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Keep Elo as is, but make it hidden, call it MMR, and have Elo be a measure just of how you did in one given season, not a skillscore
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Elo isn't the arbitrary name of some rating, it describes a comparitive rating system based on performance against other (rated) players. This is also why your elo and your w/l are two different things. The second does not factor in the quality of your opponents.

