Abstract
This paper by the noted German mathematician Ernst Zermelo (1871–1953) was long overlooked and was brought to the attention of the statistical community only in the mid-1960s, by John Moon and Leo Moser, professors of mathematics at the University of Alberta, Canada. Zermelo is concerned with the evaluation of players in chess tournaments, especially for tournaments lacking the balance of Round Robins, where all pairs of players meet equally often. There had long been an obvious method for dealing with Round Robins, namely to rank players according to their number of wins (counting draws as half-wins).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bradley, R.A. and Terry, M.E. (1952). The rank analysis of incomplete block designs. I. The method of paired comparisons. Biometrika, 39, 324–345.
David, H.A. (1988). The Method of Paired Comparisons, 2nd edn. Griffin, London.
Davidson, R.R. (1970). On extending the Bradley—Terry model to accommodate ties in paired comparison experiments. J. Amer. Statist. Assn., 65, 317–328.
Ford, L.R., Jr. (1957). Solution of a ranking problem from binary comparisons. Amer. Math. Monthly, 64, 28–33.
Kendall, M.G. (1955). Further contributions to the theory of paired comparisons. Biometrics, 11, 43–62.
Moon, J.W. (1968). Topics on Tournaments. Holt, Rinehart, and Winston, New York.
Rootselaar, B. van (1981). Zermelo. Dictionary of Scientific Biography, 13, 613–616.
Thurstone, L.L. (1927). A law of comparative judgment. Psychol. Rev., 34, 273–286.
Wei, T.H. (1952). The algebraic foundations of ranking theory. Unpublished Thesis, Cambridge University.
Zermelo, E. (1929). Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung. Math. Zeit., 29, 436–460.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
David, H.A., Edwards, A.W.F. (2001). The Evaluation of Tournament Outcomes. In: Annotated Readings in the History of Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3500-0_23
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3500-0_23
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3174-0
Online ISBN: 978-1-4757-3500-0
eBook Packages: Springer Book Archive