Tennis Player Momentum Analysis and Match Flow Prediction Model Based on PCA

Momentum is a fluctuating phenomenon that occurs during the course of a game when the seemingly dominant side scores consecutive points or influences the course of the entire game. And as tennis is a popular sport all over the world, exploring the effects and mechanisms of athletes' momentum on match changes and outcomes in tennis matches can provide reasonable match advice to athletes. To this end, this paper systematically establishes a prediction model based on tennis players' momentum analysis and match direction. In this paper, this text first cleaned the data for the 2023 Wimbledon tennis tournament obtained from the American Collegiate Mathematical Modeling Contest website and supplemented the missing values using cubic Hermite interpolation. The processed data is then analyzed using principal component analysis, where a linear combination of each principal component is defined as a momentum value, thus quantifying the momentum and creating a mathematical model between the indicator and the momentum. Finally, a momentum plot of the player is created to visualize the relationship between the player's momentum and the outcome of the race.