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Probability of Winning at Tennis I. Theory and Data
Author(s) -
Newton Paul K.,
Keller Joseph B.
Publication year - 2005
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.0022-2526.2005.01547.x
Subject(s) - tournament , champion , set (abstract data type) , point (geometry) , independent and identically distributed random variables , mathematics , random variable , mathematical economics , product (mathematics) , probability theory , computer science , statistics , combinatorics , geometry , political science , law , programming language
The probability of winning a game, a set, and a match in tennis are computed, based on each player's probability of winning a point on serve, which we assume are independent identically distributed (iid) random variables. Both two out of three and three out of five set matches are considered, allowing a 13‐point tiebreaker in each set, if necessary. As a by‐product of these formulas, we give an explicit proof that the probability of winning a set, and hence a match, is independent of which player serves first. Then, the probability of each player winning a 128‐player tournament is calculated. Data from the 2002 U.S. Open and Wimbledon tournaments are used both to validate the theory as well as to show how predictions can be made regarding the ultimate tournament champion. We finish with a brief discussion of evidence for non‐iid effects in tennis, and indicate how one could extend the current theory to incorporate such features.