How physical activity influences flourishing of adolescents: an integrated analysis of sufficiency and necessity

Abstract

Background

In response to the contemporary emphasis on promoting adolescents’ physical and mental health, this study adopted a mixed-methods approach to examine the relationship between physical activity on adolescents’ flourishing, tested the mediating roles of self-worth and boredom in this relationship, and further examined the necessity and bottleneck levels of physical activity intensity, duration, and frequency, as well as self-worth and boredom (internal stimulation and external stimulation), for adolescents’ flourishing.

Methods

Drawing on the core propositions of the Cognitive-Affective Processing System (CAPS), this study constructed a dual-path mediation model to examine how physical activity was associated with adolescents’ flourishing through self-worth and boredom. In this model, self-worth was specified as a primarily cognitive-evaluative mediator, whereas boredom was specified as a primarily affective-experiential mediator. Survey data were collected from 985 adolescents. Partial Least Squares Structural Equation Modeling (PLS-SEM) was used to test sufficiency relationships, whereas Necessary Condition Analysis (NCA) was used to examine the necessity and bottleneck levels of key antecedent variables.

Results

(1) The results showed that physical activity was positively associated with adolescents’ flourishing (p < 0.01), positively associated with self-worth (p < 0.001), and negatively associated with boredom (p < 0.001); (2) As the level of flourishing increased, the antecedent conditions required to achieve higher levels of the outcome also increased, gradually showing a pattern of multi-variable synergy; (3) Mediation analyses further showed that physical activity was associated with adolescents’ flourishing indirectly through both self-worth and boredom.

Conclusion

Physical activity intensity, duration, and frequency did not emerge as necessary conditions for adolescents’ flourishing. Nevertheless, physical activity showed a positive facilitating association with flourishing. In addition, physical activity was linked to flourishing through both cognitive-evaluative and affective-experiential pathways, indicating that physical activity contributed to higher levels of flourishing by strengthening positive self-evaluation and reducing boredom-related constraints.

Background

Adolescent mental health has become a central concern in global public health and developmental psychology. International epidemiological reports have indicated that most mental disorders first emerge during adolescence and early adulthood, and the burden of mental health problems is particularly substantial among individuals aged 5 to 24 years [1, 2]. In the context of the increasingly early onset, widespread prevalence, and growing severity of mental health problems, exploring ways to reduce psychological burden, initiate flourishing initiatives, and enhance adolescents’ levels of flourishing has gradually become an urgent practical issue in the field of exercise psychology.

As a high-level state of mental health, flourishing is intended to capture individuals’ overall psychological functioning and subjective experiences of well-being in a comprehensive manner [3]. Physical activity is widely recognized not only for its relevance to physical health but also for its association with mental health. Through participation in physical activity, individuals engage more fully with bodily experiences, develop cognitive and psychological resources, strengthen their capacity to cope with and adapt to life stressors and setbacks, and maintain greater affective stability, all of which are associated with more positive experiences of well-being [4]. Although existing evidence has deepened scholarly understanding of the relationship between physical activity and well-being, empirical research focusing specifically on the association between physical activity and flourishing has remained relatively limited, leaving the underlying pathways linking these variables insufficiently clarified. Therefore, greater research attention should be directed toward flourishing as a more comprehensive construct, so as to accumulate stronger evidence regarding the role of physical activity in relation to holistic human development.

The core proposition of the Cognitive-Affective Processing System (CAPS) is that external situational experiences do not directly produce behavioral or psychological outcomes; rather, their effects are mediated through the activation of interconnected cognitive-affective units, which shape individuals’ subsequent responses [5]. Physical activity is likely to involve both “cognitive” and “affective” factors associated with flourishing [6]. On the one hand, Basic Psychological Needs Theory suggests that physical activity can satisfy individuals’ needs for autonomy, competence, and relatedness. When adolescents are able to make autonomous choices regarding participation, experience competence through effective engagement, and develop positive interpersonal connections during activity, these experiences are likely to strengthen self-perceptions and self-evaluative processes [7]. In this sense, the need-supportive experiences embedded in physical activity contexts may serve as an important basis for strengthening adolescents’ self-worth. On the other hand, according to Arousal Theory, physical activity is associated with higher levels of physiological and psychological activation, helping individuals maintain greater enthusiasm and engagement during participation while reducing negative emotion states [8]. Taken together, drawing on the core logic of the CAPS framework, this study examines the mediating roles of both “cognitive” and “affective” factors in the relationship between physical activity and adolescents’ flourishing. By integrating Partial Least Squares Structural Equation Modeling (PLS-SEM) and Necessary Condition Analysis (NCA), this study evaluates both the sufficiency and the necessity of physical activity, self-worth, and boredom in relation to adolescents’ flourishing.

Theoretical foundation and research hypotheses

Cognitive-affective processing system

The Cognitive-Affective Processing System (CAPS), was systematically proposed by Mischel et al. (1995) as an important revision and extension of the traditional view that traits determine behavior. By integrating insights from social cognitive theory, social learning theory, and spreading activation models in cognitive neuroscience [9], According to CAPS, characteristics of the external environment in which individuals are situated can activate the cognitive and affective units within the personality system, thereby exerting an important influence on their behavioral expressions. At the same time, individual differences in personal traits can affect how these cognitive-affective units operate, thereby driving differences in cognition, emotion, and behavior. The cognitive system emphasizes that, when facing external stimuli, individuals interpret external situations through appraisals of meaning, threat, opportunity, and controllability, thereby forming self-relevant judgments and goal-directed responses. The affective system emphasizes that, situational inputs may also elicit more immediate affective reactions, which are reflected in individuals’ affective states and experiential responses [10], Importantly, these processes are not assumed to operate in isolation. Rather, CAPS emphasizes the dynamic interplay among cognitive and affective units, such that situationally activated patterns of processing influence how individuals respond psychologically and behaviorally across contexts. Introducing CAPS framework into the study of adolescents’ flourishing carries important theoretical significance. On the one hand, flourishing does not represent a single affective experience or a single cognitive outcome, but rather reflects an integrated state involving positive affective experience, psychological functioning, and social adaptation, this multidimensional nature is consistent with the CAPS emphasis on multiple, interacting cognitive-affective units. On the other hand, adolescence represents a critical developmental period characterized by rapid development in both cognitive control and affective responsiveness, during which the influence of situational experiences on psychological states is particularly salient. CAPS therefore provides an appropriate framework for understanding the complexity of psychological responses during this stage.

Drawing on the CAPS framework, the present study develops a conceptual model aimed at identifying two theoretically proximal processing pathways through which physical activity may be associated with adolescents’ flourishing. The external environment of physical activity was conceptualized as a behavioral field that can continuously generate situational psychological experience, may provide psychologically meaningful situational cues. Through participation in physical activity, adolescents may encounter experiences that activate cognitive-evaluative and affective-experiential processing, which may in turn be associated with their levels of flourishing. On this basis, the present study specifies self-worth as a predominantly cognitive-evaluative indicator and boredom as a predominantly affective-experiential indicator, with this distinction adopted for analytic parsimony. Accordingly, a dual-path theoretical model linking physical activity and adolescents’ flourishing was developed (Fig. 1).

Fig. 1.

Cognitive-affective dual-path model

Research hypotheses

The relationship between physical activity and adolescents’ flourishing

As an ideal state of mental health, flourishing is regarded as the opposite of mental illness and reflects a high level of development in individuals’ mental health and well-being. Physical activity encompasses core elements such as autonomous participation, autonomous choice, and interpersonal relationships. Physical activity of appropriate intensity is associated with lower stress levels, more positive affective states, and greater pleasure, partly through physiological processes such as endorphin release [11], thereby providing individuals with pleasurable hedonic experiences, satisfying psychological needs, and being associated with improved life satisfaction. Continuous participation in physical activity has also been associated with brain structure reshaping, including the activation of brain regions related to cognitive function and the connectivity of their functional networks, thereby being linked to enhanced neural processing efficiency. Turecek et al. (2025) found that experiences of physical activity were highly consistent with optimal states of mental health, suggesting a close association between physical activity and flourishing [12]. Mccoy et al. also found that physical activity was significantly associated with higher levels of flourishing and can serves as an important predictor of flourishing [13]. Based on this evidence, the present study proposes the following hypothesis: physical activity is positively associated with adolescents’ flourishing (H1).

The “cognitive” pathway: the role of self-worth

Within the CAPS framework, behavioral exposures may influence outcomes through cognitive units. From this perspective, self-worth can be understood as a salient cognitive indicator reflecting individuals’ appraisals of self-meaning, personal value, and competence. Self-worth refers to individuals’ cognition and evaluation of themselves in social contexts, encompassing individuals’ perceptions of the self as well as social agents (such as groups and others), including self-evaluation and the positive affective experiences derived from it [14]. The satisfaction of basic psychological needs is the key foundation for the formation and development of self-worth, and physical activity provides opportunities to satisfy these basic psychological needs. The development of self-worth is regarded as one of the mechanisms through which physical activity is associated with mental health benefits. In contexts involving autonomous selection of physical activity, enhancement of physical activity competence, and the establishment of positive interpersonal relationships, individuals who frequently engage in physical activity tend to exhibit higher levels of self-worth and are more inclined to seek more active forms of physical activity and diverse modes of participation. Reddon et al. found that physical activity was significantly positively associated with self-worth, particularly showing a positive association between aerobic physical activity and self-worth, and that the relationship between physical activity and self-worth did not vary significantly over time or across gender [15]. Wu et al. also found a significant positive correlation between physical activity and self-worth [16].

Basic Psychological Needs Theory provides an important theoretical basis for understanding how social contexts shape individual functioning and well-being [17]. In physical activity contexts, experiences related to autonomy, competence, and supportive interpersonal connection help strengthen adolescents’ self-cognition and positive self-evaluation, thereby providing a theoretical foundation for the role of self-worth as a cognitive pathway linking physical activity and adolescents’ flourishing. From the perspective of the CAPS, self-worth is conceptualized as a cognitive self-evaluative mechanism that reflects individuals’ overall appraisal of their own value and importance, whereas flourishing represents a broader positive psychosocial outcome involving meaning in life, positive relationships, mastery, self-acceptance, optimism, and social contribution. In other words, self-worth primarily concerns how individuals evaluate their own value, whereas flourishing emphasizes how well individuals function and adapt overall. Pandey et al. found that individuals with high self-worth tend to actively engage in self-improvement and self-development, accumulating greater psychological capital, which was associated with higher levels of flourishing [18]. According to the CAPS theory, participation in physical activity and related cognitive processes are closely associated with changes or stimulation in self-worth. When individuals possess stronger self-perceptive abilities, they are more likely to implement positive psychological responses such as autonomy and selective acquisition. Kim et al. suggested that physical changes induced by participation in physical activity were associated with flourishing and were also indirectly associated with flourishing through self-worth [19]. The findings of Lopes et al. further supported this result, indicating that participation in physical activity during childhood and adolescence was associated with flourishing while simultaneously being linked to lower disengagement from physical activity [20]. Based on the above, the following hypotheses were proposed: physical activity is positively associated with self-worth (H2a); self-worth is positively associated with adolescents’ flourishing (H2b); and self-worth mediates the relationship between physical activity and adolescents’ flourishing (H2c).

The “affective” pathway: the role of boredom

Within the CAPS framework, behavioral exposures may affect outcomes through affective units. From this perspective, boredom can be conceptualized as a salient affective indicator reflecting individuals’ low-arousal negative state and the accompanying tendency toward motivational depletion. According to Arousal Theory, boredom is a negative affective experience that arises in daily life due to a lack of activity and loss of interest [21]. As an internal affective experience, boredom often prompts individuals to seek external stimulation or adopt avoidance behaviors, and the resulting negative emotions may be associated with a series of maladaptive social behaviors. Boredom includes internal stimulation (a deficiency of intrinsic interest) and external stimulation (low sensitivity to environmental stimuli). It is a low-arousal, process-oriented negative affective state. Through the novel stimulation provided by physical activity, individuals can increase arousal levels and thereby reduce experiences of boredom [22]. Physical activity is also regarded as an effective means of regulating physiological and psychological arousal states. Physical activity can be associated with the release of neurotransmitters, such as dopamine and serotonin, which play important roles in regulating emotion and attention, thereby being linked to increased levels of brain arousal. By providing novel environmental stimulation and challenges, physical activity helps individuals escape the low-arousal states experienced during passive activities (such as using mobile phones or playing video games), thus being associated with reduced experiences of boredom [23]. Bösselmann et al. found that individuals who frequently engage in physical activity, particularly high-intensity physical activity, reported lower levels of boredom [24].

In discussions on how to enhance adolescents’ flourishing, the field of educational psychology has also begun to emphasize the important role of boredom. Adolescence is a critical period for individuals to enhance their capabilities, and educational interventions should focus on helping individuals escape states of boredom, become more active, and engage in meaningful activities, thereby becoming more closely associated with flourishing. According to Arousal Theory, boredom and flourishing are opposites in terms of subjective experience. Freire et al. proposed the concept of adolescents’ optimal leisure experience, suggesting that boredom and flourishing are intertwined, and that adolescents can achieve optimal leisure experiences under conditions of low boredom and high flourishing [25]. This perspective is consistent with the two-dimensional model of emotion based on valence and arousal, in which boredom is considered a low-arousal negative emotion. When individuals experience more low-arousal negative emotions, levels of flourishing decrease. Furlong et al. found that declines in adolescents’ flourishing were closely associated with boredom, and increases in boredom experiences often are accompanied by more negative emotions and problem behaviors [26]. According to the CAPS theory, McCurdy et al. found that physical activity, as a potential influencing factor of chronic boredom and flourishing, was associated with lower levels of boredom and higher levels of flourishing [27]. Based on the above, the following hypotheses were proposed: physical activity is negatively associated with boredom (H3a); boredom is negatively associated with adolescents’ flourishing (H3b); and boredom mediates the relationship between physical activity and adolescents’ flourishing (H3c).

Research design

Investigation process

From September 10 to October 12, 2025, the research team conducted a survey among adolescents from regular junior and senior high schools in five cities of X Province. The questionnaires were primarily distributed and collected online. Before participants began completing the questionnaire, the first page provided a detailed introduction explaining the purpose of the study, anonymity, confidentiality, the principle of voluntary participation, and the right to withdraw at any time. After informed consent had been obtained, adolescents were provided with an online survey link for self-administration. Participants decided independently whether to continue completing the questionnaire after reading the above information. A total of 1,162 questionnaires were distributed and all 1,162 were returned. After excluding 177 questionnaires with missing responses, patterned responses, or excessively short completion times, 985 valid questionnaires were retained, yielding an effective response rate of 84.76%.

Participants

Participants were aged 12 to 19 years (M = 15.00, SD = 2.12). The sample consisted of 579 males (58.78%) and 406 females (41.22%). In terms of grade level, 186 students were in Grade 7, 187 in Grade 8, 123 in Grade 9, 140 in Grade 10, 186 in Grade 11, and 163 in Grade 12. and key demographic variables (e.g., age) were controlled for, which served as the sample for PLS-SEM analysis.

Following the recommendations of Zhai et al., a post hoc statistical power analysis was conducted using the Monte Carlo method [28]. The statistical power analysis program for structural equation modeling developed by Schoemann et al. was employed [29]. A mediation model was specified with a sample size of 985, 1,000 replications, and 20,000 Monte Carlo draws per replication. A 95% confidence interval was selected, and the correlation coefficients and standard deviations of the four latent variables in this study were entered into the model. The estimation results indicated that the statistical power of the mediating effect of physical activity on flourishing through self-worth was 0.99, and the statistical power of the mediating effect of physical activity on flourishing through boredom was 0.95, indicating that a sample size of 985 was sufficient to adequately detect the specified effects in the model.

Measurement instruments

All variables in this study were assessed using well-established and psychometrically validated instruments that have been extensively applied in prior research. The questionnaires were translated into Chinese and culturally adapted for the Chinese adolescent population through standardized translation and back-translation procedures, ensuring both linguistic accuracy and conceptual equivalence across cultural contexts.

Physical activity rating scale

The Physical Activity Rating Scale revised by Liang et al. was used to assess participants’ physical activity in terms of intensity, duration, and frequency [30]. The scale contains three items. Example items include “What is the intensity of your physical activity?”, “When engaging in physical activity of the above intensity, how many minutes does each session last?”, and “How many times per month do you engage in physical activity of the above intensity?”. In the present study, the Cronbach’s α coefficient of the scale was 0.837.

Flourishing scale

The Flourishing Scale (FS) developed by Diener et al. was used to measure flourishing [31]. The characteristics of flourishing are assessed across eight dimensions, including purpose in life, relationships, engagement, interest, mastery, self-acceptance, optimism, contribution, comprising eight items in total. Example items include “I lead a purposeful and meaningful life” and “My social relationships are supportive and rewarding.” The scale uses a 7-point Likert format ranging from “strongly disagree” to “strongly agree.” In this study, the Cronbach’s α coefficient of the scale was 0.915.

Self-worth scale

The overall self-worth dimension of the Self-worth Scale developed by Huang et al. was used, consisting of six items [14]. Example items include “I am a person of value” and “I believe that everyone has their own inherent talents.” The scale adopts a 5-point Likert format ranging from “completely inconsistent” to “completely consistent,” with higher scores indicating higher levels of self-worth. In this study, the Cronbach’s α coefficient of the scale was 0.865.

Boredom scale

Boredom was measured using the short version of the Boredom Proneness Scale revised by Li et al. [32]. The scale consists of 12 items and includes two dimensions: external stimulation and internal stimulation. External stimulation reflects low sensitivity to environmental stimuli, with items such as “I always feel that my surroundings are monotonous and boring,” whereas internal stimulation reflects a lack of intrinsic interest, with items such as “I find it difficult to find an academic course or work task that excites me.” The scale uses a 7-point Likert format ranging from “strongly disagree” to “strongly agree,” with higher total scores indicating higher levels of boredom. In this study, the Cronbach’s α coefficient for the internal stimulation dimension was 0.751, and for the external stimulation dimension was 0.791.

Data analysis

Following the standard procedures of structural equation modeling, the reliability and validity of the measurement model were examined. Given the prediction-oriented focus of the present study and its emphasis on explaining variance in adolescents’ flourishing through the parallel mediating roles of cognitive and affective pathways, Partial Least Squares Structural Equation Modeling (PLS-SEM), as a variance-based approach, is more appropriate than covariance-based SEM (CB-SEM) for estimating predictive relationships among the antecedent variables and testing multiple mediation paths within an integrated model. Partial Least Squares Structural Equation Modeling (PLS-SEM) was conducted using SmartPLS 4.0 software to estimate the path coefficients among the latent variables in the structural model, and additional indicators, including R², f², SRMR, and Q²_predict (PLS predict), were further reported to assess the explanatory power, effect sizes, model fit, and predictive relevance of the model, and the significance of the path coefficients was tested using a bootstrapping procedure with 5,000 resamples. In addition, following the approach of Dul et al., Necessary Condition Analysis (NCA) was employed to examine the necessity of the effects of antecedent variables on the outcome variable [33].

In the PLS-SEM analysis, physical activity was modeled as a latent construct to reflect individuals’ overall level of physical activity. In the NCA analysis, by contrast, activity intensity, duration, and frequency were entered separately as independent condition variables to examine whether distinct activity components exerted necessary constraint effects on higher levels of flourishing. The integration of PLS-SEM and NCA in the present study is not intended simply to achieve statistical complementarity, but rather to reflect a differentiated examination of the theoretical propositions. Specifically, this approach allows for an assessment of how physical activity-related experiences facilitate adolescent flourishing through cognitive-affective processing pathways, while also identifying the minimum threshold conditions on which higher levels of flourishing depend. By jointly incorporating sufficiency and necessity logics, the study offers a more comprehensive account of the mechanisms and boundary conditions underlying adolescent flourishing.

Sufficiency test

Measurement model evaluation

Good reliability and validity are important indicators for evaluating the quality of measurement scales. As shown in Table 1, all composite reliability (CR) values exceeded the threshold of 0.7, indicating that all variables exhibited good reliability and that the scales demonstrated high internal consistency. The average variance extracted (AVE) values were all greater than 0.5, and the factor loadings of all measurement items for each variable were higher than 0.7, indicating that the model had good convergent validity. In addition, according to the Fornell–Larcker criterion, the square root of the AVE values for each construct was greater than the correlation coefficients between that construct and the other constructs, indicating that the scales had good discriminant validity. As shown in Table 2, the HTMT values among the latent variables were all below the threshold of 0.85, further indicating acceptable discriminant validity among the constructs.

Table 1.

Reliability and validity of the measurement model

Variable	Observed variable	Factor loading	AVE	CR
Physical activity	S1 S2 S3	0.711 0.821 0.783	0.598	0.816
Self-worth	V1 V2 V3 V4 V5 V6	0.809 0.775 0.733 0.761 0.798 0.760	0.598	0.899
Boredom	Bn Bw	0.869 0.705	0.626	0.768
Adolescents’ flourishing	F1 F2 F3 F4 F5 F6 F7 F8	0.814 0.752 0.827 0.726 0.801 0.855 0.839 0.774	0.643	0.935

Table 2.

Results of the HTMT discriminant validity test

	Physical activity	Self-worth	Boredom	Adolescents’ flourishing
Physical activity	1
Self-worth	0.223	1
Boredom	0.330	0.738	1
Adolescents’ flourishing	0.276	0.796	0.689	1

Common method bias test

The Harman single-factor test was used to examine the effect of common method bias. Factor analysis was conducted on all questionnaire items, and the first factor accounted for 34.289% of the total variance, which was lower than the critical threshold of 40%, indicating that there was no serious common method bias in this study. However, it should be noted that Harman’s single-factor test alone cannot definitively rule out common method bias, and the result should therefore be interpreted with caution.

Multicollinearity test

In addition, to further examine whether serious multicollinearity existed among the predictors in the structural model, variance inflation factor (VIF) values were calculated. Multicollinearity refers to the phenomenon in which some independent variables are highly correlated, which may lead to inaccurate confidence interval estimation of parameters and, consequently, affect the accuracy of the statistical results. The results showed that the VIF values in this study ranged from 1.000 to 1.660, all of which were below the critical threshold of 5, indicating that no serious multicollinearity was present in the model.

Sufficiency analysis

To test the sufficiency of the antecedent variables, the bootstrapping method in SmartPLS 4.0 software was used for hypothesis testing (Fig. 2). The results showed that physical activity positively influenced self-worth (β = 0.180, p < 0.001), supporting Hypothesis H2a; physical activity negatively influenced boredom (β=−0.190, p < 0.001), supporting Hypothesis H3a. Both self-worth (β = 0.517, p < 0.001) and boredom (β=−0.317, p < 0.001) had significant effects on adolescents’ flourishing, supporting Hypotheses H2b and H3b, respectively. In addition, the direct effect of physical activity on adolescents’ flourishing was significant, with an effect size of 0.069, supporting Hypothesis H1.

Fig. 2.

Path coefficient diagram

To further examine the mediating roles of self-worth and boredom in the process by which physical activity influenced adolescents’ flourishing, a bootstrapping procedure with 5,000 resamples was conducted on the original sample, and 95% confidence intervals that did not include zero were specified (Table 3). The significance tests of the mediation paths showed that the indirect effect of physical activity on adolescents’ flourishing through self-worth was significant (β = 0.093, p < 0.001), with a confidence interval of [0.064, 0.126], confirming the robustness of this indirect effect and providing strong support for Hypothesis H2c. Similarly, the indirect effect of physical activity on adolescents’ flourishing through boredom was also significant (β = 0.060, p < 0.001), with a 95% confidence interval of [0.039, 0.084], supporting Hypothesis H3c.

Table 3.

Results of direct and indirect effect tests

Path relationship	Path coefficient	t	95% confidence interval	P value	Hypothesis testing
Physical activity→adolescents’ flourishing	0.069**	7.181	[0.027, 0.111]	0.001	H1 supported
Physical activity→self-worth	0.180***	6.160	[0.124, 0.241]	0.000	H2a supported
Self-worth→adolescents’ flourishing	0.517***	18.090	[0.460, 0.573]	0.000	H2b Supported
Physical activity→boredom	-0.190***	6.033	[-0.254, -0.130]	0.000	H3a supported
Boredom→adolescents’ flourishing	-0.317***	11.065	[-0.372, -0.260]	0.000	H3b supported
Physical activity→self-worth→Adolescents’ flourishing	0.093***	5.910	[0.064, 0.126]	0.000	H2c supported
Physical activity→boredom→adolescents’ flourishing	0.060***	5.291	[0.039, 0.084]	0.000	H3c supported

* p < 0.05, ** p < 0.01, *** p < 0.001

The PLS-SEM structural model explained 59.8% of the variance in flourishing, 3.6% of the variance in boredom, and 3.2% of the variance in self-worth. In terms of effect sizes, self-worth had a large association with flourishing (f² = 0.401), boredom had a medium association with flourishing (f² = 0.150), and physical activity had small associations with boredom (f² = 0.037) and self-worth (f² = 0.033), whereas its direct association with flourishing was relatively weak (f² = 0.021). Regarding model fit, the SRMR value was 0.069, which fell within the acceptable range; therefore, model performance was interpreted in conjunction with the explanatory and predictive indices. In addition, the Q²_predict values for boredom, self-worth, and flourishing were 0.033, 0.029, and 0.046, respectively, all of which were greater than 0, indicating that the model had predictive relevance for the endogenous constructs.

Necessity test

To examine the necessity of the antecedent variables, the NCA package in R software was used to conduct necessary condition analysis. Specifically, the necessity of physical activity intensity, duration, and frequency, self-worth, internal stimulation, and external stimulation in influencing adolescents’ flourishing was tested. First, the effect sizes of the antecedent variables were analyzed. Effect size refers to the minimum level of a necessary condition required to produce a specific outcome. In the NCA package, two methods are available for generating ceiling lines: ceiling regression (CR) and ceiling envelopment (CE). The CR technique is used to analyze continuous variables and discrete variables with more than five levels, whereas the CE technique is used to analyze binary variables and discrete variables with fewer than five levels. Based on the characteristics of the sample, the CR technique was selected to generate the ceiling line for estimation, while the CE results were also reported to compare the robustness of the findings. Second, a quantitative analysis of the bottleneck levels of the condition variables was conducted. Bottleneck levels refer to the levels of necessary conditions required to achieve specific levels of the outcome variable and help identify key factors that constrain the attainment of the outcome. It should be noted that the NCA results in this study were interpreted as distributional constraints within the observed sample, rather than as evidence of absolute logical necessity, deterministic prerequisite status, or causal inevitability [34].

Necessity analysis of antecedent variables for adolescents’ flourishing

Based on the criteria proposed by Dul et al. [33], Table 4 presents the results of the necessity analysis of the antecedent variables for adolescents’ flourishing. The results showed that only self-worth met the criterion for a necessary condition in relation to adolescents’ flourishing, with a high level of statistical significance (p < 0.001) and an effect size exceeding 0.2, reaching a medium effect level. By contrast, physical activity intensity, duration, and frequency, as well as internal stimulation and external stimulation, did not meet the criterion for a necessary condition.

Table 4.

Results of the necessary condition analysis (NCA)

Variable	Method	Effect size(d)	p value
Physical activity intensity	CR CE	0.000 0.000	1.000 1.000
Physical activity duration	CR CE	0.000 0.000	1.000 1.000
Physical activity frequency	CR CE	0.021 0.042	0.269 0.269
Self-worth	CR CE	0.219 0.292	0.000 0.000
Internal stimulation	CR CE	0.000 0.000	1.000 1.000
External stimulation	CR CE	0.000 0.000	1.000 1.000

0 ≤ d < 0.1 indicates a low effect size, 0.1 ≤ d < 0.3 indicates a medium effect size, and d ≥ 0.3 indicates a high effect size

A necessary condition does not mean that the presence of a factor inevitably leads to the occurrence of the expected outcome; rather, it indicates that when the factor remains at a low level, higher levels of the outcome are typically difficult to achieve within the sample. Accordingly, the necessity of self-worth reflects a threshold-like constraining role: when adolescents’ self-worth is insufficient, higher levels of flourishing tend not to occur in the observed data. At the same time, the NCA effect size for self-worth (d = 0.219) should be interpreted as the size of the ceiling zone in the data space, that is, the extent to which high flourishing does not occur in the region where self-worth is low. This result indicates a relatively clear distributional constraint between low self-worth and high flourishing in the present sample, suggesting that self-worth carries a moderate level of necessity in relation to higher flourishing. However, such necessity should still be understood as a constraint identified from the sample distribution, rather than as evidence of logical indispensability, absolute causal necessity, or deterministic prerequisite status.

Bottleneck analysis of antecedent variables for adolescents’ flourishing

Table 5 presents the results of the bottleneck level analysis of antecedent variables for adolescents’ flourishing. The results indicate that the formation of flourishing at levels of 80% and below only requires self-worth to reach its bottleneck level. Specifically, as the level of adolescents’ flourishing increased, the minimum bottleneck level required for self-worth also increased progressively. When flourishing reached 40%, the bottleneck level of self-worth was 1.9%; when flourishing increased to 80%, the bottleneck level of self-worth rose correspondingly to 48.1%. This result further indicates that, at low to moderate levels of flourishing, self-worth constituted the most central constraining condition.

Table 5.

Results of the NCA bottleneck level analysis using the CR method (%)

Flourishing	Physical Activity intensity	Physical Activity duration	Physical Activity frequency	Self-worth	Internal stimulation	External stimulation
0	NN	NN	NN	NN	NN	NN
10	NN	NN	NN	NN	NN	NN
20	NN	NN	NN	NN	NN	NN
30	NN	NN	NN	NN	NN	NN
40	NN	NN	NN	1.9	NN	NN
50	NN	NN	NN	13.5	NN	NN
60	NN	NN	NN	25	NN	NN
70	NN	NN	NN	36.5	NN	NN
80	NN	NN	NN	48.1	NN	NN
90	NN	NN	10	59.6	NN	NN
100	NN	NN	25	71.2	NN	NN

NN indicates “not necessary.”

Further, for the formation of flourishing at levels of 90% and above, in addition to self-worth, other factors were also required to reach their respective bottleneck levels. For example, achieving 100% flourishing among adolescents required the frequency of physical activity to reach 25% and self-worth to reach 71.2%. This result indicates that, as adolescents’ flourishing continued to increase, its formation required multiple antecedent variables to jointly meet certain minimum levels; in other words, the synergistic effects of cognitive and affective factors were associated with higher levels of adolescents’ flourishing.

Discussion

The direct effect and necessity of physical activity on adolescents’ flourishing

Structural model analysis revealed a significant positive association between physical activity and adolescent flourishing. However, the interpretation of this direct effect should be tempered by consideration of its actual effect size. In substantive terms, the role of physical activity in flourishing is more appropriately characterized as a directionally clear and relatively stable, yet modest, promotive association. The results of the NCA further indicate that physical activity does not constitute a necessary condition for enhancing adolescents’ flourishing. Therefore, although physical activity constitutes an important protective factor for positive psychological development in adolescence, its role may be more likely reflected in the provision of positive behavioral experiences, developmental resources, and supportive contextual conditions. That is, although this activity is “useful,” it is not “essential.” When designing intervention related to promote adolescents’ flourishing, physical activity should be regarded as an “optional facilitating factor” rather than the “only solution pathway.”

The factors through which physical activity is associated with adolescents’ flourishing mainly include the intensity, duration, and frequency of physical activity. Compared with low-intensity physical activity, moderate-intensity physical activity is associated with lower levels of depressive and anxiety symptoms by increasing endogenous cannabinoid levels [35] and can significantly enhance individuals’ feelings of pleasure and energy after participation. However, high-intensity physical activity could be accompanied by stress responses and trigger neuroendocrine reactions, and extreme levels of stress may reduce physiological stability within a certain range [36]. In addition, the duration of physical activity should not be overlooked in its impact on flourishing. Maintaining an appropriate duration of physical activity is associated with lower negative emotions and higher levels of flourishing. Zeng et al. found that engaging in moderate-to-high intensity physical activity for durations of 60 min or longer is associated with more positive emotions and promotes improvements in flourishing [37]. Meanwhile, with regard to the frequency of physical activity, Chekroud et al. suggested that engaging in physical activity three to five times per week for 30–60 min per session is associated with higher flourishing, whereas individuals who engaged in physical activity more than 23 times per month or for more than 90 min per session may exhibit poorer flourishing [38]. Grasdalsmoen et al. found that, compared with activity duration and intensity, activity frequency has a greater impact on individuals’ flourishing, and that this effect varies by gender; specifically, physical activity frequency showed a stronger influence on flourishing among males than among females [39]. These physiological and psychological improvements are closely associated with enhancements in individuals’ flourishing. Therefore, physical activity is associated with s adolescents’ flourishing through multiple mechanisms, either directly or indirectly.

The mediating role of self-worth

Physical activity was indirectly associated with adolescents’ levels of flourishing through the mediating role of self-worth. Continuous participation in physical activity during childhood and adolescence associated with the satisfaction of individuals’ basic psychological needs and with higher flourishing, which is consistent with the findings of Doré et al. [40]. That is, the body serves as a prerequisite for mental development, and bodily actions and experiences shape and promote cognitive development, thereby further enhancing flourishing. The mediating role of self-worth was mainly reflected at the following cognitive levels. First, the peer interaction, cooperative participation, and social recognition embedded in physical activity participation helped individuals gain acceptance and recognition in social contexts and transform such external recognition into a relatively stable enhancement of self-worth [41], thereby being associated with reduced psychological burden among adolescents. Second, freedom is an enduring aspiration and pursuit of human beings, and physical activity inherently possesses the nature of freedom. Physical activity can provide an autonomy-supportive environment [42], and rule adherence, task engagement, and sustained persistence in physical activity make adolescents more likely to affirm their action capacity and self-regulatory ability, thereby enhancing their overall level of self-evaluation, thereby being associated with adolescents’ flourishing. Third, physical activity provided adolescents with opportunities to display competence, overcome challenges, and achieve goals [43]. Moreover, continuous achievement experiences helped strengthen individuals’ perceptions of competence and were further internalized into positive evaluations of personal value. This process evokes adolescents’ perceptions of self-worth and thereby associated with higher levels of flourishing among adolescents.

More specifically, the potential of physical activity to enhance adolescents’ self-worth may lie in the concrete experiential structure embedded in participation itself. Improvements in skill and task mastery may strengthen perceived competence; the attainment of incremental goals may foster self-efficacy and self-affirmation; teamwork and peer recognition may enhance social belonging and social self-evaluation; and autonomy in choosing activity forms and regulating participation pace may promote agency and perceived control. Relevant research has also shown that the association between physical activity and adolescent mental health can be explained, in part, by the satisfaction of basic psychological needs, particularly in the context of group sport participation [40]. Accordingly, self-worth should be understood not only as an abstract cognitive appraisal variable, but also as an important psychological mediator through which adolescents gradually develop a more positive sense of self by accumulating competence-related experiences, social feedback, and self-validation in physical activity contexts.

The mediating role of boredom

Physical activity was indirectly associated with adolescents’ flourishing through boredom. A lack of physical activity is associated with negative affective experiences such as loneliness, sleep problems, social isolation, anxiety, and boredom, thereby being linked to lower levels of adolescents’ flourishing, which is consistent with the findings of Gyasi et al. [44]. When individuals generate affective responses, they typically undergo a process of self-emotion regulation, and this process is often influenced by affective embeddedness and exhibits strong contextual dependency [45]. When individuals engage in physical activity, active bodily involvement and cathartic expression are enhanced, with particularly pronounced effects in alleviating boredom. Physical activity not only is associated with the disruption of negative affective states through bodily movement but also enables individuals to experience greater external stimulation during participation, thereby reactivating intrinsic interest and motivation. At the same time, physical activity can expand individuals’ daily life experiences by leveraging the perceptions of others, enhance affective awareness and acceptance, and help individuals better recognize and cope with boredom [46]. The mediating effect of boredom may operate through the following two mechanisms. First, from the perspective of physiological arousal, physical activity provides adolescents with an effective mechanism of physiological activation. During physical activity, the body undergoes physiological arousal, such as increased heart rate and respiration, and this physiological arousal helps adolescents escape negative affective states, improve attentional focus and physical activity levels, and thereby increase the likelihood of entering positive and energetic states. Second, from the perspective of psychological arousal, physical activity is associated with the release of various neurotransmitters (such as dopamine, endorphins, and serotonin), which can significantly enhance adolescents’ positive affective experiences, increase feelings of pleasure and satisfaction, and strengthen individuals’ capacity to cope with and adapt to daily challenges. These positive affective experiences are closely and positively associated with adolescents’ flourishing.

The boredom-alleviating effect of physical activity may involve a range of experiential and contextual mechanisms. Boredom is typically conceptualized as a low-arousal negative emotional state characterized by a perceived lack of meaning, insufficient stimulation, and impeded sustained engagement in the current activity; in sport and exercise contexts, it may further manifest in reduced persistence, diminished behavioral involvement, and an increased tendency toward disengagement [8]. More specifically, activity contexts marked by greater novelty, a stronger challenge–skill match, opportunities for immersive experience, and immediate social feedback may be more effective in alleviating adolescents’ low-arousal negative experiences in daily life. Consistent with flow theory, when task demands are optimally matched to individual skill levels, individuals are more likely to enter a state of intense concentration, sustained involvement, and intrinsic enjoyment [47]. Accordingly, the capacity of physical activity to reduce boredom and, in turn, promote flourishing may depend less on participation per se than on whether the activity provides adolescents with a sufficient sense of meaning, engagement, and immersion.

Bottleneck analysis of self-worth

The practical value of bottleneck analysis lies in identifying how the attainment of high levels of flourishing may be constrained when certain conditions fall below critical threshold levels. The present findings indicate that self-worth exhibits the property of a necessary condition. For adolescents, this suggests that self-worth is not merely a general positive psychological resource that facilitates flourishing, but may instead constitute a foundational psychological prerequisite for the realization of high levels of flourishing.

This finding carries important implications for educational practice and physical activity interventions. Existing practice has often emphasized increasing activity frequency, duration, or intensity as primary means of promoting adolescents’ positive development. From a necessary condition perspective, however, simply increasing the overall amount of physical activity is insufficient to ensure the attainment of high levels of flourishing. More importantly, attention should be directed to whether physical activity contexts can continuously provide the key psychological experiences that support the development of self-worth. In particular, teachers, coaches, and school administrators should place greater emphasis on strengthening adolescents’ positive self-perceptions through supportive feedback, enhancing their sense of competence through appropriately designed tasks, fostering social acceptance through cooperative activities and peer interaction, and consolidating their sense of agency and self-affirmation by providing opportunities for autonomous choice and progressive goal attainment. Accordingly, rather than treating physical activity as a simple behavioral prescription in which “more participation is always better,” greater emphasis should be placed on the quality of activity-context construction and its psychological supportive functions. This perspective not only offers a more fine-grained explanation of the boundary conditions underlying the attainment of high levels of flourishing, but also suggests that future intervention design should pay closer attention to identifying and overcoming this critical bottleneck condition.

Limitations and future directions

This study employed multiple methodological approaches to ensure the reliability and validity of the findings and to verify the proposed research model; however, several issues remain to be further explored. First, this study employed a cross-sectional design, with all variables measured at a single time point; therefore, temporal ordering could not be established and strict causal inferences cannot be made. Future research should adopt longitudinal, experience-sampling, or experimental designs to clarify the dynamic relationships and potential causal mechanisms among the variables. Second, physical activity was assessed using a brief three-item self-report scale. Although practical and easy to administer, such measurement remains vulnerable to recall bias and subjective judgment error. In addition, because all core variables were derived from single-source, single-time-point self-reports, common method bias may have influenced the findings. Future studies should incorporate more objective assessments, such as accelerometers, wearable devices, or multi-source data, to improve measurement precision. Third, although some demographic variables were controlled, other potentially important confounders were not systematically included. Factors such as socioeconomic status, academic stress, type of physical activity, and degree of organized participation may shape both physical activity engagement and flourishing. Future research should incorporate these variables more comprehensively to strengthen the robustness and explanatory power of the model. Fourth, although self-worth and flourishing were theoretically distinguished, some degree of conceptual proximity may remain, particularly in relation to positive self-evaluation and adaptive functioning. Future studies may further test their distinctiveness through competing models, alternative specifications, and more rigorous discriminant validity procedures. Accordingly, the sample was drawn primarily from in-school adolescents within a single province and was collected mainly through an online survey, which may limit representativeness and generalizability. Replication across broader regions, different school levels, and more diverse sociocultural contexts is therefore warranted.

Conclusion

The effects of physical activity, self-worth, and boredom on adolescents’ flourishing showed sufficiency relationships. Specifically, physical activity and self-worth were positively associated with adolescents’ flourishing, whereas boredom was negatively associated with flourishing. Notably, self-worth showed the strongest effect, indicating that adolescents’ self-evaluation was an important cognitive factor associated with flourishing. At the same time, both self-worth and boredom showed significant mediating effects in the relationship between physical activity and adolescents’ flourishing. The necessity analysis further showed that self-worth constituted an important necessary condition for higher levels of flourishing. In other words, self-worth alone was not sufficient to guarantee flourishing; however, when self-worth remained at a low level, higher levels of flourishing were typically difficult to achieve, indicating that self-worth functioned more as a threshold-like constraining condition. The bottleneck analysis further showed that, as the level of flourishing increased, the antecedent conditions required to achieve higher levels of the outcome also increased correspondingly, gradually reflecting a pattern of multi-variable synergy. However, it is worth noting that although boredom (internal stimulation and external stimulation) showed significant associations with flourishing, it did not emerge as a necessary condition. This suggests that boredom is better understood as an important affective factor associated with the level of flourishing, rather than as a foundational constraining condition supporting higher flourishing.

Authors’ contributions

H Z and MH Z were responsible for the conceptualization of the study, methodology design, software utilization, investigation, and writing the original draft of the manuscript. H Z played a key role in the conceptualization of the study, reviewed and edited the manuscript, and provided supervision throughout the research process. All authors reviewed the manuscript.

Funding

China Postdoctoral Science Foundation (Grant No. 2023M741080). Young Teachers' Innovation Project of Henan Normal University (2024KXON05).

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

This study was reviewed and approved by the Ethics Committee of Henan Normal University (Approval No. HNSD-2025-15-10) and in accordance with the principles of the Declaration of Helsinki. Written informed consent was obtained from all participants. For participants under the age of 16, written informed consent was obtained from their parents or legal guardians.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.