Where the numbers come from, how they are combined into one score and tier, how far the big stat sites can be trusted, and what a tier list cannot tell you.
At the same rank every site reads the same Riot match data, so their win rates nearly match. Their letter grades do not. Below is how closely each site's tiers follow winning versus popularity, as rank correlations across about 200 champion-role pairs at Diamond+.
Last column: how closely the site's win rates match OP.GG at the same rank (1 = identical). Mobalytics' expert list has no win rates.
U.GG and Blitz are the sites whose letters you can take at face value. dpm.lol, Mobalytics' expert list and METAsrc mostly tell you what people pick. That is why Kai'Sa, Lee Sin, Lulu and Nautilus sit in their top tiers while winning less than the average pick in their role.
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