a b s t r a c tPairwise 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.
Pairwise comparison matrices are widely used in Multicriteria Decision
Making. This article applies incomplete pairwise comparison matrices in the
area of sport tournaments, namely proposing alternative rankings for the 2010
Chess Olympiad Open tournament. It is shown that results are robust regarding
scaling technique. In order to compare different rankings, a distance function
is introduced with the aim of taking into account the subjective nature of
human perception. Analysis of the weight vectors implies that methods based on
pairwise comparisons have common roots. Visualization of the results is
provided by Multidimensional Scaling on the basis of the defined distance. The
proposed rankings give in some cases intuitively better outcome than currently
used lexicographical orders
Wo es auch kein System, keinen Wahrheitsapparat gibt, da gibt es doch eine Wahrheit, und diese wird dann meistens nur durch ein geübtes Urteil und den Takt einer langen Erfahrung gefunden. Gibt also die Geschichte hier keine Formeln, so gibt sie doch hier wieüberall Ubung des Urteils. 1
AbstractThe study aims to compare different designs for the World Men's Handball Championships. This event, organised in every two years, has adopted four hybrid formats consisting of knockout and round-robin stages in recent decades, including a change of design between the two recent championships in 2017 and 2019. They are evaluated under two extremal seeding policies with respect to various outcome measures through Monte-Carlo simulations. We find that the ability to give the first four positions to the strongest teams, as well as the expected quality and outcome uncertainty of the final is not necessarily a monotonic function of the number of matches played: the most frugal format is the second best with respect to these outcome measures, making it a good compromise in an unavoidable trade-off. A possible
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