494c-a452-82df3c24d7b0","added_by":"auto","created_at":"2024-01-10 16:03:15","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":39730,"visible":true,"origin":"","legend":"\u003cp\u003eThe Relationship between social support and athlete engagement: chain mediation between self-efficacy and mental toughness\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3839312/v1/d4e7580a94be1b76b7e4b1f5.png"},{"id":77622448,"identity":"24ef1e51-1ac2-4da1-ab0f-8ff26f68c12d","added_by":"auto","created_at":"2025-03-03 16:06:59","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1028292,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3839312/v1/2e5fc4af-a412-485c-9043-a208f3989d7b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Effect of Social Support on Adolescent Athletes Engagement: Self-Efficacy and Mental Toughness of the Chain Mediated Effects","fulltext":[{"header":"Introduction","content":"\u003cp\u003eEngagement is one of the core concepts in the field of positive psychology. It refers to the sustained mental state of an individual filled with positive emotions. It is an essential factor in influencing an individual's behavioral performance and the direction of behavioral development\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Lonsdale et al.\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e first introduced the concept of athlete engagement in the field of competitive sport, which is characterized by self-confidence (belief in one's ability to achieve a high level of performance and desired goals), dedication (desire to invest energy and time in the achievement of personally important goals), vitality (a state of feeling of being physically and psychologically energized), and enthusiasm (the experience of a strong sense of arousal and pleasure). Athlete engagement is an important indicator of athletes' positive psychology, which can reflect athletes' positive and healthy psychological state, and is conducive to stimulating athletes' positive qualities such as optimism, perseverance, creativity, etc., so as to effectively promote the development and maturity of athletes, and to lay a solid foundation for them to enhance their athletic ability and to improve their athletic performance\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Comprehensively exploring the factors affecting athlete engagement helps to scientifically and systematically grasp the changes and developmental laws of athlete engagement. It provides theoretical references for stimulating athletes' potential and improving sports performance. External factors such as group cohesion\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e, motivational climate\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, and coach-athlete relationship\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e and internal factors such as perfectionism\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, basic psychological needs\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e, and self-concept\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e are essential factors influencing athlete engagement. In addition, work and learning engagement studies have demonstrated that social support is a significant predictor of individual engagement\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAdolescent athletes are an important reserve resource for the sustainable development of a country's sports. At the same time, young athletes are a particular group. On the one hand, adolescent athletes are in a high-intensity training environment for a long time and must withstand many external pressures, such as coaches' harshness and external expectations. On the other hand, young athletes are in a sensitive period of sports level and physical and mental development, which is a critical stage to improve sports performance and become elite athletes\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. Therefore, this study explores the effects of social support on adolescent athletes' engagement with adolescent athletes as subjects. Based on this, it explores the internal mechanism of action of athlete engagement, aiming to provide a valuable reference basis for adolescent athletes' engagement intervention practice.\u003c/p\u003e \u003cp\u003eSocial support refers to the moral and material comfort, care, respect, and help given to an individual by various social parties such as family, relatives, and friends\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Athletes, as a high-pressure group, are constantly exposed to stressors such as training, competition, injuries, etc. They experience a higher sense of belonging and security when they have more social support. They can receive adequate advice and guidance from others to improve their athletic skills, competence, and confidence\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. A study of Olympic athletes shows that high levels of social support are necessary for athletes on the road to success\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Athletes' perceived social support can be categorized in terms of type into emotional support (meaning that others accompany and care for the individual to enhance his or her sense of security and comfort), respectful support (which is when others help the individual to enhance his sense of competence and self-esteem), informational support (which means that others provide the individual with advice and guidance on relevant issues), and tangible support (which refers to substantial help such as money, services, and sharing of responsibilities)\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Social support can be categorized as coaching, parental, and peer support\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Coaches are recognized as the primary providers of social support for athletes, and their social support is critical to their growth and development \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Improving the support provided by coaches may help create a harmonious sporting environment, allowing for quicker allocation of resources and an improved sporting experience for athletes\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. Parental encouragement and the level of emotional and respectful support shown to adolescent athletes can effectively mitigate the negative effects of stressors present in the athletic environment on self-confidence and athletic performance\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Peer support promotes positive emotions, reduces mental fatigue, and enhances athlete engagement during athletic training and competition\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Based on this, this research proposes hypothesis H1: Social support can positively predicts adolescent athlete engagement.\u003c/p\u003e \u003cp\u003eSelf-efficacy refers to an individual's assumptions and judgments about their ability to perform a behavior\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Typically, the more robust an individual's sense of self-efficacy and outcome expectations, the more likely they are to start and persist in a particular activity\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Self-efficacy is a crucial psychological factor for athletes. Athletes encounter a variety of pressures at any time during training and competition, and how to properly understand each other and master effective solutions depends on the level of individual self-efficacy\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. From the self-efficacy perspective, a positive subjective assessment of an individual can impact the level of interest and commitment to engage in a specific activity, which can play a decisive role in determining an individual's behavioral choices\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. During exercise, individuals with higher self-efficacy make a subjective assessment of their effectiveness in accomplishing the activity prior to the action, and this pre-estimation has a significant impact on regulating the athlete's mood and facilitating commitment to the game\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. In addition, obtaining more social support can promote adolescents' self-efficacy, and social support can positively and positively influence self-efficacy\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. According to self-efficacy theory, social persuasion, vicarious experience, and emotional state are the main factors that affect an individual's self-efficacy\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Social support can help individuals experience more success and thus increase self-efficacy\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. In the process of training or competition, coaches' encouragement and guidance to the athletes play a function of social persuasion to a certain extent. The training feelings, experience sharing, and communication among peers help form the athletes' alternative experiences, and parents' support and understanding of the athletes' participation in training can help enhance the athletes' emotional state of participation in training. In other words, a favorable social supportive environment can help individuals improve their confidence in training and competing and improve athletes' self-efficacy. Based on this, this research proposes hypothesis H2: Self-efficacy plays a mediation role between social support and athlete engagement.\u003c/p\u003e \u003cp\u003ePsychological resilience is the ability or trait of an individual to cope with adverse life events such as stress, frustration, and trauma\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Athletes need mental toughness to achieve athletic excellence in training and competition\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Because of this, mental toughness is viewed by athletes, coaches, and researchers in athlete psychology as one of the most important psychological traits for athletes to be successful in competition\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. On the one hand, mental toughness is significantly and positively correlated with an individual's athletic performance, with athletes high in mental toughness participating at higher levels of competition, having better performances in competitions, and achieving more success \u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Athletes with high mental toughness have higher control beliefs about stressful situations, tend to evaluate stressors as challenges rather than threats, have higher coping efficacy, and adopt more coping strategies focused on solving realistic problems\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. On the other hand, athletes with high mental toughness are less likely to experience negative emotions. A longitudinal follow-up study of adolescent athletes showed that mental toughness effectively reduced physiological and emotional exhaustion, reduced mental fatigue overall, and demonstrated sustained impact effects\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. In addition to the protective effects in stressful situations, relevant studies have found that mental toughness has significant gainful functions, such as attentional control, goal orientation, and fluency states\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Athletes with high mental toughness make more positive and accurate cognitive evaluations of the individual and engage in a more proactive attitude toward training and competition\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. At the same time, an individual's level of mental toughness is not static. In addition to innate genetic factors, enhancement through later life is equally important. Previous research has shown that social support is essential to mental toughness\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Comprehensive and diversified social support is of great relevance in improving athletes' mental toughness\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e, increasing athletes' problem-solving strategies, but also by decreasing athletes' risk appraisal of adversity\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. Based on this, this research proposes hypothesis H3: Mental toughness mediates between social support and athlete engagement.\u003c/p\u003e \u003cp\u003eRelated research has confirmed that self-efficacy significantly predicts levels of mental toughness\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. A high level of self-efficacy helps individuals cope with stress and frustration with good mental toughness, thus developing a sound personality and forming a healthy psychology\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. A study of elite marathon runners showed that self-efficacy was closely related to mental toughness, with athletes with higher efficacy having better mental toughness\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. According to the Goal-Expectation-Self-Control model, self-efficacy is considered an essential component of psychological resilience\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e, and many studies have demonstrated its contribution to psychological resilience\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. An individual with a high sense of self-efficacy will inspire greater confidence and courage to face adversity or setbacks and face changes in the environment with a positive attitude. Because of this, individuals with a high sense of self-efficacy can further increase their level of mental toughness as they proactively cope with a variety of problems\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. The relationship between self-efficacy and mental toughness is perhaps related to endogenous opioid activation\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. Related studies have noted that endogenous opioids relieve pain, self-efficacy can cause endogenous opioid activation and mental toughness is associated with pain tolerance. Athletes may experience higher levels of mental toughness because they have a stronger sense of self-efficacy to relieve pain through the body's endocrine system\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. Based on this, this research proposes hypothesis H4: Self-efficacy and mental toughness mediate between social support and athlete engagement. The hypothesized model of this study is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eParticipants and procedure\u003c/h2\u003e \u003cp\u003eThis study adopted a convenience sampling method, tested collectively on a group basis in schools, youth athletes from 7 sports schools (2 in Beijing, 2 in Guangdong Province, 1 in Fujian Province, 1 in Henan Province, and 1 in Hubei Province) were selected for the survey. A total of 541 questionnaires were distributed, and 537 questionnaires were collected. After excluding invalid questionnaires such as regular responses, incomplete demographic information, and missing options, 513 valid questionnaires remained, with a validity rate of 95.5%. The demographic information of the study population is shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\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\u003eParticipants' demographic information(N = 513)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCharacteristics\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCategory\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSample Size\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePercentage\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e264\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e51.46%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e249\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e48.54%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSixteen years old\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e94\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e18.32%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSeventeen years old\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e17.55%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEighteen years old\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e29.24%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNineteen years old\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e34.89%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSports Level\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNational elite athletes\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e47\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.16%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNational first-level athletes\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e146\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28.46%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNational second-level athletes\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e197\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e38.40%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOthers\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e123\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e23.98%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGame\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBasketball\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e244\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.56%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFootball\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e121\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e23.59%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVolleyball\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e18.71%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOthers\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e52\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.14%\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eResearch tools\u003c/h2\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003eAthletes Received Social Support Questionnaire(ARSQ)\u003c/h2\u003e \u003cp\u003eAdopted the Athletes Received Social Support Questionnaire by Freeman et al., \u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e, which consists of 22 items and includes 4 dimensions: emotional support, respectful support, informational support, and tangible support. Using a 5-point Likert scale, with 1 representing \"completely non-compliant\" and 5 representing \"completely compliant\", the higher the score, the higher the social support the adolescent athlete receives. In this study, the Cronbanch's α coefficient of the scale was 0.926. The Cronbanch's α coefficients of the three dimensions of family support, friend support, and other support were 0.869, 0.905, and 0.871, respectively, and the factor loadings of each item ranged from 0.771 to 0.878., Validated factor analysis fit index: \u003cem\u003eχ\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e/\u003cem\u003edf\u003c/em\u003e = 3.819, RMR = 0.024, RMSEA = 0.074, GFI = 0.940, TLI = 0.956, and the structural validity of the scale was favorable\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eGeneral Self-Efficacy Scale(GSES)\u003c/h2\u003e \u003cp\u003eThey have adopted the General Self-Efficacy Scale developed by Schwarzer et al.,\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e, which consists of 10 items and is scored on a 5-point Likert scale, with 1 being \" completely non-compliant\" and 5 being \"completely compliant\". The higher the score, the better the self-efficacy of the adolescent athletes. In this study, the Cronbanch's α coefficient of the scale was 0.890, the factor loadings of each item ranged from 0.715 to 0.899, and the fit indices of the validated factor analysis were \u003cem\u003eχ\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e/\u003cem\u003edf\u003c/em\u003e = 2.533, RMR = 0.016, RMSEA = 0.069, GFI = 0.964, TLI = 0.964, and TLI = 0.964, respectively., TLI = 0.966, the scale has favorable structural validity\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eMental Toughness Inventory(MTI)\u003c/h2\u003e \u003cp\u003eIt adopted the Mental Toughness Inventory developed by Gucciardi et al.,\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e, which consists of 8 items. It is scored on a 5-point Likert scale, with 1 being \" complete non-compliance\" and 5 being \"complete compliance\", with higher scores representing higher levels of mental toughness in adolescent athletes. In this study, the scale Cronbanch's α coefficient was 0.924, the factor loadings of each question item ranged from 0.827 to 0.896, and the fit indices of the validated factor analysis: \u003cem\u003eχ\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e/\u003cem\u003edf\u003c/em\u003e = 3.667, RMR = 0.020, RMSEA = 0.079, GFI = 0.943, TLI = 0.954, the scale has favorable structural validity\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eAthlete Engagement Questionnaire(AEQ)\u003c/h2\u003e \u003cp\u003eAdopted was the Athlete Engagement Questionnaire developed by Lonsdale et al.,\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e a 16-item questionnaire comprising four dimensions: confidence, commitment, energy, and enthusiasm. The questionnaire is scored on a 5-point Likert scale, with 1 being \" completely non-compliant\" and 5 being \"completely compliant\", with higher scores representing higher levels of engagement in adolescent athletes. In this study, the Cronbach's α coefficient of the scale was 0.934. The Cronbach's α coefficients of the three dimensions of family support, friend support, and other support were 0.871, 0.912, and 0.886, respectively, and the factor loadings of the items ranged from 0.800 to 0.893., Validated factor analysis fit index: \u003cem\u003eχ\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e/\u003cem\u003edf\u003c/em\u003e = 3.573, RMR = 0.022, RMSEA = 0.065, GFI = 0.932, TLI = 0.944, and the structural validity of the scale was favorable\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eResearch methods\u003c/h3\u003e\n\u003cp\u003eAMOS 26.0 software was used to calculate the model fitting index of the scale in the study, and SPSS 26.0 was used for common method bias testing, descriptive statistics, and Pearson correlation analysis. SPSS macro program PROCESS 4.2, developed by Hayes, was used for mediation and chain mediation effects analysis\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. Model 6 of 92 typical models provided by Hayes was selected for analysis. The bootstrap method was used (repeated sampling 5000 times). P\u0026lt;0.05 was set to represent the statistical result with significance.\u003c/p\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eEthics statement\u003c/h2\u003e \u003cp\u003e The study was conduct in accordance with the Declaration of Helsinki and approved by the Human Research Ethics Committee of Capital university of Physical Education and Sports. All participants agreed to participate in this research voluntarily; they provided informed consent when they completed the suevey and were able to withdraw from the study freely at any time. In addition, our data were anonymizd to ensure the privacy of all participants.\u003c/p\u003e \u003c/div\u003e"},{"header":"Result","content":"\u003ch2\u003eCommon Method Bias Testing\u003c/h2\u003e\u003cp\u003eAll questionnaires were filled in anonymously for the empirical procedure, while Harman's one-way test was used for testing. KMO test and Bartlett's test of sphericity were performed on the data, and the results showed KMO = 0.897 and Bartlett's test of sphericity \u003cem\u003eχ\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e = 8526.193, \u003cem\u003edf\u003c/em\u003e = 351, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.001, indicating that the data was suitable for factor analysis. Including all variables in the exploratory factor analysis for rotation, five factors with eigenvalues \u0026gt; 1 were extracted, and the explained variance of the first factor was 23.512%, which is less than the criterion of 40% critical value. Thus, this can indicate that there is no standard severe method bias in the data of this study\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003ch2\u003eDescriptive statistics and correlation analysis\u003c/h2\u003e\u003cp\u003eThe results of the correlation analysis showed (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) that there was no significant correlation between the demographic variables of gender and sports and the 4 research variables. Therefore, the 2 demographic variables of gender and sports were no longer considered in the mediation and chained mediation effect analyses. Instead, age and sport level were correlated with the research variables, so they were included as control variables in the model in the subsequent mediation and chained mediation effect analyses. Meanwhile, significant positive correlations existed between the 4 research variables of social support, athlete engagement, self-efficacy, and mental toughness.\u003c/p\u003e\u003cdiv class=\"gridtable\"\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=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\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\u003eDescriptive Statistics and Correlation Analysis of Variables\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"9\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM ± SD\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1. SS\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\"±\" colname=\"c2\"\u003e \u003cp\u003e4.10 ± 0.68\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\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. AE\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\"±\" colname=\"c2\"\u003e \u003cp\u003e4.18 ± 0.57\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.61\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\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\u003e3. S-E\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\"±\" colname=\"c2\"\u003e \u003cp\u003e3.76 ± 0.63\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.44\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.52\u003csup\u003e***\u003c/sup\u003e\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\u003e4. MT\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\"±\" colname=\"c2\"\u003e \u003cp\u003e3.55 ± 0.46\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.29\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.40\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.45\u003csup\u003e***\u003c/sup\u003e\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\u003e5. Gender\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.02\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\u003e6. Age\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.32\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.37\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.40\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.26\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.14\u003csup\u003e*\u003c/sup\u003e\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\u003e7. SL\u003csup\u003ec\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.38\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.25\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.44\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.31\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.24\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.20\u003csup\u003e**\u003c/sup\u003e\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\u003e8. Game\u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.12\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.10\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.13\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"9\"\u003eNote: N = 513, SS: Social Support; AE: Athlete Engagement; S-E: Self-Efficacy; MT: Mental Toughness; SL: Sports Level; a: gender is a dummy variable, with 1 for boys and 2 for girls; b: age is a dummy variable, with 1 for sixteen years old, 2 for seventeen years old, 3 for eighteen years old and 4 for nineteen years old; c: sports level is a dummy variable, with 1 for national elite athletes, 2 for national first-level athletes, 3 for national second-level athletes and 4 for others. d: the game is a dummy variable, with 1 for Basketball, 2 for Football, 3 for Volleyball, and 4 for Others, \u003cem\u003e* P\u003c/em\u003e \u0026lt; 0.05, \u003cem\u003e* * P\u003c/em\u003e \u0026lt; 0.01, \u003cem\u003e* * * P\u003c/em\u003e \u0026lt; 0.001; same below.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003ch2\u003eMediation and chain mediation effects analysis\u003c/h2\u003e\u003cp\u003eSocial support was analyzed as the independent variable, athlete engagement as the dependent variable, and self-efficacy and mental toughness as the mediating variables for mediation and chain mediation effects. The results showed (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e): that social support had a positive predictive effect on athlete engagement (\u003cem\u003eβ\u003c/em\u003e = 0.192, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.001); social support had a positive predictive effect on self-efficacy (\u003cem\u003eβ\u003c/em\u003e = 0.177, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.001); social support had a positive predictive effect on mental toughness (\u003cem\u003eβ\u003c/em\u003e = 0.146, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.001); self-efficacy had a positive predictive effect on athlete engagement (\u003cem\u003eβ\u003c/em\u003e = 0.423, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.001); self-efficacy was a positive predictor of mental toughness (\u003cem\u003eβ\u003c/em\u003e = 0.318, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.001); and mental toughness was a positive predictor of athlete engagement (\u003cem\u003eβ\u003c/em\u003e = 0.191, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.001).\u003c/p\u003e\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eRegression Analysis of a Chain Mediated Model of the Relationship Between Social Support and Athlete Engagement\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" rowspan=\"2\" style=\"width: 4.943%;\"\u003e\n \u003cp\u003eVariable\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\" style=\"width: 11.0308%;\"\u003e\n \u003cp\u003eS-E\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\" style=\"width: 12.8519%;\"\u003e\n \u003cp\u003eMT\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\" style=\"width: 12.1234%;\"\u003e\n \u003cp\u003eAE\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e\u0026beta;\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003eSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 4.7349%;\"\u003e\n \u003cp\u003et\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 4.9951%;\"\u003e\n \u003cp\u003e\u0026beta;\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003eSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 4.7349%;\"\u003e\n \u003cp\u003et\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 3.5902%;\"\u003e\n \u003cp\u003e\u0026beta;\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003eSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.4113%;\"\u003e\n \u003cp\u003et\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.943%;\"\u003e\n \u003cp\u003eAge\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.047\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.443\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\n \u003cp\u003e1.005\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.9951%;\"\u003e\n \u003cp\u003e-0.338\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.682\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\n \u003cp\u003e-0.491\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5902%;\"\u003e\n \u003cp\u003e-0.067\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.072\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.4113%;\"\u003e\n \u003cp\u003e-1.010\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.943%;\"\u003e\n \u003cp\u003eSL\u003csup\u003ec\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.345\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.078\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\n \u003cp\u003e9.488\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.9951%;\"\u003e\n \u003cp\u003e0.446\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.357\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\n \u003cp\u003e-2.997\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5902%;\"\u003e\n \u003cp\u003e1.336\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.618\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.4113%;\"\u003e\n \u003cp\u003e5.256\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.943%;\"\u003e\n \u003cp\u003eSS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.177\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\n \u003cp\u003e9.679\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.9951%;\"\u003e\n \u003cp\u003e0.146\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.014\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\n \u003cp\u003e7.707\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5902%;\"\u003e\n \u003cp\u003e0.192\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.4113%;\"\u003e\n \u003cp\u003e15.705\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.943%;\"\u003e\n \u003cp\u003eS-E\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.9951%;\"\u003e\n \u003cp\u003e0.318\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.032\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\n \u003cp\u003e9.971\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5902%;\"\u003e\n \u003cp\u003e0.423\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.044\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.4113%;\"\u003e\n \u003cp\u003e9.192\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.943%;\"\u003e\n \u003cp\u003eMT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.9951%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 4.7349%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.5902%;\"\u003e\n \u003cp\u003e0.191\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 3.1219%;\"\u003e\n \u003cp\u003e0.838\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.4113%;\"\u003e\n \u003cp\u003e8.868\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.943%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\" style=\"width: 11.0308%;\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.191\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\" style=\"width: 12.8519%;\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.267\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\" style=\"width: 12.1234%;\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.627\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 4.943%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\" style=\"width: 11.0308%;\"\u003e\n \u003cp\u003eF\u0026thinsp;=\u0026thinsp;93.689\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\" style=\"width: 12.8519%;\"\u003e\n \u003cp\u003eF\u0026thinsp;=\u0026thinsp;72.391\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\" style=\"width: 12.1234%;\"\u003e\n \u003cp\u003eF\u0026thinsp;=\u0026thinsp;222.556\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"10\" style=\"width: 41.5734%;\"\u003eNote: N\u0026thinsp;=\u0026thinsp;513, SS: Social Support; AE: Athlete Engagement; S-E: Self-Efficacy; MT: Mental Toughness; SL: Sports Level; b: age is a dummy variable, with 1 for sixteen years old, 2 for seventeen years old, 3 for eighteen years old and 4 for nineteen years old; c: sports level is a dummy variable, with 1 for national elite athletes, 2 for national first-level athletes, 3 for national second-level athletes and 4 for others\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n\u003c/table\u003e\u003cp\u003eThe mediated effects test showed that the direct effect size of social support on athlete engagement was 0.192 (95% CI=[0.168,0.216]), accounting for 62.75% of the total effect size. Therefore, hypothesis H1 was tested; social support affected athlete engagement through self-efficacy with a mediated effect size of 0.075 (95% CI=[0.377,0.745]), accounting for 24.51% of the total effect size. Therefore, hypothesis H2 was tested; social support influenced athlete engagement through mental toughness, with a mediated effect size of 0.028 (95% CI=[0.006,0.058]), accounting for 9.15% of the total effect size. Therefore, hypothesis H3 was tested; social support influenced athlete engagement through the chain mediation of self-efficacy and mental toughness, with a mediated effect size of 0.011 (95% CI=[0.003,0.101]), accounting for 3.59% of the total effect size. Therefore, hypothesis H4 was tested. Specific results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eChain Mediated Effect Test of Self-Efficacy and Mental Toughness on Social Support and Athlete Engagement\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ePath\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eStandardizedβ\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eBoot\u003c/p\u003e \u003cp\u003eSE\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e95%CI\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e下限\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e上限\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSS→AE\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.192\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.168\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.216\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSS→S-E→AE\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.075\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.377\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.745\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSS→MT→AE\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.028\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.006\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.058\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSS→S-E→MT→AE\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.101\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal Effect\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.306\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.229\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.279\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndirect Total Effect\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.114\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.018\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.045\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.080\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e"},{"header":"Discussion","content":"\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eThe relationship between social support and athlete engagement\u003c/h2\u003e \u003cp\u003eAthletes' training engagement status is closely related to their skill level, competitive performance, mental health, personality traits, etc. Enhancing athletes' training engagement will lay a solid foundation for their professional sports career and life development\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. The results of this study show that social support is positively related to adolescent athlete engagement and significantly and positively predicts athlete engagement after controlling for demographic variables. The results suggest that as an essential external resource, social support can significantly enhance athlete engagement and motivate them to devote themselves to training and competition with enthusiasm, vigor, confidence, and conviction, consistent with previous research findings\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. The social environment is not only an essential source of stress but also provides resources that can be utilized for the survival and development of the individual. External support is critical for high-pressure groups such as athletes, and its abundance will directly impact the athlete's engagement and performance\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. Coaches with solid professional knowledge and skills-rich experience in training and competition can effectively improve athletes' motivation to participate in training, promote athletes to train hard, and improve athletes' state of engagement\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Social cognitive theory indicates that peer role modeling helps to facilitate the acquisition and occurrence of individual behaviors\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e. Athletes enhance their affective performance in training by modeling their participation after their peers' excellent performance during the training process. At the same time, peer motivation and support can help athletes form a healthy and positive attitude toward sports training, enhance training effort and persistence, and promote the level of training engagement\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Related studies have found that parents or guardians are just as important in supporting, guiding, and supervising adolescent athletes as they are coaches\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. Parents' sports beliefs, perceptions, and behaviors can affect adolescent athletes' training status and effectiveness. Therefore, enhancing the level of social support for adolescent athletes is one of the most important ways to promote the improvement of their engagement status.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eThe mediation effect of self-efficacy and mental toughness\u003c/h2\u003e \u003cp\u003eThis study found that self-efficacy mediated the relationship between social support and adolescent athlete engagement. First, in the first part of the mediation pathway, the present study found that social support positively predicted athletes' self-efficacy. This finding extends the primary effects model and resource conservation theory of social support. This is because social support, as an essential psychological resource for individuals, enhances athletes' sports experience, relieves training and competition anxiety, and helps individuals maintain positive emotions \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Individuals with high self-efficacy are usually oriented towards accomplishing the tasks they set out to do in their studies and work, and their perceived social support is mainly used to complete the task successfully \u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. Adolescent athletes feel support, encouragement, and understanding from coaches, peers, and parents in daily training and life. They become more confident in accomplishing their training tasks and goals, enhancing their sense of sports efficacy. Then, in the second half of the mediation pathway, this study found that self-efficacy significantly increased athletes' training engagement. This result is consistent with previous research \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e and supports the self-efficacy theory\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Self-efficacy influences an individual's level of effort, persistence, and resilience during behavior, which in turn influences the individual's level of engagement \u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. Athletes with higher self-efficacy who face adversity, frustration, and failure in sports and engage in challenging tasks will exert more significant effort and persevere until they reach their goals, promoting the level of engagement in behavioral activities. In addition, related studies have found that students' self-efficacy influences cognitive judgments of learning tasks and determines persistence and motivation in learning activities. The higher the student's efficacy to learn, the higher the level of engagement toward learning. Adolescent athletes with high self-efficacy make more accurate cognitive judgments about training and competition tasks, can cope with various pressures more flexibly, and have higher confidence in accomplishing the tasks, thus showing a higher state of engagement.\u003c/p\u003e \u003cp\u003eThis study found that social support positively predicts adolescent athlete engagement through mental toughness. Positive psychology suggests that genetic factors do not solely determine personality and remain static but constantly change due to the combined influence of physiological mechanisms, external behaviors, and the social environment\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. Early developmental models state that mental toughness in individuals requires experiencing a severe traumatic event or natural disaster and recovering from adversity\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e. However, as researchers continue to explore, it has been found that personal abilities such as physical fitness, intelligence, and social skills, as well as protective factors such as interpersonal and self-control, also significantly influence an individual's mental toughness\u003csup\u003e\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e. According to the positive emotion broadening construct theory, a favorable social network can help individuals better perceive and utilize supportive social resources\u003csup\u003e\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. Adolescent athletes can experience more respect, encouragement, and trust in a higher social support environment. These resources can help adolescent athletes cope with the pressure of training and competition, help them overcome difficulties and setbacks, and hone their will in the process, making athletes more determined to participate in sports training and competition and significantly improve their mental toughness. Athletes' mental toughness encompasses a variety of positive psychological qualities, such as perseverance, self-confidence, and self-control, which respectively reflect athletes' persistent pursuit of goals, total confidence in themselves, and effective control of emotions\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e. These adaptive psychological strengths help athletes form a positive mental cognitive model to transform and digest the adverse effects of negative events in training and life promptly \u003csup\u003e\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e, for example, treating the stress encountered in training as an opportunity to identify and solve problems. This positive emotional cognition helps athletes suppress psychological fear, eliminate negative thinking, stimulate positive emotions, and enhance adaptive ability, which prompts young athletes to be more actively involved in sports training, and the level of sports engagement has been significantly increased.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eSocial support positively predicts chain mediation of adolescent athlete engagement\u003c/h2\u003e \u003cp\u003eThe present study found that social support can influence adolescent athlete engagement through the chain-mediated effects of self-efficacy and mental toughness. Based on previous theories and perspectives and following the process orientation concept, the study hypothesized that social support indirectly affects the engagement level of adolescent athletes through self-efficacy and mental toughness in a sequential manner, and the results of the present study confirmed the reasonableness of this hypothesis. Social cognitive theory suggests that individuals are subjective and increase their self-efficacy by actively seeking support and help from others\u003csup\u003e\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e. Social support influences the internal mechanism of self-efficacy for adolescent athletes can be explained from the perspective of social cognitive theory, in which adolescent athletes receive support and assistance from coaches, peers, and parents, which helps to optimize the athlete's sense of competence, effort, and control, among others, and significantly enhances the adolescent athlete's sense of self-efficacy. The meta-theory of psychological resilience suggests that social stressors and protective factors interact to determine whether an individual can maintain internal homeostasis, that social practices may disrupt an individual's internal homeostasis, and that an individual needs to cope with the challenge by restructuring their mental state to develop a higher level of adaptation, namely resilience restructuring\u003csup\u003e\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e. According to the goal-expectation-self-control model, self-efficacy is crucial for resilience reorganization\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. The results of the present study confirm that self-efficacy is a good protective factor for mental toughness in adolescent athletes and contributes to the promotion of resilience reorganization in athletes. The results of the study further confirm the meta-theory of mental toughness. Prior research has confirmed that in addition to its protective effects in stressful scenarios, mental toughness also has significant gainful functions\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. With the increase in mental toughness level, athletes have higher behavioral motivation, athletes' emotions can be effectively managed, the cognitive scope has been further expanded, and they can set up practical development goals for themselves, according to the reality of the conditions of the use of problem focusing, cognitive reconstruction, active help and other diversified coping methods to solve the difficulties faced by their own, so that the young athletes are fully engaged in their sports training. This will enable young athletes to devote themselves to individual sports training.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThere was a positive correlation between social support, self-efficacy, mental toughness, and athlete engagement. Social support had a positive predictive effect on athlete engagement, which had both direct and indirect effects. Among the indirect effects, social support can positively influence athlete engagement either through the parallel mediation of self-efficacy and mental toughness or the chain mediation of self-efficacy and mental toughness.\u003c/p\u003e \u003cp\u003eThe mediation effect model constructed in this study has a specific reference value for improving adolescent athletes sports engagement. In the future, we may further enrich the social support network of adolescent athletes, enhance the level of self-efficacy and psychological toughness of adolescent athletes, and then improve the level of adolescent athlete's engagement.\u003c/p\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003eResearch limitations and prospects\u003c/h2\u003e \u003cp\u003eThis study reveals the intrinsic mechanism of social support affecting athlete engagement, which has specific theoretical and practical significance. However, there are some limitations in the study. First, this study used cross-sectional data to explore the relationships among variables, and future research could further use longitudinal studies to verify the longitudinal relationships among social support, self-efficacy, mental toughness, and athlete engagement. Second, all of the data in this study were measured based on adolescent athletes' perspectives, which is somewhat subjective. Future research could compensate for the lack of self-reported statements with objective comments from coaches, peers, and parents. Finally, this study verified the mediating role of self-efficacy and mental toughness between social support and adolescent athlete engagement. However, it does not rule out that there may still be other mediating and moderating variables, and future research could further explore the effects of variables such as self-control, psychological capital, and coping styles on athlete engagement.\u003c/p\u003e \u003c/div\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data available from the corresponding author upon request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eP.W. and Y.M. designed the study and written the original manuscript. C.S. and J.C. revised the manuscript. Z.W. and X.G. collected and analyzed the data. Y.F. designed the study and revised the manuscript. All authors contributed to the article and approved the submitted version.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was supported by the National Education Sciences Planning of China (Grant No.CLA230300) and National Social Science Foundation of China (Grant No.20BTY066).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCorrespondence and requests for materials should be addressed to Y.M.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eGonz\u0026aacute;lez-Rom\u0026aacute;, V. \u0026amp; Bakker, A. The measurement of engagement and burnout: a confirmative analytic approach. 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Journal of clinical psychology 58, 307\u0026ndash;321 (2002).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"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":"adolescent athletes, social support, athlete engagement, self-efficacy, mental toughness","lastPublishedDoi":"10.21203/rs.3.rs-3839312/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3839312/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo explore the relationship between social support and adolescent athlete engagement and the role of self-efficacy and mental toughness in this relationship. A convenience sampling method was used to administer the athletes' received social support questionnaire, general self-efficacy scale, mental toughness inventory, and athletic engagement questionnaire to adolescent athletes in seven youth sports schools in China, and 513 valid questionnaires were collected. 1) After controlling for the effects of adolescent athlete age and sport level, regression analyses revealed that social support positively predicted adolescent athlete engagement; 2) Self-efficacy and mental toughness mediated the relationship between social support and adolescent athlete engagement, and this mediation consisted of three pathways: parallel mediation of both self-efficacy and mental toughness, and chain mediation of both self-efficacy and mental toughness. The mediating effects model constructed in this study can inform the promotion of youth athlete engagement levels, which can be crucial for improving youth athlete engagement in the future by enriching youth athletes' social support networks, enhancing self-efficacy, and developing mental toughness levels.\u003c/p\u003e","manuscriptTitle":"The Effect of Social Support on Adolescent Athletes Engagement: Self-Efficacy and Mental Toughness of the Chain Mediated Effects","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-10 16:03:10","doi":"10.21203/rs.3.rs-3839312/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-05-27T04:13:12+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-05-24T11:22:51+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-22T03:05:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"62e7637f-7d1f-4dbd-9603-a7fa5637af81","date":"2024-04-22T01:56:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"d301303e-901d-4f79-bf9f-c7da45407908","date":"2024-02-29T07:52:37+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-02-16T08:44:53+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-15T09:06:52+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-01-09T06:34:22+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-01-09T06:32:40+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-01-06T08:49:46+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":"48688e7b-ab7e-44cf-a146-917800a8a1fe","owner":[],"postedDate":"January 10th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":28030128,"name":"Health sciences/Health care/Occupational health"},{"id":28030129,"name":"Biological sciences/Psychology/Human behaviour"}],"tags":[],"updatedAt":"2025-03-03T16:01:14+00:00","versionOfRecord":{"articleIdentity":"rs-3839312","link":"https://doi.org/10.1038/s41598-025-92110-9","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-02-27 15:57:33","publishedOnDateReadable":"February 27th, 2025"},"versionCreatedAt":"2024-01-10 16:03:10","video":"","vorDoi":"10.1038/s41598-025-92110-9","vorDoiUrl":"https://doi.org/10.1038/s41598-025-92110-9","workflowStages":[]},"version":"v1","identity":"rs-3839312","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3839312","identity":"rs-3839312","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}