PokéBase - Pokémon Q&A
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2 Answers

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This is how Pokemon games calculate damage:

("A" is user's attack stat, "D" is target's defense stat)
Leveling up raises level (obviously) and also the user's attack stat.
Both of these numbers are above the fraction bars, so the move will do more damage if only those 2 numbers go up and everything else stays the same.

You did the genius version, I did the simple version lol.
So copy-pasting stuff from Bulbapedia is now a genius thing?
No lol you put all the sciency stuff and I just did the simple version
But all the "sciency stuff" was copy-pasted from Bulbapedia.
Yeah, I know. I was too lazy to do that lol
I still don't understand why some people think writing an original answer is easier than copy-pasting stuff from Bulbapedia.
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Yes, if the damage category stat increases. Moves have a set base power, and the power doesn't change. But if for example, a pichu levels up and gets 1 special attack stat boost(60 special attack into 61 special attack) its thunderbolt would be slightly more powerful, because of the special attack stat boost. But if the stat isn't raised(50 attack stays at 50 attack)the damage amount of wild charge wouldn't change.
Source: Experience and logic
I hope I've helped!