Beyond 0.85: Adaptive PageRank Damping Factors for Small-Scale Networks with Applications to Football Rankings

Within competitive spatial invasion games like association football, team behavior represents a continuous, cooperative multi-agent coordination problem. Traditional PageRank frameworks suffer from possession-recycling bias, misinterpreting high-volume, low-risk horizontal loops between defensive clusters as structural prestige, misallocating spectral probability mass away from critical vertical transition hubs in contested zones. To eliminate this artifact, we present a modular, user-calibrated Adaptive Dynamic PageRank Architecture optimized for multi-agent game flow networks. The framework introduces a Macroscopic Sigmoid Governor that evaluates global edge density in real time to dynamically scale the network’s teleportation threshold, paired with an Absolute Outbound Volume Weighting Matrix to anchor relative prestige against physical execution scale. Validated against empirical StatsBomb event streams spanning distinct network topologies, the model successfully deflates passive recycling loops while isolating true playmaker hubs in complete alignment with real-world tactical outcomes. Concurrently, an integrated Floyd-Warshall node-deletion sequence exposes structural dependency polarities, mathematically isolating a singular central orchestrator as the network's definitive point of failure. Stress-tests across expanding synthetic topologies up to 5,000 nodes confirm that the dynamic governor guarantees complete numerical stability against topological trapping while significantly reducing convergence iterations for real-time edge processing in complex game environments.