The ability holder increases their highest stat (ignoring HP) by one stage if the ability holder knocks out a Pokémon in the turn. The ability does not take into account the modifiers caused by status condition,moves or items.However it does take into account the following moves: Power Split, Guard Split. If two or more stat ties the ability will take the one which come first following this order: Attack, Defense, Special Attack, Special Defense, and finally Speed. Beast Boost has no effect outside of battle.
Moxie works similarly except it solely increases attack.
Soul-Heart works similarly except it solely increases special attack.
Protosynthesis and Quark Drive similarly target their respective highest stat for an increase but, their boost is only once and only during the respective field condition