Point winning rate in each score and point independence in tennis:

Intended for service games of Novak Djokovic and Kei Nishikori

Abstract

In theoretical studies on the important point count in tennis (Morris, 1977; Croucher, 1986), it is assumed that the point winning rate of a point count does not depend on the past status (the point independence) and the point winning rates in all point counts are the same (the constant point winning rate). However, it is not clarified whether they are established in individual players. The purpose of this study was as follows: In terms of the service games of Novak Djokovic and Kei Nishikori (1) to verify whether the assumptions of the theoretical studies was proven or not. (2) to clarify the difference between Djokovic and Nishikori in the increase and decrease tendency of the point winning rate of each point count and the degree of establishment of the point independence. Data for Djokovic were taken from 67 matches (consist of 176 sets, 826 games, 4,756 points) and for Nishikori were taken from 29 matches (consist of 83 sets, 375 games, 2,359 points). The matches include Davis Cup, the Grand Slams, ATP finals, and Masters1000 played on hard-court from January 2018 to January 2020. These data were collected from the match video on WOWOW on-demand. The results were as follows: (1) In the service games both of Djokovic and Nishikori, it was suggested that the point independence was nearly established, but it was clear that the point winning rate was not constant in all point counts. In other words, in the assumptions of the theoretical studies, the constant point winning rate was rejected. (2) Between Djokovic and Nishikori, in their service games, it was suggested that the increase and decrease tendency of the point winning rate in each point count differ. (3) It was clear that the degree of establishment of the point independence was higher in Djokovic’s service games than that of Nishikori’s.