I assume the following preconditions:
- I would like to give each team at least 5 rounds in prelims, but take not many more than 7 or so.
- Round robin divisions are preferred.
- Swiss pairing will not be used (there were some reasons for not using it in my situation, and in this theoretical case, it defeats the purpose of considering this question).
The two division setup would have two divisions broken up 9/8. The eight team division has a perfect round robin in 7 rounds. The nine team division has an imperfect round robin in 9 rounds (one bye per team).
My concerns with this setup were twofold when I considered it:
- The nine rounds to complete the round robin were more than I really wanted (the time could balloon out control).
- The eight team division plays in two fewer rounds than the nine team division, and thus will be sitting around a lot longer (there are creative ways to handle giving them byes, like giving them a first round and last round byes, but it doesn't conceal this issue).
As the number of teams increases in a round robin tournament, it becomes easier to handle weirder size divisions because the divisions can be broken up in more ways. After n=18, my limited investigation shows that things clear up tremendously (I wouldn't bet the farm on my supposition, but it seemed reasonable based on what I looked at).
The simplest solution would be to find an extra team for 18 teams. But sometimes that option just isn't possible, or someone drops late in the game, leaving 17 teams. It leaves a headache of a contingency issue.