How many concurrent games in clan league play?

I haven't been able to find a great deal of information for clan league set-up. My biggest question is how many concurrent games will a single player have upon entering clan league play? I can see that they are somewhat staggered, but I'm fuzzy on what the game start timing looks like.

18 games- 9 other teams, with 2 games against a member of each team.
Edit: obviously, this is only for one league. If you were in 2 leagues (e.g. 3-day and 7-day) then you would have 36 games.

Also the last division in the league may or may not have the full 10 teams, so if your team is there you might have less than 18 games pop up in your mailbox. 🙂