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

arXiv: https://arxiv.org/abs/1611.00538 · HTML: https://mlsanity.com/paper/1611.00538/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2016.

## Built on by (most cited first, 11 of 11)

- [Inconsistency thresholds for incomplete pairwise comparison matrices](https://mlsanity.com/paper/2102.10558/) (2021)
- [Ranking with Confidence for Large Scale Comparison Data](https://mlsanity.com/paper/2202.01670/) (2022)
- [Statistical inference for pairwise comparison models](https://mlsanity.com/paper/2401.08463/) (2024)
- [What Does Preference Learning Recover from Pairwise Comparison Data?](https://mlsanity.com/paper/2602.10286/) (2026)
- [Convergence analysis of a family of Zermelo-type iterations for the Bradley--Terry model](https://mlsanity.com/paper/2607.22221/) (2026)
- [Principal Trade-off Analysis](https://mlsanity.com/paper/2206.07520/) (2022)
- [Beyond Suspension: A Two-phase Methodology for Concluding Sports Leagues](https://mlsanity.com/paper/2404.00178/) (2024)
- [An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods](https://mlsanity.com/paper/2408.13297/) (2024)
- [An experimental approach: The graph of graphs](https://mlsanity.com/paper/2508.17520/) (2025)
- [Capturing Intransitive Dominance in Tennis Forecasting: A Graph Neural Network Approach](https://mlsanity.com/paper/2510.20454/) (2025)
- [Bradley-Terry model under general comparison graphs](https://mlsanity.com/paper/2610.06237/) (2026)

## Abstract (arXiv)

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.