Academic journal article Research Quarterly for Exercise and Sport

# The Use of Transition and Signal Flow Diagrams for Evaluating Formats Used in Choosing Winners in Certain Athletic Contests

Academic journal article Research Quarterly for Exercise and Sport

# The Use of Transition and Signal Flow Diagrams for Evaluating Formats Used in Choosing Winners in Certain Athletic Contests

## Article excerpt

Daniel P Connaughton and John F. Mahoney, University of Florida

This poster presentation provides an easily understood method for performing certain probability calculations, which often occur in connection with competitive sports. In determining which competitor, A or B, is better, a single head-to-head contest should be unconvincing since the laws of probability allow a slightly weaker side to win reasonably often. Doubt could be removed if the two opponents were allowed to compete a very large number of times, however, this is usually unmanageable. As a compromise, other competitive formats may be considered. For example, the better side could be defined to be the first side to win at least N meetings and to do so with a plurality of at least n wins, where (1 [less than] n [less than] N). For instance, in the World Series of baseball, N= 4, and n = 1, but in tennis a game is awarded to the first competitor to win at least four points with a plurality of two. This corresponds to N = 4, and n = 2. A method of computing the probability of winning or losing, when using the se, or similar, formats is explained. …

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