The Importance of a Game

Abstract

Organized play for many of major sports that are popular around world (baseball, basketball, hockey, tennis, and volleyball, for example) involves a contest between two opponents in which victor is team or individual that is first to win a prescribed number of subcontests. Often during these contests one will hear in conversation or on a broadcast a statement such as This game is most important game of series. Why are some games perceived as being more important than others, when each game counts same toward total number of victories required to win contest? The purpose of this article to analyze meaning and validity of such statements from a probabilistic perspective and to provide a means of quantifying importance, in order that comparative significance of games can be measured. In this paper, word game will refer to subcontests that comprise a contest, and one participant in contest will be arbitrarily denoted the contestant, or C. The key observation is that importance of a game depends on context. Two distinct versions of importance, developed below, are therefore appropriate. It will be assumed that outcome of each game in a contest is independent of all other outcomes. Participants in such contests frequently dispute reasonableness of this supposition, citing effects of momentum and other factors, primarily psychological; however, evidence from statistical analysis of contests [2] suggests that actual experience is quite compatible with independence assumption.