However, once the "certain number" is reached, wouldn't there be a pressure for players to leave and go to one of the capped arenas if they choose?
There are several reasons why not. One of them is that nobody wants to be among the first in an almost empty arena, even if they dislike the "overcrowded one"
Just think of the many players that state they would like to fly more EW, MW, AvA, WWI... if there just were more people there. The paradox is, if all of them would go there, there would be enough numbers for that. But they don't go there because nobody else does.
And each Titanic Tuesday I see quite a number of players complain about that arena, "too many players, too big furballs, only hordes, too dweeby", yet they do not go to MW (or any other low-key arena). They either stay & complain, or just log off.
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On thing that is different beyond a certain population level is communication. The bigger an arena is, the less actual communication happens between players. It's getting more and more anonymous, with veteran players sticking to their squad channels mainly. I think it's very esay for a new player to "get lost" at that time, which in part can explain why with split arenas the player retention after trial end was higher than before.
However, lack of communication doesn't necessarily equal bad player behaviour as some do think - The worst atmosphere I have encountered in my 5 years of AH was in very small (EW&AvA) arenas.