"The first known examples of a team game involving a ball, which was made out of a rock, occurred in old Mesoamerican cultures for over 3,000 years ago. It was by the Aztecs called Tchatali, although various versions of the game were spread over large regions. In some ritual occasions, the ball would symbolize the sun and the captain of the losing team would be sacrificed to the gods." https://www.footballhistory.org/

Seems like one ball/rock was enough for the team captains.