Modeling Sports Engagement: A Game Refinement Theory Perspective on Game Length and Scoring Frequency

Game structure plays a crucial role in shaping engagement for both players and spectators, with elements such as game length, scoring frequency, and outcome uncertainty significantly influencing the emotional and cognitive experience. This paper investigates how these structural components impact engagement across three globally popular sports, One Day International (ODI) cricket, Twenty20 (T20) cricket, and soccer. Using Game Refinement (GR) theory and the Motion in Mind (MiM) framework, we quantitatively model engagement dynamics by analyzing the game length, scoring patterns, uncertainty resolution, and psychological pacing. Our results reveal that ODI cricket falls within the optimal GR zone (GR ∈ {0.07, 0.08}), indicating a balanced structure that supports fairness and sustained engagement. T20 cricket, while exceeding the optimal GR range, achieves high emotional intensity due to its rapid scoring and momentum shifts. Soccer, in contrast, exhibits a low scoring rate and a GR value above the ideal range, reflecting higher unpredictability and reduced fairness. To optimize soccer’s game length and scoring frequency, we propose a hypothetical 60-minute match model. Our findings demonstrate that reducing game length while scaling scoring frequency in soccer leads to an ideal GR value (≈ 0.077), aligning structural fairness with emotional pacing. This study offers a novel computational and theoretical lens for evaluating and refining sports formats, with broader implications for enhancing engagement across competitive sports.