A mathematical model (Gale, 1971) has shown that the probability of the serving player winning a point in tennis, P, is given by P = p1.q1 + (1 - p1).p2.q2 where p1 and p2 are the probabilities of the first and second serves being in respectively and q1 and q2 are the conditional probabilities of the point being won given that the first and second serve are in respectively. Since Gale produced his model, it has been possible to measure the speed of the player`s average first serve, V1, and average second serve, V2, during matches. The purpose of the current investigation was to analyse the relationship between service speed and Gale`s model. Match statistics for each match played in the four Grand Slam tournaments in 2002 were accessed from the tournaments` web sites. Those 569 singles matches which were completed without player retirement and for which service speed data (km.hour-1) was provided were analysed. Table 1 shows the 1138 serving performances within the 569 matches. The difference between the world rankings of the server and receiver were used to represent the gap in ability between the two players within a match. A mathematical model (Gale, 1971) has shown that the probability of the serving player winning a point in tennis, P, is given by P = p1.q1 + (1 - p1).p2.q2 where p1 and p2 are the probabilities of the first and second serves being in respectively and q1 and q2 are the conditional probabilities of the point being won given that the first and second serve are in respectively. Since Gale produced his model, it has been possible to measure the speed of the player`s average first serve, V1, and average second serve, V2, during matches. The purpose of the current investigation was to analyse the relationship between service speed and Gale`s model. Match statistics for each match played in the four Grand Slam tournaments in 2002 were accessed from the tournaments` web sites. Those 569 singles matches which were completed without player retirement and for which service speed data (km.hour-1) was provided were analysed. Table 1 shows the 1138 serving performances within the 569 matches. The difference between the world rankings of the server and receiver were used to represent the gap in ability between the two players within a match. A series of two-way ANCOVAs including tournament and gender as between match effects and the gap between the players` world rankings as a covariate revealed that gender had a significant influence on each of the dependent variables (F(1,1129) > 32.9, P < 0.001). Tournament had no significant influence on p2 or q2 (F(3,1129) < 2.3, P > 0.05) but did have a significant influence on all other dependent variables (F(3,1129) > 6.6, P < 0.001). Partial correlations were used to relate service speeds to P, p1, q1, p2 and q2 controlling for the gap between the players. There were negative correlations between service speed and the probability of the serve being in on both first serve (r = -0.384, P < 0.001) and second serve (r = -0.058, P > 0.05). There was a positive correlation between service speed and the conditional probability of winning the point given that the serve was in on both first serve (r = 0.552, P < 0.001) and second serve (r = 0.237, P < 0.001). Overall the probability of winning a point on serve, P, was positively associated with V1 (r = 0.472, P < 0.001) and V2 (r = 0.395, P < 0.001). There are implications from the study as players with faster serves have been shown to have an advantage over their opponents.
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