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How much does raising your stat actually do? Like if I use Belly Drum will it time your attack by 6? Does Swords Dance times it by 2? What about moves like Minimize? How do you know how much it does? Is there a formula? Thanks!

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the max is x4 the original damage

one stage= x1.5
e.g if you use Hone Claws 6 times it will make you Attack stat x4 higher.

1st time: x1.5
2nd time:x2
3rd time: x2.5
4th time: x3
5th time: x3.5
6th time: x4

a move/ability that lowers a stat does the same thing but divides by the number instead of multiplying by it.

hope I helped. if not, comment and i'll rephrase the answer

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So does it just do damage or is it x4 your stat (eg. My Azumarill has 150 stat if I use Belly Drum will it have 600 or will it do original amount x4)
yes, it raises your actual stat (after EVs, nature, etc)
what does it do for moves such as hone claws (for accuracy) or Double team (for evasiveness)?
the same thing, idk how accuracy and evasiveness work, but these pages might help http://bulbapedia.bulbagarden.net/wiki/Accuracy
http://bulbapedia.bulbagarden.net/wiki/Evasiveness#Evasion
I found this one the best for that...Much simpler http://bulbapedia.bulbagarden.net/wiki/Stats#Stages
And if it says sharply, it means x2 first time, x3 second time, x4 third time.
The evasion/accuracy is different...