The model developed in this study is novel. A carefully structured four-dimensional football passing dynamics is formulated to analyze ball flow and possession play. The compartments: defense, midfield, forward, and goal were aggregated player roles. The model achieved analytical tractability and preserved essential and realistic directional flow of play. The study focused on the stability analysis of the model, and theoretical analysis of structured ball movement. The results of the study showed that the model remained consistent at all times. Using a constructed Lyapunov function, the study showed that under suitable conditions, the equilibrium is globally asymptotically stable. If P0 < 1, the system is stable and dominated by decay.
Nwokike et al. (2026) studied this question.