Would you call League an MMO since technically it's multiplayer is pretty big

No, for the simple reason that making that claim ends up requiring a lot of debating and arguing your point, which I'm not sure is worth the benefit of championing a technicality. I feel for a lot of people that MMO implies a lot of players able to engage at one time (say gathering in one location for instance) and maybe even a concept of a persistent world.

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