Damage Formulas
April 4, 2017
15:20
Explaining Damage Formulas always sounds math-y, so I'll try to keep it simple and sweet.
Damage formulas in this game generally look like this:
(Weapon/Magic Power - Enemy Defense) * Multiplier
The first part is exactly what it sounds like.  No stats are involved - just the raw values of your weapon or your spell's attack power, reduced by the enemy's defensive stats.  There CAN be some variance here.  For an example, Swords actually roll a random attack power value of 100-112.5% of their normal power, so they can do a bit more than usual.  This is why sometimes your attacks just do 0 damage - the weapon/spell may simply not be potent enough to pierce the enemy's armor!
If you multitarget a spell, its power is halved BEFORE enemy defense is applied.  Later spells generally completely outstrip enemy magic defense, but early on it can be important to keep in mind.
The multiplier is where things get confusing.  It looks like this:
(Stat * Level)/Rate + 2
The Stat is the stat used in the formula - generally, Strength for physical attacks and Magic for magical ones. This value is directly multiplied by your level, and then divided out by either 256 (for 'Slow' multipliers) or 128 (for 'Fast' multipliers).
The part where this gets weird is that the game drops decimals upon division.  This means it's not like your multiplier is 7.2 one level, 7.5 the next, 7.8 the next, and then 8.1 the next - instead, your multiplier on those levels will be 7, 7, 7, and 8.  Your damage will only actually increase in 'steps', instead of linearly - this is why +Strength and +Magic equipment, early on, may not even raise the damage you see.  If it doesn't push that total value of Stat * Level high enough, then it doesn't matter!
This becomes really important when effects that half the multiplier are concerned: Shell, Protect, and/or row considerations.  These half the multiplier value - however, as the decimal is dropped, this can do more than half the multiplier.  Since each of these are also applied one at a time, they stack horrifyingly: A back-row enemy under Protect would "theoretically" take only 1/4th damage.  And it might, if your multiplier was 4.  If your multiplier was 7?  7/2 = 3.5 (3); 3/2 = 1.5 (1).  You are literally dealing 1/7th of the damage.  God forbid you too are in the back row - in the worst case scenario, you can potentially be doing 1/15th(!?) the damage instead of the expected 1/8th!
The following things exist that can halve multiplier:
Using physical attacks from the back row, without a "Back Row OK" Weapon
Using physical attacks on a target in a back row (yes, enemy formations have rows) without a "Back Row OK" weapon
Using physical attacks on a target under the Protect status
Using magical attacks on a target under the Shell status
Of course, you can use this to your advantage too!  Back row characters might deal less physical damage, but they'll take a lot less too - especially if you back it up with Protect.  You can even benefit from this with the handful of weapons that ignore row!
For the record, here's the quick and dirty version of weapon damage formulas.  There are EXCEPTIONS to these, of course - the Monk's unarmed attacks don't even have a "Weapon Attack" really, or there's Axes, which have wildly variable damage and defense piercing in a way - but those will be covered by the classes and abilities where they are relevant.
Spells: ((100%-112% of MAtk) - MDef) * (Slow Magic)
Swords: ((100%-112% of WAtk) - Def) * (Fast Strength)
Knives: ((WAtk + 0-3 bonus points) - Def) * (Fast Strength)
Rods: ((0%-100% of WAtk) - MDef) * (Slow Magic)
Hitting a Weak element of the target causes the WAtk/MAtk to be doubled and the target's Def/MDef to be ignored.  It does NOT affect the Multiplier.  Critical Hits, on the few weapons they exist on, also do this exact same thing.
iOS players, please note that the damage formulas are a little different in that version, although nobody knows the specifics.