When team sports coaches instruct their team members, a sample video is needed for an offensive instruction. However, it is very difficult to search a video for the parts of interest, and it takes a long time to compile a database, for example, ball trajectories and player locations, because sports videos have many periods with no play such as timeouts. In particular, information on the ball trajectory is very important for tactical analysis. However, it is currently inputted manually, which is time-consuming. Therefore, we focus on American football, where the ball can rarely be seen. The contribution of this paper is the submission of a method of automatic ball trajectory extraction. First, we remove the no-play periods in team sports videos to leave only play time and reduce the processing time. Second, we extract the ball trajectory to enable tactical analysis. We propose a new approach to ball tracking by focusing on the ball holder prediction. Our method can be applied to situations with heavy occlusion. Finally, we construct a play search and 3D virtual display system using information on the ball trajectory and the Unity, which is the development environment of the 3D virtual visualization. We used it to construct a Virtual 3D map for watching the play from an arbitrary viewpoint.