Simultaneous McMahon is a unique and tricky tournament type. It seems no one knows how to correctly choose tournament settings though. I think it mostly comes down to the experience of tournament director and convenience. For example, 2 rounds is too few games to determine winner, 4 is too long in time, so 3 rounds it is.
How to determine if settings are good? I’m sure there’re methods but I don’t know them.
I’m thinking the main problem with Simultaneous McMahon is that players in lower groups can get so many points playing weaker players that they end up placing higher than some stronger players in higher groups. With enough rounds it’ll even out by sending those lower group players into higher groups. How much is enough?
One way to think about it is the following. In a tournament game whoever wins should generally place higher in the standings. So the final standings could be used as a sort of rating to predict the results of the individual games. In the simplest form it would be the number of games where winner ended up with higher standings rank divided by total number of games. Something like that.
Although realistically in a tournament we generally care only about the top spots. Maybe only the top players should be taken into account.
Maybe do it this way. Take 10 higher placed players of a tournament and using the games of the tournament pretend they played round robin. And see how they would place in this round robin compared to how they placed in real tournament. If there’s no game, we could assume draw. The difference between placements would be how bad the tournament worked.
Of course, it could be that results against non-top players affected the tournament placements but I think it would be a good heuristic.
To make sure that these differences aren’t just a fluke, we could simulate the tournament many many times and take average. And then do the same for the tournament with the same participants but different settings. And see how it affects things.
Naturally, the best tournament would be 12 rounder, it would get the most accurate result. But maybe there’s a cutoff point where increasing number of rounds stops giving any benefit.