A Dynamic Graph-Based Model for Optimal Ball Circulation in Basketball Offense

Abstract

This paper presents a dynamic graph-based framework for modeling and optimizing ball circulation in basketball offense. Players are represented as vertices of a directed graph, while passes correspond to weighted edges whose weights encode spatial relations such as inter-player distance and passing cost. The model is driven by sensor-based tracking data, which are stored in structured data tables and updated at each decision step.

At every time instance, the player in ball possession is identified and the current game state is retrieved from the data structure. For each potential receiver, spatial and contextual metrics are computed, including distance from the ball handler, spacing defined as the distance from the nearest defender, and defensive pressure. A constrained optimization rule is then applied: the ball is passed to the nearest feasible teammate whose spacing exceeds a predefined threshold, ensuring both efficiency and safety of the passing decision.

The framework operates as a dynamic iterative process, where graph weights and node evaluations are recomputed after each pass, enabling real-time decision-making and continuous adaptation to the evolving game state. Additionally, offensive and defensive formations are modeled as interacting graphs, capturing spatial dependencies and defensive constraints.

The proposed approach provides a mathematically grounded and data-driven methodology for analyzing offensive behavior, supporting real-time decision systems, and identifying optimal ball circulation patterns in basketball.