Efficacy of traditional sport tournament structures
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Efficacy of traditional sport tournament structures T McGarry and RW Schutz University of British Columbia The ranking abilities of some traditional sport tournaments under a variety of initial conditions were analyzed using Monte Carlo procedures. A range of outcome measures were used since a tournament’s efficacy will likely depend upon both its objectives and the playing abilities of its contestants. The traditional knockout (KO) is a weak tournament in its ability to rank all players although it requires fewer games than the round robin (RR). The KO tournament’s effifacy is notably enhanced, however, in some cases beyond that of the RR tournament if double elimination procedures are used and the seeding is reasonably accurate. Under these conditions, we consider the KO structure to be the best available structure for most tournament purposes. A secondary recommendation of this study is that the fourth and fifth placings be reversed in the traditional KO structures for ranking all players in the eight player situation. Keywords: probability; simulation; sports; tournaments
Efficacy of traditional sport tournament structures Researchers in sport and exercise science have a history of interest in sport scoring systems, most notably in their attempts to derive fair and equitable systems for determining contest outcomes. A stochastic processes model for evaluating paired contests was proposed by Schutz1 and applied to tennis scoring, a methodology that has subsequently been used to investigate the utility of alternative scoring systems in tennis2, squash3,4 and volleyball5,6. Somewhat surprisingly, virtually all of this work has concentrated on scoring systems for specific sports, and there has been little work in the more general area of sport tournaments. Thus, while we may have an optimal scoring system to determine a game or match outcome between two players in a particular sport, we do not know the most efficient method to select, for example; the best player in the minimum amount of time (contests), the maximum probability that the two best players will meet in a final match, the three medal winners or the best four teams to advance to the next level of competition. The general purpose of this paper then is to extend the work on sport scoring systems and to examine the utility of various tournament structures. To do this, we make use of the extensive work in biometrics, mathematics and statistics in the area of paired compar-isons, where paired comparisons refers to a set of binary contests or comparisons with the purpose of rank ordering the top n contests (n can vary from 1 to p, where p is the number of players). We restrict our focus to variations of the two most common tournaments, the Elimination or Knockout (KO) and the Round Robin
Correspondence: T McGarry, School of Human Kinetics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z1.
(RR) and assume that the context in which these tournaments are applied is
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