Symmetric Sequential Analysis: The Efficiencies of Sports Scoring Systems (With Particular Reference to Those of Tennis)
采用伯努利模型分析网球等体育计分系统，将其视为序贯统计检验，发现传统网球计分在顶级男子比赛中效率过低，并提出一种增加熵的简单修改方案来提高效率。
SUMMARY Bernoulli-type models are adopted for the sequence of contested points between two players (or teams). In bipoints, there are two types of point – “A serving” and “B serving” – necessary for a realistic model of top (class) men's tennis. Unipoints is the special case of bipoints in which the probabilities that A (and hence B) wins each type of point are the same–a reasonable model for top men's squash rackets. Sports scoring systems based upon such play (“uniformats” and “biformats”) may be regarded as sequential statistical tests concerning the identity of the “better player”. Provided they satisfy certain fairness criteria, these tests are symmetric, with equal probabilities of type I and II error, and a unique efficiency p; then formally 1 – p represents the average fraction of play being virtually wasted through the use of a suboptimal scoring system. Largely because in top men's tennis the proportions of service points won by both players are so high, the efficiency of traditional tennis scoring in such play is unduly low. Whilst the introduction of tiebreaker games has further reduced efficiency, it is shown how a simple entropy-increasing modification of the traditional scoring system serves to increase efficiency.