No, actually the collective of player isn't team in this case. Not all players will be on the same team, but they still participate in the league so I disagree

No, actually the collective of player isn't team in this case. Not all players will be on the same team, but they still participate in the league so I disagree with this example terminology shift. You would end up with a slightly more generalised naming like this in my opinion: - athletes - teams - leagues In this particular case there are no suitable collective terms.