The rapid development of Olympic Games and the intensification of professional sports events make the competition between excellent athletes and teams become more and more fierce, so the demands on athletes’ psychology, techniques, and physical strength are becoming higher and higher, especially that the demands on physical strength are more prominent. Therefore, physical training is an important part of sports training and the core link of competitive sports, which is widely valued by coaches and athletes all over the world. At the same time, with the influence and penetration of the rapid development of modern information technology and network big data on competitive sports, the scientific and digital process of athletes’ physical training has also been accelerated, and many new ideas, scientific training methods, and advanced sports technology have emerged. During the pandemic, many aggregation activities have been disrupted, as well as physical training. Therefore, this paper improves the quality of physical training through video, so that athletes can do physical training at any time and any place. A cut vertices spanning tree algorithm based on machine learning is proposed to distribute layered multicast streaming and dynamically adjust the number of layers of sports video streaming. The cut vertices spanning tree algorithm is mainly applied to the situation when the network bandwidth resources are relatively scarce. The evaluation results indicate that the proposed method can improve the estimated quality of experience (QoE), packet loss rate, link utilization, and video delay on Mininet simulation platform. Furthermore, it can be seen from the experiments that the proposed method has a good performance on distribution of sports video stream assisting physical training.