This study aims to quantify momentum in competitive sports and its impact on the transparency of match outcomes. Taking the 2023 Wimbledon Men's Singles Final as a case, we construct a multi-dimensional nonlinear prediction framework. First, a Bayesian state-space model is used to define momentum as an unobservable continuous latent variable, and an extended Kalman filter is applied to capture performance fluctuations. Then, the significant local impact of momentum in the late game is verified by comparing the win probability shift model with momentum factors and the benchmark win probability model. The risk rate model further identifies key turning point indicators such as double faults and net errors. Finally, Monte Carlo simulation demonstrates the generalization potential of this framework in badminton and table tennis. The results provide a quantitative tool for understanding the dynamic evolution of complex competitive systems.

tennis matches, bayesian state space, risk rate model, reversal prediction