An application of incomplete pairwise comparison matrices for ranking top tennis players
arXiv:1611.00538 · doi:10.1016/j.ejor.2015.06.069
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.
14 pages, 2 figures
References in corpus (2)
Cited by in corpus (25)
- The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices
- A characterization of the Logarithmic Least Squares Method
- Characterization of an inconsistency ranking for pairwise comparison matrices
- University rankings from the revealed preferences of the applicants
- Tournament design: A review from an operational research perspective
- On the monotonicity of the eigenvector method
- Axiomatizations of inconsistency indices for triads
- Filling in pattern designs for incomplete pairwise comparison matrices: (quasi-)regular graphs with minimal diameter
- An alternative quality of life ranking on the basis of remittances
- Revenue allocation in Formula One: a pairwise comparison approach
- Some impossibilities of ranking in generalized tournaments
- Entropy production rate as a criterion for inconsistency in decision theory
- An impossibility theorem for paired comparisons
- A lexicographically optimal completion for pairwise comparison matrices with missing entries
- Deriving Priorities From Inconsistent PCM using the Network Algorithms
- Hierarchy Selection: New team ranking indicators for cyclist multi-stage races
- Coronavirus and sports leagues: obtaining a fair ranking when the season cannot resume
- The incomplete Analytic Hierarchy Process and Bradley-Terry model: (in)consistency and information retrieval
- How to choose a completion method for pairwise comparison matrices with missing entries: An axiomatic result
- On the coincidence of optimal completions for small pairwise comparison matrices with missing entries
- Inconsistency thresholds for incomplete pairwise comparison matrices
- A DEMATEL-Based Completion Method for Incomplete Pairwise Comparison Matrix in AHP
- Optimal sequences for pairwise comparisons: the graph of graphs approach
- Limits of PageRank-based ranking methods in sports data
- Incomplete Analytic Hierarchy Process with Minimum Weighted Ordinal Violations