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So, I had an idea to run a Bulk Up + Body Press Great Tusk. I believed that the attack and defense boosts from Bulk Up would do a decent amount of damage. However, when I tried boosting attack in the damage calculator, I didn’t see any difference between the original damage and the boosted amount. So, when calculating damage, does attack actually affect the power of Body Press?

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The user's Defense stat stage-modifiers are applied (rather than Attack stage-modifiers), but otherwise its Attack modifiers are used (including held item, Ability, and burn). For example, the user's Huge Power or a held Choice Band will increase the stat used in calculation, whereas Fur Coat or a held Eviolite will not. In contrast, the user's Slow Start will decrease the stat used in calculation.

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Attack affecting held items and abilities like Choice Band and Huge Power, along with burn will thus modify Body Press, while attack stat stage modifiers like Swords Dance (or the attack boost from Bulk Up) won't make any difference.
tl;dr attack boosting items, abilities and burn are factored in, attack stat stage modifiers aren't. Conversely, defense stat stage modifiers like Iron Defense is considered, while Fur Coat or Eviolite does not affect Body Press' power.

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I did not expect this to be answered in 15 minutes. Thanks!