In previous attempts to identify dynamical systems properties in patterns of play in team sports, only 2-D analysis methods have been used, implying that the plane of motion must be preselected and that movements out of the chosen plane are ignored. In the present study, we examined the usefulness of 3-D methods of analysis for establishing the presence of dynamical systems properties, such as phase transitions and symmetry-breaking processes in the team sport of rugby. Artificial neural networks (ANNs) were employed to reconstruct the 3-D performance space in a typical one-versus-one subphase of rugby. Results confirm that ANNs are reliable tools for reconstructing a 3-D performance space and may be instrumental in identifying pattern formation in team sports generally.