• Physics 18, s80
A new algorithm efficiently ranks competitors in settings ranging from sports tournaments to food-preference surveys.
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Many competitive contests pit more than two players, teams, or products against each other. In the FIFA World Cup, for example, teams initially face off within groups of four. Although theorists have developed algorithms to rank the competitors’ performances in such contests, these procedures can take a modern desktop computer hours to complete if there are many competitors and individual competitions. An efficient alternative has now been devised by Filippo Radicchi and his colleagues at Indiana University Bloomington [1]. By implementing their algorithm on various datasets, the researchers have demonstrated its broad uses.
In 2023 physicist Mark Newman proposed a fast-ranking algorithm for boxing tournaments, chess competitions, and other contests where only two competitors battle at once. That algorithm uses an iterative process that gradually converges to the final ranking and is typically from 3 to 100 times quicker than the standard approach, first introduced almost a century ago. Radicchi and his colleagues generalized Newman’s algorithm to settings where more than two competitors are involved in each comparison.
The researchers applied their algorithm to several real-world datasets. These included every group stage of the FIFA World Cup, elections of the American Psychological Association, and surveys of sushi preferences. The algorithm was found to be from 2 to 70 times faster than the standard approach, depending on the dataset. In the World Cup ranking, the top four positions went to the teams with the most titles: Brazil, Germany, Italy, and Argentina. But somewhat surprisingly, the fifth position went to the Netherlands, despite its lack of World Cup championships.
–Ryan Wilkinson
Ryan Wilkinson is a Corresponding Editor for Physics Magazine based in Durham, UK.
References
- J. Yeung et al., “Efficient inference of rankings from multibody comparisons,” Phys. Rev. E 112, 014305 (2025).
