# A Study on the Optimisation of Tennis Players' Match Strategies from the Perspective of Momentum
## 1 Introduction  
In the context of tennis matches, the momentum of players has been shown to exert a substantial influence on the outcomes of these contests. This factor has been demonstrated to play a pivotal role in the shaping of players' individual performances [1]. The influence of momentum is evident not only in the strategic decisions of players [2, 3], but also in its substantial impact on their psychological state [4]. Specifically, the psychological benefits of momentum include enhanced confidence, heightened competitive motivation, and improved concentration, thereby exerting psychological pressure on opponents. From a match situation perspective, momentum has the potential to enhance the accuracy of pre-match prediction models. The gain or loss of a player's previous point has been shown to significantly affect their mentality, tactical choices, and subsequent shot performance, thus influencing the result of the next point. The integration of player momentum with conventional statistical methodologies has been demonstrated to enhance the predictive capacity of tennis match analysis [5]. Furthermore, the serving side, break points, and winning streaks play a pivotal role in the fluctuations in momentum. The serving side has been shown to exert significant influence over the match tempo through the implementation of high-quality serves and in-game dominance [6]. The break-point moment is characterisedby a significant shift in the match situation [7]. Finally, winning streaks have been shown to provide a psychological advantage through consecutive scoring, which is critical for changing momentum [8]. Consequently, a system for quantifying momentum can be developed based on the dynamic characteristics of tennis matches, serving situations, break points, and winning streaks. The construction of an accurate and practical tennis match analysis model based on momentum is proposed in this paper. The model is rendered effective, its structure is reasonably simplified, and its operational efficiency and interpretability are improved. To achieve this objective, it is necessary to address three fundamental issues. Firstly, the quantification of players' momentum during the match is imperative. The establishment of a unified paradigm for momentum quantification will facilitate effective comparison and integration of research results. Secondly, determining the correlation between momentum and match trends is essential. While extant studies have indicated an association between players' momentum and match trends, they have lacked systematic and comprehensive analysis [9]. The third issue pertains to the utilisation of momentum in proposing optimisation recommendations for players' match strategies. Utilising momentum to analyse players' performance at different stages and predict match trends enables the provision of targeted optimisation suggestions based on players' specific situations, thus facilitating enhanced outcomes. In response to the aforementioned issues, this paper proposes a tennis match analysis system that is based on momentum, as illustrated in Figure 1, from the aspects of data processing, quantification of tennis players' momentum, correlation analysis, construction of strategy optimisation models, and model testing, based on the data from the men's singles matches at Wimbledon in 2023. The main research contents are as follows:  
1. The development of a quantification system for tennis players' momentum. Initially, data cleansing is conducted to guarantee the precision and thoroughness of the data. The subsequent integration of the Markov chain [10] involves the utilisation of its state-transition characteristics for the purpose of capturing the dynamic changes in the match state. Concurrently, multi-dimensional indicators with a high degree of relevance to the match are selected for the purpose of comprehensively constructing a dynamic momentum quantification system, with the objective of accurately describing the changes in players' momentum during the match;
2.