What a Difference a Method Makes: Aggregating Rankings and Scores in Sports

Michael A. Jones () and Jennifer M. Wilson ()
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Michael A. Jones: American Mathematical Society, Mathematical Reviews
Jennifer M. Wilson: Eugene Lang College, The New School, Department of Natural Sciences and Mathematics

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 1335-1368 from Springer

Abstract: Abstract This chapter investigates how aggregation procedures are applied in sports to rank players or teams based on individual performances and combined results from multiple rounds, events, or tournaments. Positional voting methods, which share a similar mathematical structure with these aggregation procedures, are introduced through examples such as most valuable player and Heisman Trophy balloting, with particular attention given to the Borda rule and positional methods’ connection to linear algebra. We demonstrate how positional methods are applied directly to aggregate rankings and scores in sports like boating and golf. In other competitions, such as the heptathlon and diving, performance results are converted into scores before aggregation, introducing an additional layer of analysis. When rankings incorporate events spanning a season or a specific time period – such as world rankings in golf, tennis, soccer, and archery – a moving window scheme is employed to focus on the relevant evaluation period. To account for the passage of time, multiplicative factors inspired by arithmetic and geometric sequences may discount older events, reducing their influence on current rankings. The chapter also examines the sensitivity of outcomes to parameter changes and discusses how rankings can vary depending on the aggregation method used. Strategies for minimizing anomalies in ranking results are also considered.

Keywords: Positional methods; Voting; Aggregating rankings; Aggregating scores; Discounting scores over time (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_64

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