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The Evaluation of Tournament Outcomes

Comments on Zermelo (1929)
  • H. A. David
  • A. W. F. Edwards
Part of the Springer Series in Statistics book series (SSS)

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).

Keywords

Paired Comparison Balance Case Strong Opponent Round Robin Tournament Regular Tournament 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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.MathSciNetMATHGoogle Scholar
  2. David, H.A. (1988). The Method of Paired Comparisons, 2nd edn. Griffin, London.MATHGoogle Scholar
  3. Davidson, R.R. (1970). On extending the Bradley—Terry model to accommodate ties in paired comparison experiments. J. Amer. Statist. Assn., 65, 317–328.CrossRefGoogle Scholar
  4. Ford, L.R., Jr. (1957). Solution of a ranking problem from binary comparisons. Amer. Math. Monthly, 64, 28–33.CrossRefGoogle Scholar
  5. Kendall, M.G. (1955). Further contributions to the theory of paired comparisons. Biometrics, 11, 43–62.MathSciNetCrossRefGoogle Scholar
  6. Moon, J.W. (1968). Topics on Tournaments. Holt, Rinehart, and Winston, New York.MATHGoogle Scholar
  7. Rootselaar, B. van (1981). Zermelo. Dictionary of Scientific Biography, 13, 613–616.Google Scholar
  8. Thurstone, L.L. (1927). A law of comparative judgment. Psychol. Rev., 34, 273–286.CrossRefGoogle Scholar
  9. Wei, T.H. (1952). The algebraic foundations of ranking theory. Unpublished Thesis, Cambridge University.Google Scholar
  10. Zermelo, E. (1929). Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung. Math. Zeit., 29, 436–460.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • H. A. David
    • 1
  • A. W. F. Edwards
    • 2
  1. 1.Statistical Laboratory and Department of StatisticsIowa State UniversityAmesUSA
  2. 2.Gonville and Caius CollegeCambridgeUK

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