Improving strength of schedule metrics in sports scheduling
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Adam DeHollander
and
Mark Karwan
Abstract
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.
Acknowledgments
The authors would like to thank the sports conference for their financial support and for providing the data necessary for this study.
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Research ethics: This study did not involve human participants or animal subjects and solely utilized simulation methods. Therefore, ethical approval was not required.
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Informed consent: As no human participants were involved in this simulation study, informed consent was not applicable.
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Author contributions: Adam DeHollander: Conceptualization, Methodology, Data Analysis, Writing – Original Draft. Mark Karwan: Supervision, Project Administration, Funding Acquisition, Conceptualization, Methodology, Writing – Review & Editing.
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Use of Large Language Models, AI and Machine Learning Tools: A large language model (LLM) was used solely to assist with wording and language refinement in portions of the manuscript. The model was not used for generating original content, conducting analyses, or contributing to the conceptual or methodological aspects of the work.
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Conflict of interest: The authors declare no conflicts of interest related to this study.
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Research funding: This research was supported by funding from a sports conference. The development of the Strength of Schedule (SoS) metrics was conducted independently from this funding; the funding facilitated the application of these metrics to the conference’s data.
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Data availability: The data generated and analyzed during this study are available from the corresponding author upon reasonable request.
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