A Probability Analysis of the Playoff System in Sumo Tournaments

  • Anthony J. Hayter
Conference paper


If three rikishi are tied at the conclusion of a sumo tournament, then a playoff system is implemented to determine who will be the tournament champion. This system has the interesting property that the two rikishi who contest the first fight have an advantage over the third rikishi. Some probability calculations are presented which analyse this playoff system and which assess the relative advantages and disadvantages of the starting positions. The number of fights needed to determine the champion is also considered, and comparisons are made with a fairer playoff protocol. Extensions are also considered to situations with more than three rikishi.


Probability Analysis Probability Calculation Probability Mass Function Balance Case Balance Situation 
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  2. Brace, A. and Brett, J. (1975). An alternative to the round robin tournament. Combinatorial Mathematics, III, 62–78, Lecture Notes in Mathematics, Volume 452, Berlin: Springer.Google Scholar
  3. Sobel, M. and Weiss, G. (1970). Inverse sampling and other selection procedures for tournaments with two or three players. Nonparametric Techniques in Statistical Inference, edited by Puri, M. L., 515–543, Cambridge University Press.Google Scholar

Copyright information

© The Institute of Statistical Mathematics 2002

Authors and Affiliations

  • Anthony J. Hayter
    • 1
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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