Damage

This article covers information on the damage (ダメージ^*)^? that can be delivered and received during battle. The formulas vary between games.

Overview

Shin Megami Tensei III: Nocturne

Physical Attack

$(\text{Level} + \text{Strength}) \times \text{Skill Power} \div 15$

Weapon Attack

$\text{Max HP} \times \text{Skill Power} \times 0.0114$

Magic Attack Peak

$((\text{Limit} - \text{Complement}) \div \text{Skill Power})) \times \frac{255}{24}$

Magic Attack

If user's level is below peak:

$0.004 \times (5 \times (\text{Magic} + 36) - \text{Level}) \times ((24 \times \text{Skill Power} \times (\text{Level} \div 255) + \text{Complement}))$

If user's level is at peak:

$0.004 \times (5 \times (\text{Magic} + 36) - \text{Peak}) \times \text{Limit}$

If user's level is above peak, but below 160:

$0.004 \times (5 \times (\text{Magic} + 36) - \text{Level}) \times \text{Limit}$

If user's level is above 160:

$0.004 \times (5 \times (\text{Magic} + 36) - 160) \times \text{Limit}$

Shin Megami Tensei V

The maximum damage possible in Shin Megami Tensei V, at 99,999.

The variance of the damage is likely 5% (can be 5% lower and 5% higher; difference overall is 10%.)

One trait about stat increases is that, as the distance between the offensive Strength/Magic stat and Vitality grows higher, the multiplier will grow at a progressively smaller rate.

Although the user's stats influence their damage in a curved line as they increase, the base power of the attacks themselves are still straightforward and aren't complicated by the formula of the stats. For example, an attack with a base power of 40 will deal twice the damage against an attack with 20, should the rest of the circumstances match.

The two ranks of a single type buff do not stack with one another, but rather the second rank transforms it into a slightly stronger buff instead. Different types of buffs do stack multiplicatevely. (e.g. Tarukaja & Rakunda; 1*1.4*1.4)

Pleromas, such as Phys Pleroma, boost the user's attack by x1.2. High Pleromas, such as High Phys Pleroma, instead boost it to x1.35. Both multipliers stack accumulatively against each-other, generating a result of x1.55.

The maximum damage that can be dealt in the game is 99,999.

Damage from Poison is pre-determined, causing it to deal 100 damage by default. Poison Adept doubles it, Poison Master triples it, while stacking both multiplies it by 5. The attack doesn't follow any other formulas, but it still has variance; however, this variance presumably only goes higher than the base value.

Megami Ibunroku Persona

Party Regular Attack

$\frac{\text{(Weapon Attack)}^2}{4} \div (\text{Target's Defense} \times 1.5) \times \text{Target's Resistance} + \text{Random Number}$

Party Physical Skills

$(\text{Attack})^2 \div (\text{Target's Defense} \times 1.5) \times (1 + \frac{\text{Skill Power}}{100}) \times \text{Target's Resistance} + \text{Random Number}$

Gun Damage

$\frac{\text{(Gun Attack)}^2}{4} \div (\text{Target's Defense} \times 1.5) \times \text{Target's Resistance} + \text{Random Number}$

Enemy Regular Attack

$\frac{\text{(Attack)}^2 \times 2.25}{4} \div (1 + \text{Target's Defense}) \times \text{Target's Resistance} + \text{Random Number}$

Enemy Physical Skills

$\frac{\text{(Attack)}^2 \times 2.25}{4} \div \text{Target's Defense} \times (1 + \frac{\text{Skill Power}}{100}) \times \text{Target's Resistance} + \text{Random Number}$

Magic Damage

$\frac{\text{(Magic Attack)}^2 \times (\text{Skill Power} + 1)}{120} \div \text{Target's Magic Defense} \times \text{Target's Resistance} + \text{Random Number}$

Persona 5 / Royal

Attack Power

Melee and Gun Attacks

If the user is inflicting a basic melee or gun attack, the related weapon and the user's Strength stat will be taken into account.

The formula multiplies the square root of half the user's weapon power and the square root of the user's Strength stat by each-other. Whether the weapon is melee or ranged ultimately depends on the type of attack that is being used. The formula is as follows:

$\sqrt{\frac{1}{2} \times \text{Weapon Power}} \times \sqrt{\text{Strength Stat}}$

When the user's Strength stat is doubled, the modifier will be multiplied by approximately 1.4.

If the user's Strength stat is at the maximum of 99, the damage total of the attack will be nearly multiplied by x10 compared to a Strength stat of 1.

Skills

If the user is wielding a physical skill, the base power of the skill and the user's Strength/Magic stat are taken into consideration.

Similarly to Melee and Gun attacks, the square root of the base power of the skill is multiplied by the square root of the Strength stat. This means that you can expect Heat Wave to deal a bit less damage than Paradise Lost R while using the same persona, as will -dyne skills if your persona has equal St and Ma.

The formula is as follows:

$\sqrt{\text{Skill Power}} \times \sqrt{\text{Stat}}$

Where the Phys/Gun skills use St as their stat, and Fire/Ice/Elec/Wind/Psi/Nuke/Bless/Curse/Almighty use Ma as their stat. Both Strength and Magic-based skills use the same formula.

Defense Subtraction

After the total power of the attack has been calculated, it is divided against the square root of the sum of the target's armor defense and their Endurance stat. The formula is as follows:

$\text{Base Power} \div \sqrt{\left ( \left ( \text{Endurance} \times \text{8} \right ) + \text{Armor Defense} \right )}$

If the defense and endurance stats are doubled, the damage taken will be multiplied by approximately x0.7.

Miscellaneous Modifiers

There are several other criteria that factor in affecting the damage output of attacks besides the user's stats, weapon and attack power. These include Critical hits, Technical attacks, the effects of certain ailments, the target's elemental resistance or weakness against the attack, Baton Pass, temporary buff and debuff skills, certain passive skills and traits, whether the target is guarding or not, the difficulty setting, and so on.

If an attack exploits a weakness, the attack will be unable to deal Technical damage, so the two multipliers can't stack.

One unique factor in damage calculation is that certain types of Passive buff skills, such as Fire Boost, Fire Amp and Magic Ability, and the trait Pagan Allure, although they can stack with each-other to boost damage (via multiplication), the multiplier is capped to x2. However, the limitation only applies to said passive abilities, with the exception of Tyrant's Mind and the Country Maker trait, which ignore the limit. Additionally, accessories stack in the same way and follow the same restrictions, but accessories and skills with matching effects (Ice Boost and Blue Band) cannot stack. The traits Mighty Gaze, Intense Focus, Striking Weight and Undying Fury's multipliers are not applied to the cap.^{[citation needed]}

One important factor would be the Level difference between the attacker and the opponent. There is no change if the attacker is 4 levels lower or 1 level higher than its target, but the attack power will gradually be multiplied over time, with 10 levels and higher being capped at x1.5. Otherwise, if the attacker is 15 levels lower or more, their power will be x0.5.

The same applies for the damage taken as well. There is no change if the target is 2 levels lower and 3 levels higher, but the defense will increase if the target's level is higher, where at 10 levels or more, the damage will be x0.5, but at 10 levels less, the damage will be multiplied to x1.5.

For the protagonist, the level calculated is his own, rather than the one of his equipped Persona.

The final calculation is randomized between numbers that are close to the default result. The variance is approximately 5% (can be 5% smaller or larger at most.)

Trophies & Awards

Trophy	Icon	Description	For	Reward
Devastating Blow		Deal 999 damage in a single blow.	SMT3NHD trophy
Omnipotent Strike		Dealt over 9999 damage in a single blow.	SMT5V trophy
Destroyer		Dealt over 1,000 damage to an enemy in a single hit.	SH2 trophy
Going Nova		Deal over 999 damage in 1 attack.	P3P trophy
Get a Load of Those Numbers!		Dealt over 999 damage in a single attack (All-Out Attacks excluded).	P3R trophy
Going Nova		Deal over 999 damage in 1 attack	P4G trophy
The Ultimate Strike		Deal over 999 damage in a single attack.	P5 trophy
Ultimate Attack		Deal over 9999 damage in battle without using an All-out Attack.	Thieves Den	50P
Ultimate Strike		Dealt 2,000 damage in a single attack.	P5T trophy

References

Mechanics
General
Dungeon - Combat - Turn - Action - Level - Experience - Party - Stats - Skills - Items - Equipment - Melee Attack - Ranged Attack - Damage (Fixed) - Guard - Escape - Accuracy - Critical - Multi-hit - Insta-Kill - Ailments - Drops - Encounter - Random Encounters - Symbol Encounters - Ambush - Difficulty
Franchise-wide
Demon - Magic (Fusion Spell) - Affinities - Unique skills - Extra Skills - Macca - Yen - Magnetite - Incense - Alignment - Moon Phase System - Demon Summoning Program (COMP) - Cathedral of Shadows (Fusion - Skill Inheritance - Accidents / Special / Three-demon / Sacrificial / Sword) - Demonic Compendium - Evolution - Negotiation (Special conversation) - Rag's Jewelry - Code Breaker - Press Turn - New Game Plus - Ultimate boss - Streetpass - Password - Skill Mutation - Energy Drain - Party Talks
Shin Megami Tensei series
Terminal - Guardian (if...) - Tactical Battle (NINE) - Capacity (NINE) - RTS (NINE) - Reinforcements (NINE) - Race Shift (NINE) - Modules (NINE) - Magatama (3) - Reason (3) - Demon Co-Op (SJ) - EX Missions (SJ) - Challenge Quest (4) - Skill Potential (4/A-5) - Smirk (4) - Barrier (4) - Partners (4A) - Jade Dagger (4A) - Magatsuhi Skills (5) - Essence (5) - Glory (5) - Miracles (5) - Demon Statues (5) - Abscess (5)
Devil Summoner series
Loyalty - Personality - Mystic Change - Nemechi (SH) - Case Files (RKKA)
Majin Tensei series
Rank - Affinity (2) - Arcana (Ronde)
Persona series
Shadows / Personas (Initial / Prime / Ultimate / Ancestor / Reverse / Sub) - Skill Card - Totem (1) - Type/Subtype (1+2) - Affinity (1+2) - Rank (1+2) - Mystic Change (1+2+5) - One More (3-5) - Growth Rate (1+2) - Unknown Power (1+EP) - Personality (1+2, 5) - Material Card (2) - Mutation (2) - Follow Up - All-out Attack (Cut-in) - Heart Item (3) - Shuffle Time (3+4) - Daily Life (3-5) - Activities (3-5) - Calendar (3-5) - Social Stats (3-5) - Social Link (3+4) - Tactics (3-5) - Requests (3-5; Q+Q2) - Clock (3P+3RE) - Linked Episode (3RE) - Great Clock (3RE) - Theurgy (3RE) - Arcana Chance (4) - Forecasts (Fusion / Weather) (4+5) - Boost (Q+Q2) - Power Spot (Q+Q2) - F.O.E (Q+Q2) - Confidant (5) - Technical (5+5S) - Treasure Demon (5+5S) - Party Switch (5+5S) - Baton Pass (5+5S; Q2) - Disaster Shadow (5R) - Fusion alarm (5R) - Persona Traits (5R) - Third Eye (5+5S) - Master Arts (5S) - BOND (5S) - Persona Points (5S)
Devil Children series
Trainer - Bank - BattleNet - Relic Fusion - Power Fusion - Powers
Digital Devil Saga series
Berserk Mode (2)
Devil Survivor series
Devil Auction - Extra Turn Battle - Skill Crack - Titles (DSO / DS2 / RB) - Fate System (2) - Add-On (2)
Other
Equip Type (GMT:TM) - Skill Systems (GMT:TM) - Sword Exchange (GMT:TM) - Class (TMS♯FE) - Class Change (TMS♯FE) - Topic System (TMS♯FE) - Side Quests (TMS♯FE) - Ad-lib Performance (TMS♯FE) - Session (TMS♯FE) - Dual Arts (TMS♯FE)