Interpersonal competition and coordination in sports can manifest complex behaviors. We present examples demonstrating that common regularities underlie these sports behaviors, as well as certain physical phenomena from dynamical systems. In one-on-one sports such as kendo, practitioners exhibit abrupt phase transitions corresponding to 0.1-m differences in the distance from their opponent, which was used as a control parameter. We classified competitive movements into six coordination patterns, using a return map analysis. Coordination patterns involving more than two people were modeled as coupled oscillators with symmetry breaking. Expert soccer players maintain high symmetry during three-on-one ball possession. Furthermore, the `pass' behavior in football games exhibits network dynamics that is characteristic of other huge networks. Finally, the real-time dynamics of football games possesses self-similarity characteristics, similar to those found in the laws of physics, regardless of players' psychological status or level of training.