EO1/Formulas

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

Damage

Damage in general is calculated as $Damage=(ATK-DEF)\times DamageReduction\mathrm{\%}$ but there is a lot more math behind these parameters.

• DamageReduction% applies to one-time defensive boosts from skills like Protector's Front Guard.
• If the attack is a critical hit, treat DEF as 0.
• If target's DEF exceeds attacker's ATK, the attack inflicts a random value of 1 to 5 damage, ignoring the damage formula.
• If attacker's ATK is more than the target's DEF, but less than 110% of target's DEF, replace the formula with $Damage=(ATK÷100\times var)\times DamageReduction\mathrm{\%}$
  • var in this case is a random number from 8 to 12 (for STR-based attacks) or 8 to 15 (for TEC-based attacks)
• Otherwise, after fully calculating Damage, the game also adds a random value on top of that:
  • If Damage is 100 or less, then add a random value from 0 to 5 (for STR-based attacks) or 0 to 10 (for TEC-based attacks)
  • If Damage is more than 100, then add a random value ranging from -5% to +5% of Damage (for STR-based attacks) or -10% to +10% of Damage (for TEC-based attacks). Round up any decimals.
• If the attacker is performing a Boosted normal attack, Damage is doubled after every other calculation.

Physical Attacks

$ATK=(STR+wATK\times [1+Mastery\mathrm{\%}])\times Damage\mathrm{\%}\times Vuln\mathrm{\%}\times PAtkBoost\mathrm{\%}$

• STR caps at 127, but can be pushed higher than this number from ATK Up bonuses, Ronin's Sight, and Dark Hunter's Fury.
  • Effective STR is halved if the attacker is in the back row and not using a bow. If their arms are bound, apply a ×0.7 multiplier to effective STR. These multipliers stack if both conditions are fulfilled.
• wATK is the ATK bonus of your weapon, and Mastery% is the bonus applied from any weapon mastery passives. Enemies don't use weapons, so this part of the equation uses only their STR (equivalent to ATK, as per the Monstrous Codex).
• Vuln% refers to the combatant's vulnerability to that damage type. For neutral hits, this value is 100%. Resisted hits apply a value less than 100%, hits to weakness apply a value higher than 100%. Against immunities, this value is 0%.
  • Resistance buffs like Protector's Defender or Medic's Immunize or defensive passives like DEF Up give compounding bonuses that change the vulnerability modifier.
  • Defending combatants get a 70% vulnerability multiplier. Sleeping combatants get a 150% vulnerability multiplier to physical attacks. Multiply this with all other factors that alter damage vulnerability.
• Damage% refers to the Damage % of the skill you're using. For example, a Level 5 Landsknecht's Cleaver has a Damage% of 165%. A normal attack has a Damage % of 100%.
• PAtkBoost% compounds the effects of all buffs/debuffs that affect ATK (this is different from STR increase). For example, a Landsknecht under the effects of a Level 10 War Cry and level 5 Troubadour's Bravery has a PAtkBoost of 140% × 130% = 182%.

Elemental Attacks

$ATK=(2\times TEC+SpellATK\times [1+ElementUp\mathrm{\%}])\times Damage\mathrm{\%}\times Vuln\mathrm{\%}\times MAtkBoost\mathrm{\%}$

• TEC caps at 127.
• As Alchemist skills don't rely on weapons, the skill of your choice has its own Spell ATK. Note that the Spell ATK numbers are miniscule, and the ElementUp%, applied from Element Up passives, only apply to that variable. Increasing TEC is far more impactful on Alchemist damage.
  • Other TEC-based skills treat their Spell ATK as 0.
• Vuln% refers to an enemy's vulnerability to that damage type. For neutral hits, this value is 100%. Resisted hits apply a value less than 100%, hits to weakness apply a value higher than 100%. Against immunities, this value is 0%.
  • Resistance buffs like Troubadour's Ifrit or Medic's Immunize or defensive passives like Protector's Shields give compounding bonuses that change the vulnerability modifier.
  • Defending combatants get a 70% vulnerability multiplier. Sleeping combatants get a 150% vulnerability multiplier to physical attacks. Multiply this with all other factors that alter damage vulnerability.
• Damage% refers to the Damage % of the skill you're using. For example, a Level 10 Fire has a Damage % of 130%.
• MAtkBoost% is 100% under most circumstances as there are very few ways that magic damage can be modified in this game.

Physical/Elemental Hybrid

$ATK=([STR+wATK\times (1+Mastery\mathrm{\%})]\times Damage\mathrm{\%}\times Vuln\mathrm{\%}\times PAtkBoost\mathrm{\%})+([TEC+wATK\times (1+Mastery\mathrm{\%})]\times ElemDamage\mathrm{\%}\times Vuln\mathrm{\%})$

• This formula is applied for hybrid physical/elemental skills, including the Ronin's hybrid attacks or any normal attack with a elemental imbue from a Troubadour.
• ElemDamage% counts the Damage% of the elemental component of the skill. If you're using a normal attack with an elemental imbue, treat this as 100% instead.
• If you're attacking an enemy with different Vuln% between the physical and elemental components, each component is calculated separately before being summed up into total ATK.

DEF

Against any STR-based attack: $DEF=[50\mathrm{\%}\times (VIT+DEF)\times DefBoost\mathrm{\%}]$
Against any TEC-based attack: $DEF=[25\mathrm{\%}\times (VIT+DEF)\times DefBoost\mathrm{\%}]$

• A character in the back row has doubled (VIT+DEF) against a physical attack.
• For enemies, (VIT+DEF) is replaced with just their VIT stat (equivalent to their DEF as per the Monstrous Codex).
• DefBoost% compounds the effects of all damage buffs/debuffs that affect DEF, like the Stonard item, Troubadour's Shelter, or Hexer's Frailty.

Hit Rate

$Hitrate=(attackAGI+attackLv+500)÷(targetAGI+targetLv+500)\times HitRate\mathrm{\%}\times Buff\mathrm{\%}$

• AGI caps out at 127 but can be increased with AGI-boosting skills like the Survivalist's AGI Up.
• HitRate% equals the Hit Rate of the skill you are using. For normal attacks, this is 100%.
• Buff% compounds hit rate and evasion multipliers from all active buffs and debuffs between attacker and target. Treat an evasion buff as a hit rate debuff and vice-versa.

Activation Speed

Speed is determined as a product of the user's AGI.

• AGI caps out at 127 but can be increased with AGI-boosting skills like the Survivalist's AGI Up or the Troubadour's Mercury.
• The game takes everyone's effective AGI (after applying multipliers), divides it by 5 and rounds off decimals. Those with the higher result go first, while speed ties are broken with a small random variable assigned to each tied combatant.
• Most in-battle actions that don't involve skills will give a ×1.00 multiplier to AGI.
• When using a skill, multiply the user's AGI with the Activation Speed, and compound any other speed bonuses accordingly. (Treat Activation Speed as 100% if unmentioned) For example, a level 60 Troubadour with level 10 Songs using a level 10 Bravery (and no other AGI modifiers) has an effective AGI of 56 × 102% × 1.30 = 74.256, rounded up to 75.
• Leg binds impose a 70% multiplier to the combatant's AGI.

Ailment/Bind Infliction

$Rate=[(BaseChance\times CursesBoost)+(LUC÷10)]\times Vuln\mathrm{\%}$

• BaseChance is the Infliction Rate of the skill you're using.
• CursesBoost is the bonus provided by the Hexer's Curses passive + 100%. Other classes don't get this skill and so this variable is treated as 100%.
• LUC caps out at 127 and cannot be increased past that point. LUC in this game has no effect in resisting ailments/binds.
• Vuln% is the target's vulnerability to the ailment/bind you're inflicting. For normal enemies, treat a neutral affinity as a 100% multiplier. Weakness is a value higher than 100% and resistance is a value lower than 100%. For FOEs and bosses, the neutral affinity starts at 50% multiplier. Treat the value as 0% against immunities.

Accumulative Resistance

These only apply for binds, not ailments.

• In Etrian Odyssey:
  • For binds, first include a ×0.9 multiplier to Vuln%.
  • Apply a ×1.25 multiplier to Vuln% for each failure to inflict a bind, until the bind lands.
  • After a successful bind, remove all of the above multipliers, then apply a ×0.75 multiplier to Vuln% for that bind instead, repeating this multiplier for every additional time that body part was bound in battle.
• In Etrian Odyssey HD:
  • For every failure to inflict the bind, add a flat 25% success rate, to a maximum of 90%. Remove these bonuses once the bind is successful.
  • After a successful bind, reduce Vuln% by 25%, to a minimum Vuln% of 5%. This modifier does not stack, no matter how many times the bind is inflicted this battle.

Ailment/Bind Recovery

All ailments and binds have a randomly-determined duration once they are inflicted, counting the turn of infliction as turn 1. The duration is then divided by the modifier from the Troubadour's Recovery or Hexer's Relapse, rounding up any decimals.

The odds of the max duration of the ailment/bind are as follows:

Ailment/Bind	3 turns	4 turns	5 turns	6 turns	7 turns
Sleep, Paralysis, Fear, Poison	--	10%	40%	30%	20%
Head/Arm/Leg Bind	--	20%	50%	30%	--
Panic, Blind, Curse	15%	55%	30%	--	--

Enemy Aggro

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Level Scaling

Unique to this game is a hidden modifier that influences damage dealt and damage received based on the level difference between your party members and their target. These modifiers are applied after doing all other damage calculations.

Level Difference	Damage Taken	Damage Dealt
-20	219%	44%
-15	180%	54%
-10	148%	66%
-5	122%	82%
-4	117%	85%
-3	112%	88%
-2	108%	92%
-1	104%	96%
0-3	100%	100%
4	90%	100%
5	90%	101%
10	80%	106%
15	70%	110%
20	60%	110%

Difficulty Modifiers

In Etrian Odyssey 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 Let's Play by Crosspiece