PokéBase - Pokémon Q&A
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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.
Orange Gaimer is wrong. As stated in the answer, Beast Boost ignores any battle-exclusive stat modifiers, including the Speed Boosts passed onto it.