18 team plays billiards (16 colored balls). What kind of competition system can minimize the number of competitions? Or do you play the most games at the same time?

Eighteen teams, two teams in a group, won nine teams, and then the team with the most wins among the nine eliminated teams advanced at the same time. * * * won ten teams, and then divided into five groups, winning five teams counts as one team, * * * won six teams, divided into three groups, and then counted as one team, and * * * won four teams.