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If you give a electric type a light ball it doubles the power of the move (eg a 50 power move would be 100) but if the pokemon was an electric type it gets STAB which also doubles power. but if you have both does the light ball double the power of the moves base power (50) or the already doubled power from STAB which would bring the moves power to 200 instead of 150.

So if you had an electric type with a light ball and the move had a power of 50 would it do 150 damage or 200 damage?

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Light Ball simply doubles the Attack and Special Attack of Pikachu. It doesn't directly affect the power of the move, but yes the damage of the move will be effectively doubled. STAB is only 50%, not 100%, extra damage. So basically you get a 150% increase in power of the attack. STAB applies after stat increases (though I'm not sure the math matters either way in that sense).

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