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so I'm using a clawitzer and I have aura sphere and water pulse on it. with the mega launcher boost aura sphere is 120 power and water pulse is 90 but my question is how much does water pulse STAB add to the 90 power? is it 50% of the 90? or 50% before the mega launcher boost?

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STAB and Mega Launcher both increase a certain moves power by 1.5X, so the order doesn’t matter since it’s multiplication and there are no fractions to round with these numbers

Water Pulse would be boosted by 60 X 1.5 X 1.5, which is 135

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STAB technically boosts damage, not power. This means it applies after the damage formula, which includes numbers like levels, attack stats, and defense stats.
Just a correction, 60 X 1.5 is 90 and 90 X 1.5 is 135, not 130