From Opening to Endgame: When Does the Game Get Engaging and Exciting? Exploring Phase-Based Velocity Dynamics Using the MiM Framework

Understanding how engagement and excitement evolve throughout different phases of a sporting event is essential for advancing research in sports analytics, psychology, and game design. Previous models, like Game Refinement theory, have effectively quantified overall game sophistication but often overlook the dynamic, temporal nature of gameplay. This study addresses this gap by applying the physics-inspired Motion in Mind (MiM) framework to explicitly examine phase-specific gameplay dynamics in three globally popular sports: ODI cricket, T20 cricket, and soccer. Each match was segmented into opening, middle, and endgame phases, enabling detailed computation of key MiM parameters including velocity, acceleration, jerk, momentum, and potential reinforcement energy. Notably, ODI cricket showed initial high excitement that gradually declined toward the end, highlighting strategic shifts from aggressive to more calculated gameplay, whereas T20 cricket exhibited rising momentum and heightened excitement towards the endgame. In contrast, soccer unexpectedly revealed intense peaks during its middle phase. These findings provide novel theoretical insights into how temporal structures shape spectator and player engagement and offer practical strategies for optimizing match design, coaching tactics, and spectator enjoyment across competitive sports contexts.