EO4/Formulas

Detailed explanation of how Etrian Odyssey IV: Legends of the Titan calculates damage, ailment/bind infliction, recovery, and so on. This also explains how various modifiers in the Skills pages impact gameplay.

If a combatant's head is bound, halve their TEC for all TEC-using calculations.

Damage

$Damage=(BaseDmg\times StatScore\times Damage\mathrm{\%}\times Passive\mathrm{\%}\times Vuln\mathrm{\%}\times Forge+random(0,5))\times Buff\mathrm{\%}\times CritDmg\times SleepBonus$

• BaseDmg is defined as:
  • For STR-based attacks from the party members, $weaponATK-targetVIT$
    • If user is unarmed, $weaponATK=(Level+STR)÷2$
  • For TEC-based attacks from the party members, $attackTEC\times 4-targetVIT$
  • For STR-based attacks from enemies, $attackSTR\times 3-(ArmorDEF÷3)$
  • For TEC-based attacks from enemies, $attackTEC\times 5-ArmorDEF$
• StatScore is defined as:
  • For any STR-based attack, $StatScore=\sqrt{attackSTR÷targetVIT}$
  • For any TEC-based attack, $StatScore=\sqrt{attackTEC÷targetTEC}$
• Damage% is the Damage % of the skill being used. For all normal attacks, this is treated as 100%.
• Passive% is the damage bonus from all relevant passives. Apply Diminishing Returns if multiple passives of the same category are in effect.
• Vuln% is the damage multiplier based on the target's vulnerability to that damage type. Neutral vulnerability is treated as 100%. Resistance means a vulnerability of 99% or lower, weakness means a vulnerability of 101% or higher (qualifying for bonus damage from Runemaster's Runic Guidance). Immunities means a 0% multiplier.
  • Buffs and passives that increase resistances are treated as decreases to Vuln% and vice-versa. They are exempt from Passive% and Buff% variables.
  • In case of attacks that use more than one damage type, apply only the highest Vuln% among those damage types. The exception is when the weapon carries any elemental forges - see below for how they are handled.
• Forge is the total damage bonus gained from ATK/ELM Forges, starting from 100% for zero forges. Each ATK Forge grants an additive 3% to cut/stab/bash attacks, while each ELM Forge gives an additive 3% to fire/ice/volt attacks. Count both for physical/elemental hybrids.
• Buff% is the total modifiers between all active buffs and debuffs multiplied together, including temporary modifiers like Bushi's Charge and any Burst Skills. Treat attacker's damage buffs the same as the target's defense debuffs, and vice-versa. Apply Diminishing Returns if multiple buffs/debuffs of the same category are in effect.
• CritDmg is the damage modifier if the attack is a critical hit. This value is normally 150%, but the Sniper's Class Skills can increase this value. Enemies cannot deal critical hits.
• SleepBonus is the 150% damage multiplier when attacking a sleeping enemy with a physical attack.
• If the weapon has any elemental forges, repeat the damage calculation for the elemental component, including the target's elemental Vuln%, multiply by 7% × number of matching elemental forges, then add this to the physical component. Check only the right-most elemental forge and its duplicates. Do this only for normal attacks or skills that use the properties of the weapon, like the Landsknecht's Sonic Raid.
  • If this attack qualifies for bonus damage from Runemaster's Runic Guidance, apply the bonus damage to both physical and elemental components.
• If the attacker's arms are bound, also halve any physical damage they deal.
• If the target is defending, halve any damage they take.

Diminishing Returns

When calculating Passive% and Buff%, the game first sorts the buffs/passives of the same category in descending order of strength. The second strongest buff/passive onward takes an increasing additive penalty to its bonus, to a minimum bonus of 1%:

• 2% for damage or defense increasing passives.
• 5% for damage or defense increasing buffs.

For example, for a dual-wielding Bushi/Landsknecht that has learned a level 10 Power Boost, level 8 Defiance and has an additional level 4 Power Boost and Level 4 Initiative from the Landsknecht subclass:

• Ferocity, as the strongest passive (30%), has no modifiers
• The Initiative bonus is adjusted from 30% to 28%
• Power Boost (Bushi) is adjusted from 25% to 21%
• Power Boost (Landsknecht subclass) is adjusted from 15% to 9%

After adjusting the bonuses accordingly, add 100% to each and multiply them together. In total, Passive% becomes 130% × 128% × 121% × 109% = 219%. Without diminishing returns, Passive% would have been 243%.

For a Landsknecht/Bushi under the effects of their Enlightenment Class Skill, level 6 Vanguard, an allied Dancer's level 8 Attack Tango, the Charge Order Burst Skill, and a level 2 Charge that's attacking an enemy debuffed by a level 4 Atrophic Eye:

• Charge's damage multiplier, giving the highest bonus, is unmodified (×2.0 is equivalent to +100%)
• Vanguard's bonus drops from 40% to 35%
• Charge Order's drops from 40% to 30%, Attack Tango's drops from 40% to 25%
• Enlightenment's bonus goes from 30% to 10%
• Atrophic Eye's bonus drops from 25% to the minimum of 1%

After adjusting the bonuses accordingly, add 100% to each and multiply them together. In this situation, Buff% is calculated as 200% × 135% × 130% × 125% × 110% × 101% = 487%; without diminishing returns, it would have been 891%.

The Bushi's Blood Surge, Landsknecht's Link Mastery, resistance adjustments from the Runemaster's skills, and damage penalty from Nightseeker's Blade Flurry are exempt from diminishing returns. Modifiers to healing, critical rates, hit rates, action speed, evasion, etc. are also exempt from diminishing returns.

Hit Rate

$HitRate=(BaseAcc+Buffs)\times BlindMod+HITForge$

• BaseAcc is calculated by:
  • Weapon's innate hit rate for normal attacks.
    • Most weapons have an innate hit rate of 98.
    • Unarmed attacks have a hit rate of 95.
    • Enemy normal attacks have an innate hit rate of 99.
  • For skills dependent on weapons, apply their Hit Rate modifier to the weapon's innate hit rate. Treat Hit Rate Modifier as ±0 if unmentioned.
  • For skills independent of weapon, use only their Hit Rate value.
  • Then a modifier is added to BaseAcc, based on the attacker's and target's AGI and LUC stats.
    • $var=[\frac{attackTEC+attackLUC}{2}+attackAGI\times 2]-(targetLUC\times 2+targetAGI)$
    • If var ≤ -139, apply a -30 modifier.
    • If var ≥ 140, apply a +30 modifier.
    • Otherwise, the modifier is $30\times sin(var÷100)$
  • After performing all above calculations, correct BaseAcc to a maximum of 100 (for party members' attacks) or 200 (for enemy attacks).
• Buffs is the sum of all Hit Rate/Evasion modifiers between the attacker and target. Treat an evasion increase as a hit rate penalty and vice-versa. After adding all modifiers to BaseAcc, correct this value to a maximum of 150, then apply a ×0.33 multiplier if the combatant is Blind (this is the BlindMod variable).
• HITForge is the total hit rate bonus from all HIT forges across all equipment. Each HIT forge adds a +3 to hit rate.
• Final Hit Rate is corrected to a maximum of 100.

Critical Hits

$CritChance=BaseCrit+CRIForge+random(0,5)+Buffs$

• BaseCrit is first defined by this variable:
  • $A=attackLUC-targetLUC$
    • If A ≤ -11, BaseCrit = 0
    • If A ≥ 42, BaseCrit = 30
    • Otherwise, $BaseCrit=15+15\times sin(A÷20-0.75)$
• CRIForge is the total critical rate bonus from all CRI forges across all equipment. Each CRI forge adds 3 to this value, to a maximum of 24.
• Buffs is the sum of the integer values of all Critical Rate increasing skills on the attacker.
• Only normal attacks and bow skills from Snipers with investment in their Class Skill can inflict critical hits. Monsters can never inflict critical hits.

Action Speed

$Speed=AGI+EquipSpeed+SkillSpeed+SPDForge+random(0,4)+2000$

• EquipSpeed is the total Speed modifiers summed between the character's equipment.
  • Weapons
    • Knife: +3
    • Rapier: +2
    • Katana: +2
    • Sword: +0
    • Bow: +0
    • Staff: +0
      • Mirage Rod has a -1 speed modifier instead.
    • Mace: -3
    • Drive Blade: -4
  • Armor
    • Boots: +4
    • Clothing: +2
    • Glove: +1
    • Helmet: +0
    • Accessory: +0
    • Light Armor: -1
    • Shield: -1
    • Heavy Armor: -2
• SkillSpeed is the Action Speed modifier from the skill you're using. Treat this as ±0 for normal attacks, +90 if a party member is defending, ±0 if an enemy is defending. Also treat as ±0 if Action Speed modifier is unmentioned.
• SPDForge sums the Action Speed modifiers from all SPD Forges among all equipment. Each SPD Forge gives +2 action speed.

Ailment/Bind Infliction

$Rate=[(InfictionRate\mathrm{\%}+random(0,9))\times Vuln\mathrm{\%}+AilmentBoost\mathrm{\%}]\times LethalResistance$

• InflictionRate% is defined by the following variable:
  • $X=(2\times attackLUC+attackTEC)-(2\times targetLUC+targetTEC)$
    • If X ≤ -18, InflictionRate% is the skill's base infliction rate.
    • If X ≥ 22, InflictionRate% is double the skill's base infliction rate.
    • Otherwise, $InflictionRate\mathrm{\%}=[1.17+0.83\times sin(0.07\times X-0.20)]\times BaseInflictionRate$
• Vuln% is the target's vulnerability to that bind/ailment. Treat neutral vulnerability as 100% for random encounters, 50% for FOEs and bosses. Any modifier that increases resistance is a decrease to vulnerability and vice-versa.
• AilmentBoost% is the bonus granted by the Arcanist's Ailment Boost. Ignore this bonus against immunities.
• Lethal Resistance applies only for bosses and FOEs that have petrify/instant death resistance instead of outright immunity. In those cases, treat their Vuln% as 1%, and apply the Lethal Resistance modifier after accounting for Ailment Boost.
• Correct Rate to a maximum of 90%.

Accumulative Resistance

• After a combatant (ally or enemy) gets inflicted with an ailment/bind, apply an additive 30% resistance bonus to that ailment/bind for the rest of the battle.
  • For example, a combatant with a base of 100% vulnerability to Blind drops to 70% vulnerability after getting blinded the first time, then 40% after the second infliction, then 10%, then 0% (the minimum), effectively gaining immunity to blindness for the rest of the battle after four inflictions.
• If a party member dies in battle and gets revived, their Accumulative Resistance is reset.
• An Arcanist's Releasal Spell will reset the target's Accumulative Resistance.

Poison Damage

• Poison Damage from a skill is calculated by $PoisonDamage+random(1,10)$
• Poison Damage inflicted by a weapon's normal attack is $wpnATK÷2+random(1,10)$

Ailment/Bind Recovery

Ignore recovery calculation on the turn the ailment/bind is inflicted.

$RecoveryChance=random(0,10)\times DisableTurns+StatMod+KnightsBoon$

• StatMod is determined by the following:
  • $A=LUC-(Level\times 0.58+5.7)$
    • If A ≤ -10, StatMod = 0
    • If A ≥ 10, StatMod = 40
    • Otherwise, $StatMod=sin(A\times 0.14)\times 20+20$
• RecoveryChance is then treated as a percentage.
• KnightsBoon is the bonus granted by the Fortress's Knight's Boon.
• If RecoveryChance exceeds 80%, set it to 80%.

Healing

$Healing=TEC\times TECMod\times HealingPower\mathrm{\%}\times Passive\mathrm{\%}+random(0,5)$

• TECMod is determined by the following:
  • $X=TEC-(Level\times 0.63+5.28)$
    • If X ≤ -15, TECMod = 1
    • If X ≥ 15, TECMod = 3
    • Otherwise, $TECMod=sin(X÷10)+2$
• HealingPower% is the Healing Power value of the skill you're using.
• Passive% is the total modifiers from any healing-increasing passives in use, multiplied together.

Preemptives and Blindsides

For preemptives,

$PreemptiveRate=BaseRate+SneakAttack+random(0,10)$

• First define the following variable by $A=(PartyAvgTEC+PartyAvgAGI)-(EnemyAvgTEC+EnemyAvgAGI)$
  • If A ≤ -12, BaseRate = 0
  • If A ≥ 42, BaseRate = 30
  • Otherwise, $BaseRate=15+15\times sin(A÷20-0.75)$
• SneakAttack is the integer value bonus of the Nightseeker's Sneak Attack skill.

If you get a preemptive round, bypass the blindside check. Otherwise, calculate for blindside.

For blindsides,

$Blindside=BaseRateB+random(0,10)-(100-PreemptiveRate)$

• Take A from the same preemptive formula.
  • If A ≤ -12, BaseRateB = 30
  • If A ≥ 42, BaseRateB = 0
  • Otherwise, $BaseRateB=15+15\times sin(A÷20-0.75)$

Enemy Aggro

When an enemy attacks, each party member is first assigned a random aggro value from 0 to 4.

The enemy then first performs this check:

• 75% chance to target the front row.
• 20% chance to target the back row.
• 5% chance to target an entirely random party member.

If it targets a row this way, the party member with the highest current HP in that row has a random number from 0 to 6 added to their aggro value. If it instead chose to target randomly, do this only for the party member it has targeted.

Then, apply the aggro value modifier from Fortress's Taunt or Nightseeker's Decoy Sign if that skill is active. This modifier is also a random number, with its maximum and minimum determined by the skill's level.

After performing all checks, attack the party member with the highest aggro value. This means that if an enemy has already targeted someone randomly through the first check, they can turn their sights to the party member with a high enough aggro value granted by their draw rate buff.

Escape

On a pre-emptive round, or if Full Retreat is being used, Escape Rate is 100%.

Otherwise, define the following values:

• A = The greatest value between the escaper's AGI, LUC, and level.
• B = The average level of all the enemies currently in the fight.
• C = A - B
  • If C < 0, D = 0.
  • If C > 5, D = 20.
  • Otherwise, D = 5
• T = Turn Count. Maximum value for this is 5.
• R = A random value between T and T × 2 is rolled for. That value is then multiplied by T.
• E = 6 × Number of times an ally has died this battle. Maximum value for this is 60.

Escape Rate = D + R + E.

• If Escape Rate is greater than 90, then it is capped at 90.

Difficulty Modifiers

Apply these multipliers in addition to the above.

Variable	Normal	Casual
Damage Dealt	100%	150%
Damage Taken	100%	50%

References

• Etrian Odyssey IV: Legends of the Titan GameFAQs Formulas page