# Gaming Tree Based Evaluation Model for Badminton Tactic Benefit Analysis and Prediction
## 1 Introduction  
Badminton is one of the most popular sports in the world [1; 2], and is also the racquet sport with the highest speed in the world [3], with its competitive form being two single/pair athletes completing tactical implementation quickly and accurately [4; 5] on an 80 square meter court. As a result, tactical strategies (strategical strokes) are one of the key factors for winning badminton matches [6].  
With the rapid development of information technology, advanced statistical methods such as data mining and artificial intelligence are commonly used in tactical analysis. Such methods can mine implicit information from performance data of competitions to provide decision support for coaches and athletes, which is an important aspect of tactical strategy research for sports such as basketball [7; 8], football [9; 10], tennis [11; 12], table tennis [13; 14], and badminton [15; 16] and is also a promising direction for improvement and development of traditional performance diagnosis and evaluation methods [17; 18]. In recent years, predicting match results (scores, wins/losses) using these methods has become a hot research topic [19; 20]. Through prediction models, key tactical factors affecting match results can be analyzed. For example, [PERSON] et al. [21] uses four data mining methods (including lazy learners, artificial neural networks, support vector machines, and decision trees) to evaluate classification-based and regression-based methods for predicting match results (home team win or lose) in Major League Baseball (MLB) regular season games over 10 years; [PERSON] et al. [22] used Bayesian networks to predict home wins, away wins, and draws in the English Premier League; [PERSON] and [PERSON] [23] constructed a bivariatePoisson model to analyze scores between two teams, etc. However, there has been no prediction research on badminton so far.  
Game theory studies how rational actors make decisions and the equilibrium of such decisions under the assumption of mutual interaction and influence among relevant actors. The prediction ability, actual behavior selection and optimal selection between the two sides of the game are the research focuses of game theory. Taking the concept of Nash Equilibrium as an instance. Nash Equilibrium describes a state where each player in a game has chosen a strategy, and no players can improve their outcome by changing their strategies while others keep their strategies unchanged. Thus, Nash Equilibrium helps find each player's optimal decision for scoring. Consequently, game theory has been widely applied in sports science, including sports teaching [24; 25], tactical strategies [26; 27; 28], etc., while research on its prediction in the sports field has not yet been studied.  
Badminton matches have strong confrontation and competition and have obvious interactive and interdependent characteristics of tactics and strategies between opponents, which is consistent with the research object characteristics of game theory. Therefore, this study intends to use the game tree method with game theory to explore the winning rate of badminton matches. By using the important badminton match data of recent years, this study constructs the gaming tree to model the tactic strategies of players in existing matches and proposes the evaluation model to predict the winning rate based on the given strokes.