Network topology fundamentally determines how cascading failures propagate through sports systems, yet the risk thresholds governing this relationship remain unquantified. We developed a network-agent model comparing four structural configurations through failure propagation dynamics, protection strategies, and recovery mechanisms across random, regular, small-world, and scale-free networks. Scale-free structures, characteristic of star-player dependent teams, exhibit 57% higher vulnerability than regular counterparts, with a Network Vulnerability Index of 1.24 versus 0.79. Immediate recovery interventions ( ) effectively prevent cascading failures, while delayed responses ( ) trigger exponential propagation. Phase space analysis reveals distinct stability basins, with scale-free configurations occupying the largest failure-dominant region at 43% of the phase space. Empirical validation against professional injury cascade records and international league shutdown data confirms strong agreement between model predictions and observed outcomes, with leagues implementing immediate interventions recovering 26.9% faster. These findings establish quantitative thresholds for topology-aware management strategies to mitigate cascading failures in professional sports.