An application of incomplete pairwise comparison matrices for ranking top tennis players
This provides a domain-specific ranking for tennis enthusiasts, but it is incremental as it applies existing methods to a new dataset.
The paper tackled the problem of ranking top tennis players using incomplete pairwise comparison matrices, resulting in Nadal, Federer, and Sampras being identified as the top three players over four decades.
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.