An application of incomplete pairwise comparison matrices for ranking top tennis players

TL;DR

This paper applies incomplete pairwise comparison matrices to rank top tennis players based on their match results, demonstrating the methods' effectiveness and raising questions about their properties.

Contribution

It introduces a novel application of incomplete PCMs for ranking tennis players and compares eigenvector and logarithmic least squares methods in this context.

Findings

Nadal, Federer, and Sampras ranked top over four decades.

Both eigenvector and least squares methods produced consistent rankings.

The study highlights open questions about properties of incomplete PCMs.

Abstract

Pairwise comparison is an important tool in multi-attribute decision making. Pairwise comparison matrices (PCM) have been applied for ranking criteria and for scoring alternatives according to a given criterion. Our paper presents a special application of incomplete PCMs: ranking of professional tennis players based on their results against each other. The selected 25 players have been on the top of the ATP rankings for a shorter or longer period in the last 40 years. Some of them have never met on the court. One of the aims of the paper is to provide ranking of the selected players, however, the analysis of incomplete pairwise comparison matrices is also in the focus. The eigenvector method and the logarithmic least squares method were used to calculate weights from incomplete PCMs. In our results the top three players of four decades were Nadal, Federer and Sampras. Some questions have been raised on the properties of incomplete PCMs and remains open for further investigation.