Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/51853

Title

Moment generating function for a tennis match

Author(s)

Pollard, Geoff;  Pollard, Graham

Abstract

The moment generating function of the number of points played using a particular scoring system can be used to estimate the actual distribution of the number of points played. Estimates can also be made of the tails of the distribution, so that an estimate can be made of the proportion of time very long matches will occur. In this paper an explicit expression for the moment generating function of the number of points in a game of tennis conditional on the server winning (and conditional on the server losing) is derived. These expressions are used to detennine an explicit expression for the moment generating function of the number of points in a set of tennis conditional on player A winning (and conditional on player A losing) in an odd (and in an even) number of games. Finally, an explicit expression for the moment generating function of the number of points in a best of three advantage sets match of tennis is determined. The Normal Power Approximation and the first four moments from the moment generating function can be used to estimate the distribution of the number of points, which can then be used to estimate some useful statistics for a tennis match. Importantly, the methods in this paper can be used to determine the moment generating function of the number of points for any tennis scoring system, or indeed to determine the moment generating function for nested scoring sytems for many other sports.

Publication type

Conference paper

Research centre

Swinburne University of Technology. Faculty of Life and Social Sciences

Source

Proceedings of the 9th Australasian Conference on Mathematics and Computers in Sport (9M&CS), Tweed Heads, New South Wales, Australia, 30 August-03 September 2008, pp. 204-207

Publication year

2008

FOR Code(s)

010404 Probability Theory;  010406 Stochastic Analysis and Modelling

Keyword(s)

Moment generating function;  Nested scoring systems;  Sports statistics;  Tennis point distribution

Publisher

MathSport (ANZIAM)

ISBN

9780957862340, 0957862342

Publisher URL

http://www.anziam.org.au/Ninth+MCS

Peer reviewed