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Lower Elo on fast games

I noticed that most of the players on Lichess (and maybe also on other chess websites) have classical Elo > blitz Elo > bullet Elo. I am wondering why. Of course, players are stronger on a longer match, but as Elo rating is comparative (meaning it is calculated compared to other players with same time control) this should not be the reason.

Is there really a way to calculate Elo so that classical Elo is comparable to bullet Elo? Or maybe Lichess sets the average classical Elo to a higher value than average bullet Elo?

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