Visualizing heterogeneous associations: economic capital and adolescent football participation in China: a cross-sectional study using quantile regression with school-level fixed effects

Background Fair participation in sports is a key focus of public health, but socioeconomic barriers limit youth participation. Although family wealth is related to participation, its specific differences at different levels of opportunity are not yet clear. This study goes beyond the average correlation and deeply analyzes the differentiated relationship between adolescent family economic capital and opportunities for football participation. Methods We conducted a cross-sectional survey among 1,860 adolescents aged 12–18 years (from 42 schools) in Jilin Province. The sample was selected by multi-stage stratified cluster sampling. Data were collected using a standardized questionnaire. The study constructs a comprehensive “Football Participation Opportunity Index” and “Family Economic Capital Index.” After controlling for a range of personal, family, and environmental factors, we estimated the coefficients of economic capital at the 10th, 25th, 50th, 75th, and 90th quantiles of the FOI distribution using quantile regression models with school fixed effects. At the same time, we have drawn a series of charts to visualize the data base, methodological principles, core findings, potential mechanisms and policy implications. Results The analysis revealed a significant J-type association pattern. The impact of economic capital was strongest in the group with the lowest chance of participation (10th quantile; β = 0.341, 95% CI: 0.250–0.432), suggesting that it may constitute a critical participation threshold. The effect weakened around the median but strengthened again at the top of the chance distribution (90th quantile; β = 0.260, 95% CI: 0.145–0.375), suggesting that it may be related to access to elite-level opportunities. Visualization analysis further illustrates that other factors, such as urban household registration, parental contacts and school facilities, also show different patterns of association throughout the opportunity spectrum. Conclusion The correlation between family economic capital and youth football participation shows a significant random level change, revealing inequality at both ends. We need to adopt a dual track strategy: providing economic support for disadvantaged youth, while ensuring transparency and merit based selection in elite selection. The visualization framework enhances the understanding and conversion potential of discoveries.