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If I recall correctly back when I was in highschool (5-6 years ago) there was an app on the chrome store that did this for you. I don't know if it's still available or compatible but I remember it doing this specific thing.
instead of only apearing when you hover over it, could it apear under the move like in the pokemon games? hovering over it requires the user to know about this feature, and this would be most useful for people new to showdown.