Maths Section
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For description of skills, see Spells
Damage FormulaEdit
I have come up with a theory/model as for the way numerical datas are calculated in battle, depending on the different involved parameters: the damage output of one given damaging skills depends on one particular stat of the attacker (ATK or MAG), on elemental sensibility of the target (including physical resistance/vulnerability) and on active buffs/nerfs.
AlgorithmEdit
- Choose an attack/skill to use;
- Take the actual value of the stat which the skill depends on, for the character who must use it (value indicated on EQUIP screen in the menu, which includes bonuses from weapon and accessories);
- Multiply the value by a coefficient, specific to the chosen skill;
- Multiply the result by another coefficient, the one describing the elemental sensibility of the target (100% in the Bestiary means a coefficient of 1,...);
- Multiply the result by another coefficient, the one describing the buffs/nerfs active on both attacker and target (including Guard status);
- Multiply the result by another coefficient, in case of critical hit (2 for critical, 1 otherwise);
- Keep the result, which represents the Inferior Bound ;
- Multiply the Inferior Bound by a last coefficient, specific to the chosen skill, thus getting the Superior Bound;
- The final/actual damage value should be situated between the Inferior Bound and the Superior Bound (both included).
Notes:
- I recommend to always apply the final coefficient (Step 8) after the others, whereas Steps 3 to 6 may be executed in any order;
- The elemental sensibility coefficient (Step 4) can be negative, meaning that the damage will end up negative as well; this is the instance in which the target is healed by the attack that should have damaged them, for a percentage given by the Algorithm;
FormulaEdit
STAT x M x E x S x C < D < (STAT x M x E x S x C) x V
Where:
- STAT is the actual value of the statistic related to the skill including assets from equipment;
- M is the intrinsic multiplier related to the skill;
- E is the multiplier due to the elemental sensibility of the target to the element of the skill (natural sensibility, or, for heroes, bonus from equipment, like a Wind Charm), stated as a number between 0 and 1 (not in %);
- S is the multiplier due to the possible buffed/nerfed statuses affecting the attacker and the target (if both are buffed, multiply the associated coefficients with one another); (*)
- C is the critical multiplier: it equals 1 for a normal hit, and 2 for a critical hit;
- V is the "variance" multiplier related to the skill.
Notes:
- A more condensed way to approach to this Formula could be to first calculate the "potential" damage output Do:= STAT x M x E x S x C and consider the final damage D being included between it and its variation: Do < D < Do x V ( or D ∈ [Do ; Do x V] ).
- For skills that hit more than once (on one or several targets), the game recalculates the damage for each hit...
- (*)Important : There seems to be a glitch regarding the DEF/MDEF DOWN nerfs ; in fact, they appear to have no effect at all! Neither on enemies nor on heroes.
ExamplesEdit
- Example 1 : I decide to launch a standard physical attack (M=1, V=1.1) with a character who has an actual 300 of ATK stat (STAT=300), on an enemy whose physical sensibility is 100% (E=1) ; none of them is buffed/nerfed (S=1), and the hit is not critical (C=1). So we have: Do = 300 x 1 x 1 x 1 x 1 = 300 , and Do x V = 300 x 1.1 = 330. The final damage my character will deal to the target will then be D such as : 300 < D < 330.
- Example 2 : An enemy with 265 of MAG (STAT=265) casts the skill Water I (M=1.4, V=1.2) on one of my characters, that I have equipped with a Water Charm (-20% for water) and a Helm (-5% for magic) (which adds up to -25% for water, remains 75%, that is to say E=0.75) ; still no (de)buff on anyone (S=1) and no critical hit (C=1). So we have: Do = 265 x 1.4 x 0.75 x 1 x 1 = 278.25 (to round down to 278) , and Do x V = 278.25 x 1.2 = 333.9 (to round up to 334). The final damage my character will take from the enemy's attack will then be D such as : 278 < D < 334.
- Example 3 : I inconsiderately decide to cast Earth I (M=1.4, V=1.2) on an Earth Golem (E= -0.25), with a character who has an actual 949 of MAG (STAT=949) and buffed with Magic Up (S=1.8) ; the hit happens to be critical (C=2). So we have: Do = 949 x 1.4 x (-0.25) x 1.8 x 2 = -1195.74 (to round up to -1196), and Do x V =-1195.74 x 1.2 = -1434.888 (to round up to -1435). The final damage my character will deal to the target will then be D such as : -1435 < D < -1196, Which means that the golem will be healed for 1196 to 1435 HP!
Nota BeneEdit
This model is just what I could deduce from experimentation; if anyone manages to prove it wrong/inaccurate, feel free to correct it as you like.
Coefficient TablesEdit
After statistical experimentation (repeatedly recording damage dealt by characters/foes in identical conditions), I have already figured out the intrinsic coefficients M and V for a few skills.
(For coefficient E, see the Bestiary or Armors)
(For coefficient S, see Statuses)
Offensive SkillsEdit
- It is assumed that a skill depending on ATK will result into physical damage, and one depending on MAG into magical damage; except for the [Element] Attacks which deal magical damage.
- Guesswork: It seems that elemental skills of same level (ex: Fire Attack / Earth Attack... , or Fire I / Water I... , or Earth III / Lightning III... , or Blizzard II / Storm II...) have the same coefficients within a group respectively.
Skill | STAT which skill depends on | M | V |
---|---|---|---|
Standard Attack | ATK | 1 | 1.1 |
Bash | ATK | 1.4 | 1.4 |
Cleave | ATK | 1 | 1.4 |
Barrage | ATK | 0.5 | 1.4 |
Shockwave | ATK | 1.6 | 1.4 |
[Element] Attack | ATK | ||
Quick Attack | ATK | ||
Pilfer | ATK | ||
[Element] I | MAG | 1.4 | 1.2 |
[Element] II | MAG | 1.8 | 1.2 |
[Element] III | MAG | 2.2 | 1.2 |
[Elements] I | MAG | 1.2 | 1.2 |
[Elements] II | MAG | 1.6 | 1.2 |
Healing Skills
- Their healing output do not depends on the sensibility or buffs applied to the ally target, but for the rest, they work the same way; you just have to give a value of 1 to the E factor, and ignore buffs of the targeted ally.
- Only Auto Raise do not depend on buffs of the wearer, as all buffs vanish upon death...
Skill | STAT which skill depends on | M | V |
---|---|---|---|
Quick Heal | MAG | 0.75 | 1.25 |
Heal | MAG | 1 | 1.25 |
Greater Heal | MAG | 1.5 | 1.25 |
Heal All | MAG | 0.75 | 1.25 |
Holy Light | MAG | 1.5 | 1.25 |
Raise | MAG | ||
Raise All | MAG |
Enemy SkillsEdit
- It is assumed that hero skills also known by enemies will work the same ways that they do for heroes (except for explicit exceptions, then included in the table below)
- All poisoning skills seem to work like the Poison skill, whether they deal initial damage or not.
- As it is not possible to directly know which Stat an enemy skill depends on, it is assumed that a skill dealing physical damage actually depends on ATK, and one dealing elemental damage depends on MAG; although some skills may be really doubtful about this: a few do not have any element of output, and the burst ones are torn between physical and magical...
Skill | Element | M | V | Particularity |
---|---|---|---|---|
Drain | None | Heals attacker for 100% of damage dealt | ||
Bite | Physical | Damage over time works like Poison | ||
Lick | None | |||
Impale | Earth | |||
Burst | Fire | Deals Fire damage but is hindered by Physical resistance | ||
Entomb | Earth | |||
Charm | None | |||
Confuse | None | |||
Double Attack | Physical | |||
Crab Claw | Physical | |||
Stampede | Earth | |||
Wing Sweep | Wind | |||
Roar | Physical | |||
Blink | Wind | 0.75 | 1.5 | |
Frost Nova | Water | 1 | 1.4 | |
Rend | Damage over time works like Poison | |||
Burst All | Fire | Deals Fire damage to entire party but is hindered by Physical resistance | ||
Flame Eater | Fire | |||
Spores | None | |||
Poison Tentacles | ||||
Lovesick | ||||
Debuff | ||||
Stun All | ||||
Dargon Claw | Physical | 0.5? | 1.4? | Presumably Dargon King's version of Barrage. |
Judgement | None | N/A | N/A | Always deals about 90% of HP and removes all buffs (but does not counteract Last [x] items). Unknown if ability can kill; evidence suggests it is a percentage attack (think Supernova). |
Special casesEdit
- These are skills that do not obey the Formula, for various reasons ; however, they still possess their own factor(s), characteristic of their functioning...
Skill | Particularity | Characteristic Factor(s) |
---|---|---|
Burst | All 3 Levels deal Fire Damage, yet do not seem to depend on the character who casts it (and so on their Stats) ; however, they seem to react to the Attack Up buff ; their output also vary a lot... | M =1.0; V=2.0; Stat=ATK; critical between 5-10%; affected by ATK UP |
[Nerf] / [Nerf] All | Damage output depends on MAG, but not on target sensibilities, and is the same for any nerf, including 'All' versions (except Sleep and Poison) : M x S x C x MAG < D < V x (M x S x C x MAG) | M= 0.2 ; V= 1.1 |
Poison / Poison All | Primary damage outputs depends on MAG, but not on target sensibilities : M x S x C x MAG < D < V x (M x S x C x MAG) ; secondary output does not vary : works by 30 increments of I = F x MAG | M= 0.5 ; V=1.1 ; F= 1/6 |
Recovery / Regen | Output depends on MAG of caster, but independent from buffs in battle; and does not vary : works by 30 increments of I = F x MAG | F≈ 0,124645(*) |
Auto Raise | Amount Healed after reviving the fallen wearer does not depend on their buffs (since they vanish when dead) nor on the caster, or anything else but the maximal HP of the wearer : H = F x HP | F= 0.25 |
Guard | (See also Guard Weapons) With the GUARD PLUS bonus, the Guard status triggers reflected damage on any foe that attacked or used a skill on the caster ; this damage depends on ATK Stat of the caster, but not on buffs nor sensibilities of the attacker : D = R x ATK | R= 0.75 |
(*I don't know where on Earth they found this number... but I know it was hell for ME to find it --' )
Burst is affected by the Item+ weapon, and M=1.5 but V is still 2.0.
Heals are affected by the Heal+ weapon.
Nota BeneEdit
(Just like above) These data and assumptions are just what I could deduce from experimentation; if anyone manages to find that anything is wrong/inaccurate/missing, feel free to correct it as you like.