Abstract

Mathematical model of football goal's hazardous area based on matlab simulation

Author(s): Limin Yan

This paper studies the threat degree of shot goal in different locations for the football game players and maps out the dangerous zone of the goal. Under certain conditions, for the same quality players shooting at any point on the field, we mainly study the goal threat degree and define the threat degree as the successful goal probability. This paper studies the hazardous area problem in both cases with goalkeepers and without goalkeepers in football door, establishes a one-dimensional normal model and two-dimensional normal distribution model using football rules and carries through model simulation and analysis with MATLAB software. Studies have shown that the successful shot goal position on the pitch of the players is normally distributed. The shot path of any point on the pitch of the players is decomposed into horizontal and vertical direction. The angle alpha and beta are introduced to build two one-dimensional normal distribution models. In the defense case with a goalkeeper, we further study the playersÂ’ shot threat degree and dangerous zone to re-establish the two-dimensional normal distribution model of the alpha and beta.