Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-23T15:46:15.244Z Has data issue: false hasContentIssue false
  • English
  • Français

An unexpected characteristic of tournament predictive power

Published online by Cambridge University Press:  21 June 2021

Leonard M. Wapner
Leonard M. Wapner*
Affiliation:
Division of Mathematical Sciences, El Camino College, 16007 Crenshaw Boulevard, Torrance, CA90506, USA e-mail: lwapner@elcamino.edu
Get access Rights & Permissions [Opens in a new window]

Extract

A tournament is a series of games (matches) among competitors for an overall prize. Beyond sporting events, tournament structure can relate to elections, applicants competing for an employment position, etc. Tournament structure also exists within certain species of birds and mammals where dominance relations develop, forming a tournament-like pecking structure [1]. The format of the tournament depends on the tournament’s objective giving consideration to time, financial, geographical, and other constraints. The two most common formats where players compete pairwise are the single elimination (knockout, sudden death) tournament and the round robin tournament. Our discussion includes both. A third popular format is that of a contest, where all players perform simultaneously only once. Examples of this type include most golf tournaments as well as track and field athletic events. A detailed analysis of contests as they relate to topics discussed here is given in [2].

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 563 , July 2021 , pp. 201 - 208
Check for updates
Copyright
© Mathematical Association 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Harary, F. and Moser, L., The theory of round robin tournaments, The American Mathematical Monthly 73(3) (1966) pp. 231–246.CrossRefGoogle Scholar
Ryvkin, D. and Ortmann, A., The predictive power of three prominent tournament formats, Management Science 54(3) (2008) pp. 492–504.CrossRefGoogle Scholar
Zermelo, E., Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung, Mathematische Zeitschrift 29 (1929) pp. 436–460.CrossRefGoogle Scholar
Schwenk, A., What is the correct way to seed a knockout tournament?, The American Mathematical Monthly 107(2) (2000) pp. 140–150.CrossRefGoogle Scholar
Groh, C., Moldovanu, B., Sela, A., and Sunde, U., Optimal seedings in elimination tournaments, Economic Theory 49(1) (2012) pp. 59–80.CrossRefGoogle Scholar
Kendall, M., Further contributions to the theory of paired comparisons, Biometrics 11(1) (1955) pp. 43–62.CrossRefGoogle Scholar