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EOU/Formulas
Detailed explanation of how Etrian Odyssey Untold: The Millennium Girl calculates damage, ailment/bind infliction, recovery, and so on. This also explains how various modifiers in the Skills pages impact gameplay.
Damage
- Damage% uses the Damage modifier of the skill in use. Treat as 100% for a normal attack.
- Buffs% is the combined bonus between all passive bonuses, buffs and debuffs between attacker and defender. Treat attacker's ATK increase and defender's DEF decrease as increases to damage, and vice-versa. Apply Diminishing Returns if multiple buffs/debuffs of the same category are in effect.
- Vuln% is the target's damage vulnerability. This variable is 100% for neutral hits. Resisted hits are treated as 99% or lower, hits to weakness are treated as 101% or higher. Immunities are treated as 0% (although the Codex will only depict them as RS).
- In case of attacks that use more than one damage type, apply only the highest Vuln% among those damage types.
- Revenge Curse adds an additional step to the formula, after Damage is calculated.
- After all above damage calculations, multiply damage by a random variable chosen between 0.98 to 1.02, then add a random integer from 0 to 4.
STR-based damage
- wpnATK is the equipped weapon's ATK.
- If no weapon is equipped,
- If the attacker is using Shield Smite or Shield Rush, wpnATK is the equipped shield's DEF ×3.
- As monsters do not use weapons,
- armorDEF is the total DEF bonus from the combatant's equipped armor pieces.
- As monsters don't use armor, treat this variable as their VIT (DEF in the Codex) ×2.5
- If the attacker's arms are bound, halve their STR and round down while calculating StatMod or unarmed wpnATK.
- If the attacker is using Clear Strike, substitute all instances of the attacker's STR in this formula with the attacker's TEC.
- If the attacker is using Clear Strike while their head is bound, halve their TEC and round down while calculating StatMod.
TEC-based Damage
- armorDEF is the total DEF bonus from the combatant's equipped armor pieces.
- If any combatant has a head bind, their TEC is halved and rounded down while calculating Defense or StatMod.
Diminishing Returns
When calculating total Buffs%, the game first sorts the buffs/passives of the same category in descending order of strength. The second buff/passive onward takes a compounding multiplier to their percentage bonus, to a minimum bonus of 1%:
- ×0.9 for damage or defense increasing passives.
- ×0.85 for damage increasing buffs. (This includes ATK buffs and enemy DEF debuffs)
- ×0.8 for defense increasing buffs. (This includes DEF buffs and enemy ATK debuffs)
For example, a Landsknecht using a sword skill while having level 10 Sword Mastery and level 10 ATK Up:
- The ATK Up bonus (20%) is unchanged
- The Sword Mastery bonus is reduced to (15% × 0.9 = 13.5%)
After applying diminishing returns, add 100% to the bonuses and multiply. For defense-reducing effects (ATK debuffs or DEF buffs), deduct from 100% before multiplying. Together, the Buffs% is calculated as 120% × 113.5% = 136%
If a Landsknecht (without any passives) is under the effects of a level 10 War Cry, a level 10 Warrior Song, and is attacking an enemy under the effects of a level 10 Savage Cry:
- The War Cry bonus (50%) is unchanged
- The Warrior Song bonus is reduced to (30% × 0.85 = 25.5%)
- The Savage Cry bonus is changed to (28% × 0.85 × 0.85 = 20.23%)
After applying diminishing returns, add 100% to the bonuses and multiply. For defense-reducing effects (ATK debuffs or DEF buffs), deduct from 100% before multiplying. Together, the Buffs% is calculated as 150% × 125.5% × 120.23% = 226%
Altogether, between the above passives and buffs, Buffs% is 136% × 226% = 307%. Without diminishing returns, Buffs% would instead be 120% × 115% × 150% × 130% × 128% = 344%.
The Troubadour's Elemental Prelude skills and Fantasia skills are classed as elemental imbues and elemental resistance modifiers and are exempt from diminishing returns. Charge skills like Highlander's Limitless and temporary defense skills like Protector's Front Guard are also exempt from diminishing returns.
Hit Rate
- Treat HitRate as 100% (and skip all other calculations) if target is petrified, asleep, panicked, blinded, paralyzed, or leg bound, or the attack itself cannot miss.
- StatMod is first defined by a variable:
- A is rounded down.
- If A < 10,
- If A ≥ 10,
- 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 (usually 98%), or 95% if unarmed.
- 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 (usually 98%) and SkillMod is the Hit Rate Modifier of their skill. Treat SkillMod as ±0% if unmentioned.
- Buffs% is the total modifier between hit rate and evasion buffs/debuffs + 100%. Treat an evasion debuff as a hit rate buff, and vice-versa.
- After calculating between StatMod and Buffs%, reduce the value to 150% if it exceeds that amount.
- If the attacker is blinded, include a ×0.33 multiplier (this is BlindMod)
Critical Hits
- Correct CritRate to a minimum of 3% and maximum of 30%.
- Buff% is the Critical Rate bonus from skills like Medic's Diagnosis and Ronin's Crit Up. Apply this modifier after adjusting for the original crit rate cap.
- Only normal attacks can deal critical hits. Critical damage is 150% at base but can be increased with Gunner's High Caliber.
Action Speed
- EquipMod is the total action speed modifier among all the user's equipment.
- ActivationSpeed% is the Activation Speed modifier from the skill being used. Treat as 100% for a normal attack, and if unmentioned on a skill.
- 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
- 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 passives and buffs, multiplied together.
- 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:
- If ailment/bind was inflicted more than three times this battle:
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
Ailment/Bind Recovery
- If StatMod ≤ 5,
- If StatMod > 20,
- Otherwise,
- 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.
- Buffs% is the bonus from Troubadour's Recovery Aria or the penalty from Hexer's Relapse Curse.
Healing
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.
- If StatMod ≤ 0.2, Preemptive Rate = 1.2%
- If StatMod ≥ 5, Preemptive Rate = 30%
- Otherwise Preemptive Rate = (StatMod × 6) %
- If a party member has any investment in Survivalist's Predator, if the standard preemptive check fails, make an additional check, using the Predator skill's success rate. Do this for each instance of Predator in the party, until a check succeeds or all checks fail.
If preemptive is not successful, roll for blindsides.
- If StatModB ≤ 0.2, Blindside Rate = 0.8%
- If StatModB ≥ 5, Blindside Rate = 20%
- Otherwise Blindside Rate = (StatModB × 4) %
- If the blindside check passes and a party member has any investment in Survivalist's Awareness, run a check against the Awareness activation rate. If Awareness activates, the blindside fails.
If both preemptive and blindside checks fail, start combat as per normal.
Enemy Aggro
- Each party member starts with a Target Value of 2. Maximum of 6, minimum of 1.
- +1 if in front row
- +1 if they have the highest current HP among the party
- +1 if asleep
- -1 if they have the lowest current HP among the party.
- Target Value influences whether an enemy even considers attacking them.
- First, the game notes the highest Target Value among your party, then performs a check with a 50% success rate. If successful, every party member with a Target Value lower than the highest is excluded from the enemy's targeting check. If it fails, lower this threshold Target Value by 1 and repeat the check. If the Target Value threshold reaches 1, do not exclude anyone as potential targets.
- At base, enemy attacks have a 50% chance of automatically going after the party member in the front with the highest current HP, 25% chance of picking between the all members in the front row, and 12.5% chance of even considering the party member with lowest current HP in the back.
- A Protector in the front with the highest current HP using a level 10 Provoke to reach the max Target Value of 6 gives them an 87.5% chance of getting targeted by an attack.
- Each party member starts with a Target Chance of 10. Maximum of 255, minimum of 1.
- After conducting the Target Value check and excluding all ineligible party members, Target Chance among all remaining targets is summed up to determine who is attacked.
- Protector's Provoke and Survivalist's Chain Dance increase Target Value and Target Chance. Dark Hunter's Shadow Veil decreases both those variables.
- Starting from the leftmost party member in the first slot, perform this calculation
- Assuming no modifiers to Target Value or Target Chance, a party member in a group of five has a 20% chance of getting attacked.
- If nobody is targeted with the first calculation, 75% chance to target the party member with the highest HP in front, then 25% chance to target the party member with the highest HP in the back.
Escape
- If StatMod ≤ 2,
- If StatMod ≥ 40,
- Otherwise,
- D = Number of allies who are either sleeping or panicked + (number of allies who are either dead or petrified × 2).
- E = Previously attempted escapes.
- P = Allies in party.
- Add the bonus from Flee (if it is being used) × number of times Flee has been attempted this battle.
- Triple EscapeRate if Boost is used on the Escape command.
- Cap EscapeRate at 90%, or 99% if Flee is being used.
- Essentially, escape rate increases if you have an advantage in AGI and LUC combined, and if more members of the party are incapacitated.
Difficulty Modifiers
Apply these multipliers in addition to the above.
Variable | Expert | Standard | Picnic |
---|---|---|---|
Damage Dealt | 100% | 150% | 200% |
Damage Taken | 100% | 60% | 20% |
Ailment/Bind Vulnerability Multiplier | 100% | 60% | 20% |
Healing Power | 100% | 100% | 150% |
References
- Etrian Odyssey Untold: The Millennium Girl Let's Play by Rea, algorithms page
- Etrian Odyssey Untold: The Millennium Girl algorithms pastebin