To calculate the standard deviation of each attribute in the training control data, the normalized results of the standard deviation coefficient vector of basketball sports metrics are used as weights. Lagrange’s equation is used to analyze the behavioral trajectories of both players to enhance the offensive and defensive transitions of individual players. The weights used to calculate the standard deviation of each attribute of the training control data are based on the normalized results of the standard deviation coefficient vector of basketball sports metrics. It was found that the compression efficiency in the basketball sports teaching video with AR technology was 98.65%, the dominance ratio of offense-defense transition was 1.089, and the variance estimation of the disturbance term was 0.4621. Scientific training with AR technology can adjust training ideas, theories, and methods in real-time to realize the sports ideas of winning the standard and nurturing people.