Affiliation:
1. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, the Netherlands
Abstract
Abstract
A shootout is a popular mechanism to identify a winner of a match between two teams. It consists of rounds in which each team gets, sequentially, an opportunity to score a point. It has been shown empirically that shooting first or shooting second in a round has an impact on the scoring probability. This raises a fairness question: is it possible to specify a sequence such that identical teams have equal chance of winning? We show that, for a sudden death, no repetitive sequence can be fair. In addition, we show that the so-called Prohuet–Thue–Morse sequence is not fair. There is, however, an algorithm that outputs a fair sequence whenever one exists. We also analyze the popular best-of-$k$ shootouts and show that no fair sequence exists in this situation. In addition, we find explicit expressions for the degree of unfairness in a best-of-$k$ shootout; this allows sports administrators to asses the effect of the length of the shootout on the degree of unfairness.
Funder
The NWO Gravitation Project NETWORKS
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Management Science and Operations Research,Strategy and Management,General Economics, Econometrics and Finance,Modelling and Simulation,Management Information Systems
Cited by
7 articles.
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