PokéBase - Pokémon Q&A
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All sources say the move "doubles power" or "doubles damage", but those two words are very different.

The power of a move is the base power with calculated stat boosts, stab, base attack, etc.

Damage means the damage dealt to a target after defense has been calculated on top of all of the power calculations.

I've never really tested this myself. Anyone know how moves like counter are calculated?

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Counter doubles the damage inflicted on the user and hits the enemy for that amount as long as it was physical damage. (I.e. "X" Pokemon takes 50 damage, uses counter. "Y" Pokemon take 100 damage)

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So in this case, it can sometimes be unwise to invest in defense EVs/nature on a counter Pokemon because the lower defenses yield higher damage taken, and therefore greater counter damage.  Am I understanding this correct?