Incomplete pairwise comparison matrices: Ranking top women tennis players

Temesi, József ORCID:, Szádoczki, Zsombor ORCID: and Bozóki, Sándor ORCID: (2023) Incomplete pairwise comparison matrices: Ranking top women tennis players. Journal of the Operational Research Society . pp. 1-13. DOI

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The method of pairwise comparisons is frequently applied for ranking purposes. This article aims to rank top women tennis players based on their win/lose ratios. Incomplete pairwise comparison matrices (PCMs) were constructed from data obtained from the WTA (Women’s Tennis Association) homepage. The database contains head-to-head results from the period between 1973 and 2022 for 28 players who had the position No. 1 in the official rankings of WTA. The weight vector was calculated from the incomplete PCM with the logarithmic least squares method and the eigenvector method. The results are not surprising: Serena Williams, Steffi Graf, and Martina Navratilova stand in the first three positions, and Martina Hingis, Kim Clijsters, and Justine Henin follow them. We also tested the frequently used probability-based Bradley-Terry method and found high rank-correlation values. Using graph representations, the results gave us a deeper insight into the properties of incomplete PCMs. Special attention was given to the nontransitive triads. A data modification was necessary to remove ties in order to apply the commonly used tests. The results indicate that ordinally nontransitive triads are not significant in the data we analysed.

Item Type:Article
Uncontrolled Keywords:Multi-criteria, sports, decision analysis, graphs
Divisions:Institute of Operations and Decision Sciences
Subjects:Decision making
Projects:TKP2021-NKTA-01 NRDIO
ID Code:8265
Deposited By: Ádám Hoffmann
Deposited On:08 Jun 2023 07:03
Last Modified:08 Jun 2023 07:03

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