Improving strength of schedule metrics in sports scheduling

: This paper studies sports Strength of Schedule (SoS) metrics and their utility for decision-makers in creating season schedules. We identify limitations of the widely used Bowl Championship Series (BCS) SoS metric, including infrequent rank changes and reduced variance, which limit its effectiveness in assessing true schedule difficulty. In response, we introduce two novel metrics: Probabilistic Random Walk Length (PRWL) SoS and Customized-Distributional (CD) SoS. The PRWL SoS leverages random walks on a graph to provide a comprehensive measure incorporating the difficulty of a team’s opponents schedules. The CD SoS offers a customizable approach, incorporating team-specific goals and preferences, for a more tailored assessment of schedule strength. Additionally, we propose a SoS variability metric to evaluate the variability of SoS among teams, promoting schedule balance. Through a detailed case study involving a large sports conference, we demonstrate the practical application and impact of our proposed metrics. The case study illustrates the superiority of the proposed scheduling format over the existing one, prompting the conference to adopt a new schedule format and eliminate their previous divisional structure. Our contributions provide more accurate tools for evaluating schedule difficulty, enhancing schedule balance, and optimizing sports schedules, ultimately promoting fairness and competitiveness in sports leagues.