EO5/Formulas

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

Damage

$compScore=Defense÷Attack$

• For physical attacks,
  • Defense is target's VIT + DEF bonus from armor. As monsters or summons don't wear armor, use their VIT ×2.
  • Attack is attacker's STR + ATK bonus from their weapon. As monsters or summons don't use weapons, use their STR ×2.
• For magic attacks,
  • Defense is target's WIS + MDF bonus from armor. As monsters don't wear armor, use their WIS ×2.
  • Attack is attacker's INT + MAT bonus from their weapon. As monsters don't use weapons, use their INT ×2.

• If compScore > 1 (target's defense outpaces attacker's offense): $BaseDamage=([(1.0-\sqrt[4]{compScore}\times 0.7)\times Attack\times 3]-Defense÷5)\times 0.717$
• Otherwise: $BaseDamage=([(0.3+(1.0-compScore{)}^3\times 1.7)\times Attack\times 3]-Defense÷5)\times 0.717$

$Damage=BaseDamage\times SkillDamage\times Vuln\mathrm{\%}\times Buffs\mathrm{\%}\times Charge\times Guard\mathrm{\%}$

• SkillDamage is the Damage% variable from the skill in use. Treat as 100% for normal attacks.
• 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. Immunities means a 0% multiplier.
  • Buffs and passives that increase resistances are treated as decreases to Vuln% and vice-versa.
  • In case of attacks that use more than one damage type, apply only the highest Vuln% among those damage types.
• Buffs% is the total modifiers between all active buffs and debuffs. Treat attacker's damage buffs the same as the target's defense debuffs, and vice-versa.
• Charge is the Damage Multiplier offered by the charge skill in use.
• Guard% is the temporary Damage Reduction modifier applied by skills like Dragoon's Line Guard.
• When using the Impact Brawler Pugilist's Death Edge, apply a further multiplier: $Damage\times (1+TotalPartyMissingHP÷100)\times [(PartyAverageMissingHP\mathrm{\%}+PartyAverageMissingHP{\mathrm{\%}}^2)+0.02]÷2$
• After doing the all above, multiply the result by a random number from 0.98 to 1.02, then add a random integer from 0 to 4

Diminishing Returns

Buffs and passives that increase the damage dealt are calculated additively, onto a base of 100%. For example, for a combatant under the effects of a level 10 Shaman's Ruinous Prayer and level 10 Masurao's High Ground, attacking an enemy affected by level 10 Deathguard Harbinger's Eroding Miasma with a physical attack, Buffs% is calculated as 100% + 35% + 40% + 35% = 210%. (In contrast, doing this multiplicatively leads to a result of 135% × 140% × 135% = 255%)

Buffs and passives that reduce damage received are calculated multiplicatively, with each modifier deducted from a base of 100%. For example, a combatant under the effects of level 10 Dragoon's Defense Form, level 10 Shaman's Aegis Prayer, while taking a physical attack from an enemy affected by a level 10 Barrage Wall and level 10 Harbinger's Stifling Miasma, damage taken is (100-34)% × (100-25)% × (100-20)% × (100-20)% = 66% × 75% × 80% × 80% = 32%.

Hit Rate

$StatMod=\frac{(attackAGI\times 2+attackLUC)\times 10}{targetAGI\times 2+targetLUC}$

• AGI is halved and rounded down if the entities involved have their legs bound.
• If StatMod < 10, $HitRate=[1-(1-StatMod÷10{)}^2]\times (BaseHit\mathrm{\%}+SkillMod)\times 100$
• If StatMod ≥ 10, $HitRate=(87.5+StatMo{d}^2÷8)\times (BaseHit\mathrm{\%}+SkillMod)$
  • If the attacker is using a skill that does not require a weapon, BaseHit% is the skill's own Hit Rate, and treat SkillMod as 0.
  • If the party member is doing a normal attack with a weapon, BaseHit% is that weapon's accuracy stat, or 95% if unarmed.
    • Swords: 99%
    • Scythes: 98%
    • Cestus, Staves, Bows, Coffins: 97%
    • Katanas: 96%
    • Cannons: 92%
  • BaseHit% is 99% for normal attacks from enemies.
  • If the party member is using a weapon-dependent skill, BaseHit% is their equipped weapon's accuracy stat and SkillMod is the Hit Rate Modifier of their skill. Treat SkillMod as ±0% if unmentioned.
• Then sum all hit rate modifiers between attacker and target. Treat hit rate buffs on the attacker the same as evasion debuffs on the target, and vice versa.
• Correct HitRate to 150% if it exceeds that amount.
• If the attacker is blinded, divide HitRate by 3 after the above step.
• Treat HitRate as 100% if target is petrified, asleep, panicked, blinded, paralyzed, or leg bound, or the attack itself cannot miss.

Critical Hits

$CritRate=\frac{(attackLUC+25)\times 10}{targetLUC+25}$

• Correct CritRate to a minimum of 3% and maximum of 30%.
• If the user has invested in Blade Master Masurao's Sword God, add the critical rate bonus to CritRate. This bypasses the usual maximum of 30%.
• Only normal attacks or physical skills from a Blade Master Masurao that knows Sword God can deal critical hits. Critical damage is 150% at base but can be increased by Sword God.

Action Speed

$ActionSpeed=(EquipMod+100)\times AGI\times SkillMod\times random(90,110)÷10000\times Buffs\mathrm{\%}$

EquipMod is the total action speed modifier among all the user's equipment.

• Weapons:
  • Swords: 0
  • Cestus: -5
  • Staves: -5
  • Katanas: -5
  • Bows: 10
  • Scythes: 5
  • Cannons: -15
  • Coffins: 5
• Armor:
  • Heavy Armor: -10
  • Light Armor: 0
  • Clothes: 5
  • Helmets: 0
  • Gloves: 5
  • Boots: 10
  • Shields: -5
  • Accessories: 0
• SkillMod is the Activation Speed modifier from the skill being used. Treat as 100% for a normal attack, and if unmentioned.
• Buffs% is the total modifier among buffs/debuffs/passive skills.
• Rare Breed enemies multiply their AGI by 10 every time they act.

Ailment/Bind Infliction

$Rate\mathrm{\%}=InflictionRate\mathrm{\%}\times Vuln\mathrm{\%}\times Buffs\mathrm{\%}$
$StatMod=\frac{attackLUC+attackStat\times 2+76.5}{targetLUC\times 3+76.5}$

• attackStat is STR for STR-based damaging skills, INT for INT-based damaging skills, and LUC for skills that inflict the disable without doing damage.
• If StatMod ≤ 0.2, InflictionRate% = BaseRate% (the infliction rate of the skill being used)
• If StatMod ≥ 5, InflictionRate% = BaseRate% × 5
• Otherwise, InflictionRate% = BaseRate% × StatMod
• Vuln% is the target's vulnerability to that ailment/bind. A neutral vulnerability for random encounters is 100%, while this is 50% for FOEs and bosses. Weakness to that ailment/bind means a higher vulnerability multiplier, resistance means lower vulnerability. Immunity is 0%.
• Buffs is the bonus infliction multiplier from skills and passives. Treat decreases to resistance as bonuses to infliction and vice-versa.
• Adjust Rate% to a maximum of 150%.

Accumulative Resistance

Each time a combatant is affected by an ailment/bind, they receive an additive 50% reduction to vulnerability. Afterwards, for every turn they spend without that ailment/bind, their vulnerability goes back up by 7%, until it reaches a cap (that ensures it will never revert to the original vulnerability). If the ailment/bind is successfully re-applied, the recovery process is paused and another 50% resistance is applied. The combatant can become temporarily immune to the ailment/bind if vulnerability drops to or lower than 0% this way.

The vulnerability cap is determined by this formula:

• If ailment/bind was inflicted three or fewer times this battle: $MaxVuln\mathrm{\%}=0.85^{inflictions}\times Vuln\mathrm{\%}$
• If ailment/bind was inflicted more than three times this battle: $MaxVuln\mathrm{\%}=0.85^{1+inflictions÷2}\times Vuln\mathrm{\%}$

For example, if a combatant with base 100% blind vulnerability is first blinded, their blind vulnerability first drops to 50%, then slowly recovers to a maximum of 85% over five turns after recovering from blindness. When they get inflicted by blind after that point, blind vulnerability drops to 35%, and after recovering, the vulnerability slowly goes up to a maximum of 72% (which will take six turns).

If a combatant with 50% blind vulnerability is first blinded, they become immune to it, but the vulnerability slowly goes back up to a max of 42% (over six turns) after recovering from blindness. On the next infliction, their vulnerability drops to -8% (still an immunity), and after recovering, slowly recovers to 36% (over seven turns), and it is immune to blindness for the first two turns as the vulnerability is still negative then.

Poison Damage

$PoisonDamage=random(0,5)+(random(0,5)+BaseDamage+\frac{Level}{5})\times (1+\frac{Level}{100})$ ^{[This formula seems to be slightly wrong]}

Ailment/Bind Recovery

$RecoverRate\mathrm{\%}=BaseRate\mathrm{\%}+Antibodies\mathrm{\%}$
$StatMod=\sqrt{\frac{LUC+51}{EnemyAvgLUC+76.5}}\times 10$

• If StatMod ≤ 5, $BaseRate\mathrm{\%}=(15\mathrm{\%}\times TurnsInflicted)-30\mathrm{\%}$
• If StatMod > 20, $BaseRate\mathrm{\%}=(30\mathrm{\%}\times TurnsInflicted)$
• Otherwise, $BaseRate\mathrm{\%}=(TurnsInflicted\times (StatMod+10)+StatMod\times 2-40)\mathrm{\%}$
• Antibodies% is the bonus recovery rate from Herbalist's Antibodies
• RecoverRate% = 0% if it's the same turn this combatant was inflicted with the ailment/bind. This ensures the ailment/bind lasts a minimum of 1 turn.
• RecoverRate% = 100% if the combatant has been afflicted with the ailment/bind for 4 or more turns. This means that ailments and binds in this game cannot last for more than 5 turns.

Healing

$[HealingPower\times WIS\times 2÷459+HealingPower÷6+WIS\times 53÷25000\times \sqrt{HealingPower}]\times HerbMastery\mathrm{\%}+random(0,9)$

• HealingPower% is the Healing Power of the skill being used.
• HerbMastery% is the Healing Power increase conferred by Botanist's Herb Mastery + 100%.

Preemptives and Blindsides

If the party was caught from behind by an FOE, ignore all calculations and trigger an immediate blindside. If the party catches a boss or FOE from behind, ignore all calculations and trigger an immediate preemptive.

$StatMod=\frac{PartyAvgAGI\times 2+PartyAvgLUC+51}{EnemyAvgAGI+EnemyAvgLUC\times 2+51}$

• If StatMod ≤ 0.2, Preemptive Rate = 1.2%
• If StatMod ≥ 5, Preemptive Rate = 30%
• Otherwise Preemptive Rate = (StatMod × 6) %
• If any Therians in the party know Precaution, add 3% to Preemptive Rate for each instance of that skill.
• If the preemptive fails and the Warlock's Levitation is in effect, perform an additional check against the Levitation success rate to check for preemptive.

If the preemptive ultimately fails, roll for blindsides.

$StatModB=\frac{EnemyAvgAGI\times 2+EnemyAvgLUC+20}{PartyAvgAGI+PartyAvgLUC\times 2+20}$

• If StatModB ≤ 0.2, Blindside Rate = 0.8%
• If StatModB ≥ 5, Blindside Rate = 20%
• Otherwise Blindside Rate = (StatModB × 4) %
• If blindside succeeds but any character is wielding the Killing Shot bow (which grants the Wary Eye skill), perform an additional check against Wary Eye's success rate. If successful, the blindside fails and combat starts as normal.

If both preemptive and blindside checks fail, start combat as per normal.

Escape

Escape is impossible if the combatant's legs are bound or if the enemy is a boss.

$StatMod={\left(\frac{LUC+AGI}{EnemyAvgLUC+EnemyAvgAGI}\right)}^2\times 10$
$DeadRatio=(deadAllies+incapacitatedAllies)\times 15÷totalAllies$
$Repeats=75÷totalAllies+escFailures\times 2$

• Incapacitated Allies counts allies who are dead, petrified, panicking, or asleep. DeadRatio effectively puts twice as much weight on dead allies.
• If StatMod ≤ 5: $Flee\mathrm{\%}=DeadRatio+(Repeats\times \sqrt{TurnCount}÷4)+2$
• If StatMod > 55: $Flee\mathrm{\%}=DeadRatio+(Repeats\times \sqrt{TurnCount}\times 8)+2$
• If 5 < StatMod ≤ 10: $Flee\mathrm{\%}=DeadRatio+(StatMod\times Repeats\times \sqrt{TurnCount}÷20+1)+2$
• Otherwise: $Flee\mathrm{\%}=DeadRatio+((StatMod+5{)}^2\times Repeats\times \sqrt{TurnCount}÷450)+2$
• Correct Flee% to a maximum of 90%.
• Finally, if all enemies are either petrified, asleep, panicking, blinded, leg bound, afraid, or failed to act because of paralysis, fleeing is guaranteed.

Difficulty Modifiers

Apply these modifiers in addition to the above.

Variable	Advanced	Basic
Damage Dealt	100%	120%
Damage Taken	100%	80%
Ailment/Bind Infliction	100%	120%
Ailment/Bind Vulnerability	100%	80%
Enemy Hit Rate modifier	0%	-10%
Escape Rate modifier	0%	+20%
EXP gained	100%	120%

References

• Etrian Odyssey V: Beyond the Myth formulas