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I recently noticed something. Choice Band gives a pokemon the equivalent of +1 attack, a 50% increase. But attack boosts stack with themselves additionally, while attack boosts and choice band stack multiplicatively since they're 2 different sources. Meaning +2 attack is a 2x multiplier, but +1 attack with a choice band is a 2.25x multiplier. If you have a band not only do you get an additional boost, but each attack boost is itself worth 50% more than normal.
Of course, a band prohibits boosting, unless those boosts were gathered passively. Say with the help of something like Moxie.
