EO3/Formulas

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

Damage

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

• BaseDmg is defined as:
  • For STR-based attacks from the party members, $weaponATK-targetVIT$
    • If user is unarmed, $weaponATK=(Level+STR)÷2$
    • If the user has invested in Monk's Fist Mastery, $weaponATK=(Level+STR)\times (1+FistMastery\mathrm{\%})$
  • 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, including Weapon Masteries and Class Skills. Multiply each passive together (adding 100% to each passive first)
  • A Gladiator with level 10 Endless Battle and Level 10 Sword Mastery gets 125% × 111% = 139% Passive% for their normal attack with swords.
• 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 (and qualifies for Zodiac's Singularity). 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.
• ATKForge is the total damage bonus gained from ATK Forges, starting from 100% for zero forges. Each ATK Forge grants an additive 3% to this bonus, but only applies to STR-based attacks.
• Charge is the damage multiplier gained from Charge or Etheric Charge.
• Buff% is the total modifiers between all active buffs and debuffs multiplied together. Treat attacker's damage buffs the same as the target's defense debuffs, and vice-versa. For example, a combatant under the effects of a level 10 Berserker Vow and level 10 Attack Order, attacking an enemy under a level 5 Eagle Eye has a Buff% factor of 190% × 145% × 135% = 372%.
• If the weapon has any elemental forges, repeat the damage calculation for the elemental component, including the target's elemental Vuln%, multiply by 10% × 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 any follow-up attacks from the Shogun's Warrior Might.
  • If this attack qualifies for the Zodiac's Singularity, apply the bonus damage for both physical and elemental components.
• CritDmg is the damage modifier if the attack is a critical hit. This value is normally 150%, but can be different with an Yggdroid's Data Mining. Enemies cannot deal critical hits.
• SleepBonus is the 150% damage multiplier when attacking a sleeping enemy with a STR-based attack.

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. The Panic Fleuret, Dagger of Mercy, Stunning Knife, and Stone Songs all have a hit rate of 50.
    • Unarmed attacks have a hit rate of 95.
    • Enemy normal attacks have an innate hit rate of 99.
  • For skills dependent on weapons, use weapon's innate hit rate and add the skill's Hit Rate Modifier. Treat the Hit Rate Modifier as ±0 if unmentioned.
  • For skills independent of weapon hit rate, 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 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: +1
    • Sword: +0
    • Fist: +0
    • Gun: -1
    • Tome: -1
    • Crossbow: -2
    • Spear: -3
    • Club: -4
  • Armor
    • Boots: +4
    • Clothing: +2
      • Summer Tweed gives a +0 speed modifier instead.
      • Bikini Armor gives a +10 speed modifier instead.
    • 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, and for skills that do not mention an Action Speed modifier.
• SPDForge sums the Action Speed modifiers from all SPD Forges among all equipment. Each SPD Forge gives +2 action speed.

Ailment/Bind Infliction

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

• 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.
• VirusScanner% is the penalty to infliction rates from enemies from Yggdroid's Virus Scanner.
• WildMastery% is the infliction rate boost from Wildling's Wild Mastery. This bonus will not apply if calculating against an immunity.
• 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 Wild Mastery.
• 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.

Poison and Plague Damage

$Damage=BaseDamage+random(1,10)$.

• If the Poison or Plague is inflicted using a Forged weapon, the base damage is half the weapon's ATK stat.

Ailment/Bind Recovery

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

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

• 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.
• For ailments, add the bonus from Monk's Waking Chakra skill to RecoveryChance.
• If RecoveryChance exceeds 80%, set it to 80%.

Healing

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

• 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.
• FormQi% is the modifier from the Monk's Form Qi + 100%.

Preemptives and Blindsides

For preemptives,

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

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

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

For blindsides,

$Blindside=BaseRateB+random(0,10)$

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

If blindside check passes, then conduct a check against Wildling's Alertness success rate. Do this for each instance of Alertness among the party, stopping if an Alertness check passes (combat starts as normal) or all checks fail (blindside triggers).

Enemy Aggro

When an enemy attacks, each party member is first assigned a random aggro value from 0 to 4. Decoys created by Ninja's Kagerou/Ninpo: Mirage instead are assigned a random aggro value from 3 to 9.

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 modifiers from skills like Hoplite's Provoke, Farmer's Play Possum, Ninja's Otori, or Shogun's Dafuhensha/Great Warrior. 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.

Escape

Define the following variable: $A=(AGI+LUC)-(EnemyAvgAGI+EnemyAvgLUC)$

• If A ≤ -32, then B = 0
• If A ≥ 10, then B = 80
• Otherwise, $B=40+40\times sin(A\times 0.03-0.53)$

$EscapeRate=B+TurnCount\times random(5,10)$

• Adjust EscapeRate to a maximum of 90%.
• If using the Ninja's Tonsou Jutsu or Shogun's Retreat, replace B with their skill's Escape Rate value, and raise the final Escape Rate cap to 99%.

Difficulty Modifiers

In Etrian Odyssey III HD, apply these multipliers in addition to all the above.

Variable	Expert	Basic	Picnic
Damage Dealt	100%	120%	500%
Damage Taken	100%	80%	10%
Ailment/Bind Infliction Rate	100%	120%	200%
Ailment/Bind Vulnerability Multiplier	100%	80%	10%
Party's Ailment Damage	100%	120%	500%
Enemy's Ailment Damage	100%	80%	20%
Healing Power	100%	100%	300%
Party Accuracy	100%	100%	120%
Enemy Accuracy	100%	100%	80%
Party Action Speed	100%	100%	200%
Preemptive Rate	100%	100%	200%
Blindside Rate	100%	100%	20%
Escape Rate	100%	100%	150%
Environmental Damage	100%	80%	20%
EXP Gain	100%	100%	150%

References

• Etrian Odyssey III: The Drowned City Let's Play by Araxxor, Formulas page

V • T • E	Etrian Odyssey III: The Drowned City (Category • Gallery)
Publisher/Developer: Atlus • Console: Nintendo DS
Locations	Armoroad Aman's Inn • Napier's Firm • Butterfly Bistro • Explorers Guild • Inver Port • Via Senatus • Forest Entrance Click to toggle hidden content: Deep City Twinkling Tavern • Napier's Branch • Celestial Palace • Forest Entrance
	Yggdrasil Labyrinth Waterfall Wood • Undersea Grotto • Molten Caves • Abyssal Shrine • Porcelain Forest Click to toggle hidden content: Cyclopean Haunt
	South Sea Skandalia Lighthouse • Trade City of Batavia • Ayutthaya Port • Tortuga Island • Giant's Ruins • Trade City of Ugarit Click to toggle hidden content: North Sea Marine City of Sheba • Dark Forest • Trade City of Damavand • Tower of Victory • Trade City of Aeaea • Aerial Forest
Classes	Arbalist • Buccaneer • Farmer • Gladiator • Hoplite • Monk • Ninja • Prince/Princess • Wildling • Zodiac Click to toggle hidden content: Shogun • Yggdroid
Characters	Edie Napier • Missy • Flowdia • Gutrune • Kujura • Olympia • Agata • Hypatia • Lindworm • Wealh • Hiiragi & Agamede Click to toggle hidden content: Abyssal King • Angie • Eldest One
Items	Weapons • Armor • Accessories • Consumables • Materials
Lists	Monsters • Missions • Quests • Maps
Mechanics	Forging • Limit Skills • Seafaring • Subclasses • Formulas