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How does the ranking system work?
The Rainbow Six Siege skill rating system is based on the Trueskill algorithm. It's an evolution of the ELO/Glicko rating systems that works better for multiplayer games (ELO and Glicko are designed for 1v1 games like chess).
Your skill rank is initially computed after 5 placement games, from your skill rating value (for math geeks, the mu variable). Following that, it's updated after each Ranked game you play.
Your skill rank is specific to the region you're playing in (Europe, North America, Asia, etc.). Players from different regions almost never play against each other, and since skill isn't an absolute measure but a relative one (it doesn't tell precisely how good you are -- only whether or not you're better than another player), ranks can't be directly compared across regions (RTS and MOBA players call that the "Korean bronze" effect).
This means that if you move halfway across the world, you will have to go through your placement games again and find out how good you are compared to other players in your new region.