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How are players ranked?
Two scores are determined for each summoner/champion/role (one for the current season, one for the past 30 days). Then a third score is computed (geometrical average of the two previous scores). Summoners are ranked by champion according to their best "averaged score" (one averaged score per role) for that champion.
The two scores (the one for season and the one for past 30 days) are computed using those rules:
+1 tier → score * 4 (The tier taken into account is the average tier of each game where the champion was played)
+12% winrate (compared to the average for that champion/role) → score * 2
+100% KDA (compared to the average for that champion/role) → score * 1.33
Players must play a minimum of 10 games to be ranked. If a player has played fewer than 50 games with that champion/role → score * 0.75 for each missing game.
You need to have played at least 1 ranked game in the past 30 days to be ranked with that champion.
If you played less than 5 games with the given champion in the less 30 days, a penalty is applied → score * 0.5 for each missing game
Those rules are exponentials (ie +2 tier → score * 16)
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