The Number of Games to Win by Two Points

Abstract

Sometimes draws or ties occur in sports. Tiebreakers are the forms of competition that break ties and decide the winner when a draw or a tie occurs. Depending on types of tiebreakers, some take shorter and some take longer to end the competition. In this article, we are interested in calculating the expectation and variance of the number of games that will continue after a draw from types of tiebreakers that require players to win by two points. We focus on three types of win by two points that are used in many popular sports, such as tennis, volleyball and racquetball. By calculating the expected number of games, we can compare the number of games in each type of tiebreakers that will approximately be taken to end the game. In these kinds of sports, the rules to gain each point are usually the same. This means that there are the same finite states that the players or teams can reach in each point and each possible state depends only on the previous state. Since we know that a Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event, we can use an application of Markov chains to solve the problems.