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For example, it says Mega Aggron has a 1½ weakness to Fire-. Is that with the Filter ability or without it?

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It reduces damage of super effective moves by 25%. It does not actually reduces tier effectiveness, it only cuts their damage .

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Somewhat, Filter does indeed affect the premade super-effectiveness of an attack by lowering the damage taken, but this affect doesn't affect resistances or neutral damage taken. This is because the ability Filter weakens the effects of super-effective hits by 25%, not neutral or not very effective moves, so if Mega Aggron's ability was suppressed or changed to something other than Filter, its weakness to Fire type attacks would be ×2 instead of ×1½, but it would still have a ×½ resistance to Fairy type moves.

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Good answer.