Calculations in Shin Megami Tensei V: Vengeance

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To-do:
* Status effect tables could be improved.
* Stat scaling section

This page details the methods and formulas involved in various mechanics in Shin Megami Tensei V: Vengeance.

Terminology

  • Attacker: The character executing the attack.
  • Defender: The character targeted by the attack.
  • Player character: Any character under the player's control, such as the Nahobino and his allied demons.
  • Enemy character: Any character in the enemy party.
  • Boss: Any enemy in the Boss section of the Analyze menu[a].

Mathematical

The formulas displayed here use some notations which may be considered uncommon to reduce redundancy. These are defined here:

  • Intervals: An interval is a range of numbers between a lower bound A and an upper bound B. When the bound uses parenthesis, it means it excludes that bound, while square brackets include it. For example: "(0, 3]" is an interval of numbers between 0 and 3, excluding 0 and including 3, so the integers in that interval are 1, 2 and 3.
    • x ∈ [A, B]: Signifies that x is in the interval on the right-hand side. For instance, "x ∈ (0, 3]" means 0 < x ≤ 3.
  • ⌊x⌋: The floor function. It rounds x down to the nearest integer. For example: ⌊1.2⌋ = 1, and ⌊-1.2⌋ = -2.
  • Max(x, y): The Max function returns the largest value in a set of values.
    • For example: If x > 1, then Max(x, 1) = x. If x < 1, then Max(x, 1) = 1.
  • Min(x, y): The Min function returns the smallest value in a set of values.
    • For example: If x > 1, then Min(x, 1) = 1. If x < 1, then Min(x, 1) = x.
  • Clamp: To restrict a value to a given interval. For instance, clamping x to between 0 and 1 means that, if x > 1, then x is set to 1, or else if x < 0, then x is set to 0. If x is already between 0 and 1, then nothing happens.

Damage

The following method only applies damage from attacks. Ailment damage is detailed below.

Initial value

Damage calculation (including damage dealt to the defender's MP) begins by calculating a value based off of the attacker's stats, which is their Attack value before any other parameters and modifiers are applied. The first factor in their Attack is their level:

LvAttacker≤150:FactorLv=LvAttacker+10LvAttacker>150:FactorLv=LvAttacker10+145

This factor is added to the relevant Stat of the attacker, corresponding to the attack's damage type: Physical skills use Strength, Magical skills use Magic, and Level-based skills use FactorLv itself.

Stat≤FactorLv:Attack=FactorLv+StatStat>Root:Attack=Stat−FactorLv+Stat+3⋅FactorLv2

The defender's Vitality is subtracted from Attack. This value will be referred to as Attack′, and it determines how Vitality is applied to reduce damage, giving the base amount of damage the attacker inflicts on the defender:

Attack′=Attack−ViDefenderAttack′≤Attack2:DamageBase=Max(1,2⋅Attack−ViDefender−ViDefender−Attack23)Attack′∈(Attack2,3⋅Attack4]:DamageBase=Max(1,Attack−ViDefender)Attack′>3⋅Attack4:DamageBase=Max(1,2.5⋅Attack−ViDefender+Attack4−ViDefender3)

Base Power

The attack's base power acts as a percentage multiplier to DamageBase. For instance, an attack with 165 base power multiplies DamageBase by 165%.

The following special cases exist for base power:

  • Basic attacks have a base power of 100.
    • Lahmu uses a Physical skill named "Attack" that targets all enemies with a base power of 120 instead of a basic attack. Additionally, it has a damage multiplier of 1 that decreases by 0.1 for each of his tentacles that died.
    • Lucifer uses a Physical skill named "Attack" that has a base power of 150 instead of a basic attack.
  • Level-based skills multiply their base power by 1+LvAttacker50
  • Beatdown and Power Punch increase their damage based on the user's remaining HP multiply their base power by 1+Current HPAttackerMax HPAttacker. Current HP is treated as Max HP if it would be larger.
  • Heavenly Ikuyumi and Megido Ark add to their base power directly.

Modifiers

Any further effects apply as a multiplier to DamageBase.

For brevity, the modifiers for Passives, Innate skills and Skill Potentials have been omitted from this page and can be instead found in their respective pages.

Resistances and Critical Damage

Resistance multipliers for damage are uniform, with the exception of Mitamas, Tehom and the Demi-fiend's demons. Neutral resistances simply use 1. Note that this table does not generally apply to Ailment resistances.

Resistance Normal Mitama Tehom
Demi-fiend
RpRepel, DrDrain 1 1 1
WkWeak 1.25 9 3
RsResist 0.5 0.5 0.5

Critical Hits add 0.5 to the above values. The calculation for Critical rates can be found below.

If the defender's natural resistance to the attack is Drain, and they also have the corresponding Resist Passive for that attack, but no other Passives that affect their resistance (such as a Null Passive), the drained damage will be halved by the Resist Passive.

The only Innate skills that affect repelled damage are Elephantine Ricochet and Four Oni.

Guard

Guarding applies a 0.8 multiplier. It also prevents the attack from being a Critical Hit or a weakness and lowers its chance of inflicting Ailments.

Stat Buffs

Attack status effects share the multipliers with their equivalent Defense status effects. Omagatoki: Doubler affects these values, but when the attack is a counter, repelled damage or an attack from a Confused ally, Doubler erroneously inverts the effects of the Defense status effect. The values are as follows:

Attacker Effect Multipliers
Status Effect Normal Doubler
Attack Up EX 1.4 2.32
Attack Up 1.2 1.66
Attack Down 0.8 0.34
Attack Down Ex 0.7 0.01
Defender Effect Multipliers
Status effect Normal Omagatoki: Doubler
Normal Inverted
Defense Up EX 0.7 0.01 2.32
Defense Up 0.8 0.34 1.66
Defense Down 1.2 1.66 0.34
Defense Down EX 1.4 2.32 0.01

Damage multipliers from other status effects can be found in their respective pages.

Level Scaling

Level scaling is applied only for enemies that can be recruited through Negotiation and if the difference between the attacker and defender's levels is greater than 2. It first uses a Sum value derived from the sum of their levels:

LvAttacker+LvDefender≤30:Sum=0LvAttacker+LvDefender∈(30,130]:Sum=LvAttacker+LvDefender−301000LvAttacker+LvDefender>130:Sum=0.1

An intermediary value, Sum′, is calculated from this:

Sum′=|LvDefenderLvAttacker−1|⋅Sum⋅(|LvDefender−LvAttacker|−2)

This value is used for the final level scaling multiplier:

LvDefender>LvAttacker+2:MultLv=1−Sum′LvAttacker>LvDefender+2:MultLv=1+Sum′⋅1.2

MultLv is clamped to between 0.5 and 1.5.

Difficulty

Difficulty modifiers are as follows:

Difficulty Defender
Enemy Player
Safety 10 0.1
Casual 1.2 0.8
Normal 1 1
Hard 0.7 1.3

Repelled damage uses the difficulty multipliers of the one receiving the damage.

Final Damage

After all modifiers have been applied, the result is rounded down to give a Damage value and set to 1 if it would be lower, including if it had overflowed into a negative value. If the damage is being dealt by the player to the defender's MP, then it is also subject to an upper limit of 50 before rounding, unless it is specifically Soul Drain.

Then, Damage is subjected to random variance. If it overflows at this point, then no damage is applied.

Finally, the damage cap of 99999 is applied, with the following exceptions:

  • There is no cap if the attack is being drained[b].
  • If damage is being dealt to the defender's MP, it is also capped to their current MP.
  • If the attack is an HP drain, it is also capped to their maximum HP, even if their current HP is greater than their maximum.

Ailment Damage

Poison

Damage inflicted by Poison uses a separate method from normal damage. It starts with a Root value defined as such:

LvAttacker≤150:Root=LvAttacker+5LvAttacker>150:Root=⌊LvAttacker10+140⌋

The same difficulty modifiers as normal damage are applied, then random variance is applied. Finally, the multipliers for Poison Adept and Poison Master are applied, giving the final damage value.

Shroud

MP damage inflicted by Shroud is similar to that of Poison. The Root value is defined as:

Root=⌊LvAttacker+59⌋

The same difficulty modifiers and random variance as normal damage are applied, giving the final damage value.

Healing

This section only applies to healing by Healing skills. Healing by draining damage is instead calculated in the Damage section.

Most Healing skills have two components: a percentage and base power. The percentage represents the fraction of the target's HP or MP that will be healed, and the base power adds to that amount. Mathematically, the amount the skill heals is represented by:

Healing=Max HPTarget⋅Percentage+Power

For skills with more than 0 Power, effects that modify healing will apply by multiplying the Healing amount directly. Those multipliers can be found in their respective pages. The following exceptions apply:

  • The only modifier that applies to MP healing is Oath of Plenteousness.
  • Items are not affected by any multipliers or healing variation.

Healing is subject to random variance.

Critical Hit Rates

Firstly, the following conditions are verified in sequence; if any of them are true, there are no further steps and the attack will be guaranteed to be Critical or not:

  1. The defender's resistance is Null, Repel or Drain: The attack cannot be Critical.
  2. The defender is guarding: The attack cannot be Critical.
  3. The attacker is under the effect of Omagatoki: Critical: The attack will be Critical.
  4. Fickle Personality applies to the attack: The attack will be Critical.
  5. The defender's resistance is Resist: The attack cannot be Critical.
  6. Critical Aura applies to the attack: The attack will be Critical.

Only attacks that are of the Physical attribute or of the Physical damage type are inherently allowed to be Critical[c]. Level-based and Magical damage skills cannot be Critical unless they are also Physical, forced to by one of the above conditions, or allowed to by an Innate skill. The attack's Critical rate does not change if multiple effects allow it to be Critical.

Should none of the above conditions be true, and if the attack is allowed to be Critical, then calculation proceeds by calculating the base Critical rate from the characters' Luck and Levels:

FactorLu=Min(4,LuAttacker+10LuDefender+10)Rate=3⋅(LvAttacker+10LvDefender+10+FactorLu2)

If the attacker has Bloody Glee, Rate is multiplied by 1.8. If the attacker has Murderous Glee, it is multiplied by 2.5. Both skills stack additively, resulting in a final multiplier of 3.3.

The attack's Critical chance represents an integer value to be added to Rate. For instance, skills that are described as "always Critical" have a Critical chance of 200. Most attacks, including basic attacks, have a Critical chance of 0, representing no Critical rate bonus.

Following that, the level scaling multiplier is calculated via one of the following equations:

LvAttacker≤LvDefender:Scaling=1−(LvDefender−LvAttacker60+LvDefender−LvAttacker120)LvAttacker≥LvDefender+11:Scaling=1.25−(LvAttacker−LvDefender−1060+LvAttacker−LvDefender−10120)LvAttacker∈(LvDefender,LvDefender+11):Scaling=1+0.025(LvAttacker−LvDefender)

Scaling is clamped to between 0.5 and 1.5. Base is then multiplied by Scaling.

If the attacker is the player, difficulty modifiers are applied at this point:

Difficulty Multiplier
Safety 1.5
Casual 1.2
Normal 1.0
Hard

Finally, the effects of any applicable Innate skills apply, the values of which can be found in their respective pages. The final value is rounded down to the nearest integer and represents the percentage chance of the attack being Critical (for instance, a value of 1 means the attack has a 1% chance of being Critical).

Accuracy and Evasion

The accuracy of an attack is determined as follows:

First, if any of the following conditions, checked in the following order, are true, then the attack will automatically hit or miss and all further steps are skipped:

  1. The defender is affected by Absolute Evasion: the attack misses.
  2. The defender would not receive damage from the attack due to a resistance: the attack hits.
  3. The attacker has Critical Charge and is using an applicable attack (except a counter): the attack hits.
  4. The defender is afflicted by Sleep, Confuse or Charm: the attack hits.
  5. The attacker is affected by Warrior Trainer and is using an applicable attack (except a counter): the attack hits.
  6. The attack's accuracy is 255%: the attack hits.
  7. The defender is affected by Tablet of Destinies and is being targeted by an applicable attack: the attack hits.

If none of the above apply, then the calculation starts with a Root value derived from the Agility and Luck stats from both the attacker and defender.

Root=3⋅AgAttacker+LuAttacker+203⋅AgDefender+LuDefender+20

Then, Root is used to compute a Base value depending on whether Root is greater than or lesser than 1:

Root<1:Base=1−1−Root30+1−Root12Root≥1:Base=1+Root−115+2⋅(Root−1)3

The skill's accuracy is multiplied with Base. For the Nahobino's basic attack, this is 100, while other basic attacks use 98. All further accuracy-altering effects are applied as multipliers to that value. Values for Passives and Innate skills can be found in their respective pages.

Level scaling is applied only when the player is attacking using the following formula:

MultLv=LvAttacker+10LvDefender+10−15+1+LvAttacker−LvDefender200

MultLv is clamped to between 1 and 1.2. When an enemy is attacking, MultLv is always 1.

Accuracy/Evasion status effects apply different multipliers for the attacker and defender. The sole exception is boss Matador's Red Capote, which applies an increased multiplier. Omagatoki: Doubler only affects the attacker.

Status effect Attacker Defender Omagatoki: Doubler
Accuracy/Evasion Up EX 1.2 0.85 1.66
1.7Boss Red Capote 0.35Boss Red Capote
Accuracy/Evasion Up 1.1 0.9 1.33
1.6Boss Red Capote 0.4Boss Red Capote
Accuracy/Evasion Down 0.9 1.1 0.67
Accuracy/Evasion Down EX 0.85 1.2 0.505

Difficulty multipliers are as follows:

Difficulty Attacker
Player Enemy
Safety 1.5 0.8
Casual 1.1 0.9
Normal 1 1
Hard 0.95 1.1

At this point, the modified Base value is scaled into the final accuracy rate as follows:

BaseModified<99:Rate=BaseModifiedBaseModified∈[99,114):Rate=BaseModified−9930+99BaseModified∈[114,149):Rate=BaseModified−11470+99.5BaseModified≥149:Rate=100

Mirage applies by halving Rate. Omagatoki: Hit applies by multiplying Rate by 2.5, and is the only way to increase it beyond 100.

The evasion check consists of generating a random integer between 0 and 32767 (inclusive), then multiplying it by 100/32767, resulting in a number between 0 and 100. If Rate is greater than that number, the attack will hit. If both the generated number and Rate are 100, the attack will miss, meaning all attacks unaffected by Omagatoki: Hit have a minimum inaccuracy of 1 in 32768.

Random variance

Random variance is a mechanic that applies to damage and healing which adds a random amount to the final value.

Random variance is done with two variables, A and B, which are generated randomly in the following ranges:

A∈[0,Max(0,⌊Value10−1⌋)]B∈[0,3]

Both A and B are added to the final value.

Experience

Acquisition

Experience gained by a character varies depending on the level difference between that character and the enemy[1]. More specifically:

ΔLv=LvEnemy−LvCharacterScaling=1.15ΔLv

Where ΔLv is clamped to between -10 and 10. For example, this means that a character that is 10 or more levels above the enemy will only receive approximately 1.15-10 ≈ 0.24 times the default Experience from that enemy. Conversely, a character that is 10 or more levels below the enemy will receive 1.1510 ≈ 4.04 times as much Experience.

Additionally, demons in the stock only gain a quarter of the Experience they would normally receive, or half if the Demonic Discipline Miracle applies.

Inspiring Leader, when equipped by an user whose level is lower than the Nahobino's level, will double acquired Experience. Omagatoki: Luck will also double Experience gains for the party if it is active as the battle ends.

Next Level Scaling

The Nahobino and Guest characters level up at the "standard pace", receiving no modifications to the amount of Experience required to level up. Demons, however, receive a multiplier depending on how many levels they are above their base level, which is given in the table below[1]:

Current − Base level Multiplier
0 1.5
1 2
2 2.57
3 3.23
4 3.96
5 4.77
6 5.66
7 6.63
8 7.67
9 8.8
10 or greater 10

Unforgotten Memories

The Unforgotten Memories Miracle ("Newly-fused demons will gain EXP based on the stats of the demons fused.") has a scaling effect that reduces how much EXP is given by demons that are more than 5 levels above their base level.

Normally, the expected amount of EXP given by Unforgotten Memories is the exact amount of EXP required to reach the demon's current level (ignoring any EXP acquired for the next level), which remains true until the demon is at their base level plus 5. Starting at their base level plus 6, the resulting demon will only receive approximately 74% of the expected EXP, which decreases exponentially. Starting at their base level plus 13, this scaling plateaus to approximately 4.93% EXP.

Initiative

Some encounters are programmed to have one party go first. When that isn't the case, there is a method to decide which side gains the first turn.

The first turn is automatically granted in these circumstances:

  • In a consecutive encounter outside of Virtual Trainer: The player goes first.
  • If the Nahobino attacked the Demon Symbol to start the battle: The player goes first.
  • If the Demon Symbol attacked the Nahobino's back, and the Panoptes Miracle does not apply: The enemy goes first.

Outside of those circumstances, the first turn is given randomly, with chances varying based on the Nahobino's stats and the stats of whichever enemy is considered to be the first one in the encounter.

The player has a 60% chance of going first, which changes depending on the product of three modifiers based on difficulty, level and stats. The level modifier is given as follows:

LvNahobino>LvEnemy:ModLv=Max(2,LvNahobino+10LvEnemy+10+LvNahobino−LvEnemy40)LvNahobino=LvEnemy:ModLv=1LvNahobino<LvEnemy:ModLv=Max(2,LvNahobino+10LvEnemy+10+LvNahobino−LvEnemy20)

The stat modifier is based on an "Initiative" value that is calculated for both sides:

InitiativeNahobino=AgNahobino+LvNahobino2+LuNahobino5+10InitiativeEnemy=AgEnemy+LvEnemy2+LuEnemy5+10ModStat=InitiativeNahobinoInitiativeEnemy

The current difficulty modifies both the chance of the player going first and the minimum chance of going first, the latter of which is 25 times the former.

Difficulty ModDifficulty Minimum
Safety 2 50%
Casual 1.2 30%
Normal 1 25%
Hard 0.7 17.5%

The percentage chance of the Nahobino going first is given by the following formula:

Chance=Max(60%⋅ModLv⋅ModStat⋅ModDifficulty,Minimum)

Virtual Trainer and Godborn Scaling

Virtual Trainer and Godborn use the same method to scale parameters when increasing an enemy's level beyond its base value. The generic formula for determining the scaled value of a parameter is as follows:

ParamScaled=Param⋅Factor(Current Lv)Factor(Base Lv)

Factor varies for HP, Stats, EXP and Macca, and whether the enemy is a Boss or not. See the "SMT5V NKM Base Table" linked in the References section for specific values.

Notes

  1. ↑ More accurately, any enemy which cannot be recruited is considered to be a Boss.
  2. ↑ It is possible for the defender's current HP to become negative if the sum of the defender's current HP and the drained attack's damage overflows. However, the defender's current HP is immediately set to 0 in this case. This will not kill the defender, as death is only caused by receiving damage.
  3. ↑ This statement is technically false, as Strength-based skills that scale off of the user's current HP cannot inherently be Critical, but as the only two examples of this (Beatdown and Power Punch) are allowed to be Critical due to being Physical-attribute skills, it is true in practice.

References

General
Specific
  1. ↑ 1.0 1.1 hyperT'sブログ. Retrieved July 31, 2026. Japanese.