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According to it's description it says it boosts the Pokemon's most proficient Stat after knocking someone out, but I was wondering if this meant the base stat, the in game stat (affected by IVs and the like), and if its affected by in-battle status moves.

Cuz, I just fought a Celesteela that got Baton Passed from Speed Boost Ninjask, and after it knocked out of my Pokemon, it's Beast Boost boosted it's speed. Which seems super weird, cuz I thought it was a slow Pokemon.

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Beast Boost increases the user's highest stat (ignoring the HP stat) by one stage after knocking out a Pokémon. It does not take into account any modifiers caused by status conditions, items, or moves, except Power Split and Guard Split. In the case of a tie, it will boost whichever stat is first, using the following order: Attack, Defense, Special Attack, Special Defense, and Speed.

According to this, Beast Boost ignores stat modifiers, so the highest stat of the Celesteela you fought must have been Speed.

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Why the HECK was a Celesteela's speed stat higher than it's rest ;_; and is that even possible? T_T
The speed was baton passed by ninjask, which is why Celesteela has the highest stat of speed.