# Women's Singles Tennis Match Analysis and Probability of Winning a Point
## 1 Introduction  
The analysis of sport competition performance is crucial to identify successful patterns of play and to anticipate the final outcome of matches [1]. In addition, it offers the possibility to assess one's own and opponents' strengths and weaknesses, which, in turn, contributes to the optimisation of training sessions, particularly from a tactical point of view [2]. In the last decade, tennis has undergone a significant evolution in terms of notational analysis, despite being considered one of the least developed sports in this aspect in 2012 [3]. In any case, most of the scientific publications on data analysis in competition have focused on men's tennis, leaving women's tennis in the background, although this also seems to be in the process of changing, with several scientific publications on women's tennis appearing recently [4, 5]. Tennis is a sport played primarily on three types of surface (clay, grass, and hard or synthetic courts), each with distinctive characteristics derived from their coefficient of friction and restitution [6]. This means that players must adapt to these surfaces throughout the season [7]. Therefore, coaches should adjust training approaches and game tactics considering the surface in question [8], as substantial differences have been identified inseveral variables that influence the final outcome of matches [5; 9; 10; 11]. Therefore, when analysing key performance indicators in this sport, it is imperative to take this variable into account. From previous research, it appears that net play plays a crucial role on grass and hard courts, but is less relevant on clay [12]. On the other hand, the mastery of medium and long rallies is more decisive for winning matches on slow surfaces, such as clay, compared to fast surfaces, where rallies tend to be short [13]. A common problem in previous research, in addition to the limitation in its focus on men's tennis, is the isolated analysis of performance variables [5], such as serve [14], break points [15; 16], and aspects of physical performance [17], without taking into account that these indicators are embedded in a context that also requires a comprehensive analysis. The scientific literature of the last several decades has shown that, from a technical-tactical perspective, several variables influence performance in tennis. These variables include the playing surface, the serve, the length of the rally, the bounce locations of the ball, and the type of shot made in each action, among others [5; 18]. For example, it has been observed that tennis players start a point with a first serve 62-67% of the time and win 62-66% of points depending on the surface. In contrast, with a second serve, the probability of winning the point decreases to 50-52% [5]. Short rallies (0-4 shots) account for 65-66% of all points in a match on both slow and fast surfaces, while medium rallies (5-8 shots) make up 23-24% and long rallies (9+ shots) make up approximately 10-12% [7]. On clay, it has been found that in 84.5% of matches in which a player dominates short rallies, she wins the match, while this percentage drops to 67.8% in medium-length rallies and 55.7% in long rallies. In addition, dominating points from the baseline (85.9% probability of winning the match) is more relevant than dominating at the net (53.6%) [3]. Although not in large numbers, there are some studies that explore the bounce location of the ball before the final stroke, as well as the players' position, the technical gesture, and the area of the court towards which the final stroke is directed, mostly related to men's tennis [19]. Despite the valuable information provided by these data, the present study proposes a more holistic approach by combining the analysis of several performance indicators to generate more useful information for optimising training and match strategies. The rationale behind this approach is that tennis performance cannot be fully understood by examining variables in isolation.