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I was curious about some of the specifics of battling, so I decided to test some things and share the results here. Disclaimer: these are apporximations from the testing I've done; there's some degree of uncertainty to these estimates
Damage Calculation
My approximation of the damage formula in this game is
Atk/Def*17*multipliers
Atk is the attacker's Attack or Sp. Attack stat, Def is the target's Defense or Sp. defense stat, and multipliers are:
STAB(same type attack bonus) 1.5x damage if the attack is the same type as the pokemon using it(includes delta type, does not include typeless attacks or attacks from holding a gem) *this bonus applies twice(1.5x1.5=2.25) for double typed Pokemon such as Apocalyptic Arcanine or "double delta" pokemon
type effectiveness
Same as usual in Pokemon games, super effective is x2, not very effective is x1/2, and immune is x0
Critical Hits
critical hits multiply damage by 1.5, and each hit has ≈6.1% of being a critical hit.
IQ and move selection
A Pokemon with max IQ will select its best move ≈75% of the time.
I might gather some more data over time and update this if needed, but for now I think my estimates are reasonably close. Hope someone finds this information helpful :]