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.