Background: School bullying represents a critical global public health issue among adolescents. Although existing evidence suggests physical activity (PA) may reduce bullying risk, longitudinal data on bidirectional associations and gender-specific variations remain limited. This study employed a cross-lagged panel model (CLPM) to investigate the temporal dynamics between PA and school bullying (SB) and examine gender-moderating effects. Methods: A cohort of 577 middle school students (294 boys, 283 girls; mean age = 14.31 ± 2.1 years) from seven schools across Wuhan, Shijiazhuang, and Chengdu completed three-wave longitudinal assessments over 9 months (September 2024–March 2025). Validated instruments included the School Bullying Scale (SBS) and Physical Activity Rating Scale (PARS). The CLPM analysis evaluated bidirectional predictive pathways, with gender-stratified multi-group comparisons. Results: Significant bidirectional negative associations emerged: (1) PA at T1/T2 predicted reduced SB at T2/T3 (β = −0.14 to −0.26, p < 0.001). (2) SB at T1/T2 predicted decreased PA at T2/T3 (β = −0.27 to −0.38, p < 0.001). (3) Gender significantly moderated these relationships, with PA conferring stronger protective effects against subsequent SB in males (β = −0.35 vs. −0.21 for PA→SB paths). Conversely, SB triggered earlier and more pronounced PA reductions in males (β = −0.42 vs. −0.29 for SB→PA paths). Conclusions: PA and SB demonstrate stable bidirectional negative associations in adolescents, with significant gender divergence. Males exhibit greater resilience to bullying through PA engagement but heightened vulnerability to PA reduction post-victimization. These findings underscore PA-based interventions as promising bullying mitigation strategies, necessitating gender-tailored implementation approaches.

Objective: The study aims to explore how sensation seeking relates to college students sports lottery purchasing behavior, mediated by fear of missing out and moderated by perceived risk.Methods: A study surveyed 409 college students using various scales to assess sensation seeking, sports lottery purchasing behavior, fear of missing out, and perceived risk. Data analysis included descriptive stats, t-tests, partial correlations, mediation and moderation effects, and Bootstrap testing to understand the psychological drivers behind sports lottery purchases among students.Results: (1) Sensation seeking significantly and positively predicted college students sports lottery purchasing behavior; (2) Fear of missing out played a partial mediating effect in the influence of sensation seeking on college students sports lottery purchasing behavior; (3) Perceived risk had a moderating effect in the second half of the path of the mediating effect of fear of missing out.Conclusion: The study concludes that sensation seeking directly affects college students sports lottery purchasing behavior, mediated by fear of missing out. The mediating effect is moderated by perceived risk, highlighting the complexity of psychological factors in risk-taking behaviors. This insight calls for tailored interventions addressing these multifaceted factors.