Martial arts is a comprehensive sport. It requires the athlete to have speed, explosiveness, and coordination. Injuries are common among athletes in martial arts training. In this paper, the mathematical statistics method of the ROC curve is used to predict athletes’ sports injuries. At the same time, the author uses the firefly algorithm to establish the relevant factors for evaluating the degree of foot and ankle injury of martial arts athletes. In this way, the fitness function of the damage degree evaluation index is obtained. Finally, this paper verifies the effectiveness of the method by computer simulation. The mathematical statistics method of the ROC curve and the firefly algorithm-based injury evaluation method for martial arts players have particular guiding significance for improving the technical ability of Chinese martial arts players.

Linear programming is a widely applicable mathematical operation method. In this paper, two solutions of linear programming and state parameter extraction can be used to simplify the inequality group and transfer the high-dimensional state utility function in football. This can speed up the generation of joint strategies for football teams in the game. This paper uses the free-kick technical football cooperation as an example to conduct an empirical study on the linear programming method of state parameters. In this paper, combined with the traditional motion information modeling method, a free ball path planning based on the linear programming gradient method is established. At the same time, this paper adopts an asymptotic method based on linear programming to solve the trajectory of any football. Finally, an experimental study on the linear programming gradient method for state feature vectorization is carried out. Experiments verify the effectiveness of this method. The mathematical model accurately predicts the linear programming of football training.