The relationship of excitement, importance and entropy to the efficiency of statistical hypothesis tests

[摘要] Sports scoring systems can be seen as statistical hypothesis tests, and the tennis scoring system in particular can be viewed as a particular sequential 2-sample binomial test. Thus, the excitement of a point (or observation) within a scoring system can be seen to have a place within hypothesis testing. The 2-sample binomial tests known to be the most efficient are shown to have related characteristics with respect to the measures of excitement and importance in sport and with Shannon entropy in information theory. This paper also includes several new, interesting and quite general scoring systems theorems.

[关键词] Sports scoring systems;excitement of a point;importance of a point;entropy of a point;efficiency of a scoring system;efficiency of a hypothesis test