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1. INTRODUCTION The widespread interest in sports in our culture provides a great opportunity to catch students' attention in mathematics and statistics classes. Many students, whose eyes would normally glaze over after ten minutes of algebra, will happily spend hours analyzing their favorite sport. In recent years the mathematical literature on sports (e.g. [1] and [2]) has expanded greatly and covers a broad spectrum of sports, including baseball, football, soccer, tennis, and track and field.
Volleyball, an increasingly popular sport, has a mathematically interesting scoring system. The purpose of this paper is to show students, through an analysis of volleyball scoring systems, how we can model volleyball games as Markov chains, obtaining formulas for the proportion of points won by each team in the long run. We can also calculate the exact probabilities of winning a point, a game and a match for each scoring system.
Under careful guidance of a faculty instructor, this paper can be well appreciated by college or high school students who have finished a first probability and statistics course. This study may also be of interest to volleyball players, coaches and fans, since the USA Volleyball official rules for scoring were changed in 1999. Our model predicts that the...