Calculating Bonuses (2024)

When modding anything in WARFRAME, the order in which bonuses are applied follows a pattern. With the exception of mods that provide elemental damage bonuses, the order in which mods are installed does not matter; the resultant stats will always be the same regardless of the mod configuration.^[1] The same goes for temporary or conditional buffs and debuffs from abilities, mods, Arcane Enhancements, and enemies.

Last updated: Sat, 30 Mar 2024 02:51:58 +0000 (UTC) by User:Cephalon Scientia

Semantics[]

Percent Bonuses vs. Multipliers[]

In most cases in WARFRAME, percent bonuses to stats (not to be confused with flat percentage points) can also be represented as stat multipliers using the following conversion:

Converting percent bonuses to multipliers.

For simplicity, calculations in this article (and throughout the wiki) will represent percent bonuses as decimals and will use 1 + Net Percent Bonus as a decimal expression instead.

Complementary Percentages[]

Many stat modifiers in WARFRAME are expressed in terms of percentages, but there may be more than one way to describe the same stat modifier.

For example, Damage Vulnerability can be expressed in terms of Damage Reduction. If an enemy is 25% more vulnerable to taking Impact damage (e.g. +25% Impact damage bonus), one can also say that the enemy:

• Is 25% less resistance to taking Impact damage (e.g. -25% Impact damage reduction)
• Is 125% vulnerable (100% + 25%) to Impact damage (notice "more" is omitted)
• Has -25% resistance to incoming Impact damage (negative resistance is equivalent to vulnerability)
• Has a 0.75x multiplier (100% - 25%) to incoming Impact damage

Overview[]

Types of Bonuses

Operation On Base Stat	Bonus Stacking Behavior	Internal Name	Typical Context	Example(s)
Addition	Additive Stacking	ADD	Flat value or percentage point bonuses: ±X Energy Rate ±X Health ±X Punch Through Etc.	EntropyBurst's status chance bonus Final Status Chance = Base Status Chance + 20 Laetum's Elemental Excess perk (-10 critical chance percentage points) Final Critical Chance = Base Critical Chance + -10
Multiplication	Additive Stacking	STACKING_MULTIPLY	Most common bonus, applies to almost all percentage-based bonuses: ±X% Ability Strength ±X% Armor ±X% Energy Max ±X% Fire Rate ±X% Health Etc.	Serration's and HeavyCaliber's damage bonus Final Damage = Base Damage * (1 + 1.65 + 1.65)
Multiplication	Multiplicative Stacking	MULTIPLY	Damage Reduction bonuses Affinity bonus Resource Drop Chance bonus	Antitoxin's and ToxinResistance's damage resistance to Toxin Damage Taken = Initial Toxin Damage * (0.55 * 0.85) Affinity bonuses Total Affinity = Initial Affinity * 2 * 1.3 * 1.25
Override	N/A	SET	Very rare bonus type used to set a stat at a particular value, ignoring all other bonuses	NoCurrentLeap disables energy rate by setting it to 0 VolatileQuickReturn sets Punch Through to 0m

• Note that there are known instances where a particular stat can have flat value and percentage-based bonuses. For example, StingingTruth provides a flat increase to Magazine Capacity for the Viper while SlipMagazine provides a +30% Magazine Capacity bonus at max rank. In these scenarios, typically percentage-based bonuses are applied to the base stat first then flat value increases. For example:

Final Magazine Capacity = 14 * (1 + 0.3) + 40

Additive Stacking[]

Percent Bonuses[]

Generic formula for additive stacking percent bonuses.

All sources that add a percent bonus of the same type will typically have their bonuses added together. This commonly referred to as additive stacking (internally represented as STACKING_MULTIPLY operation type). For example, if a primary weapon has Serration (+165% damage) and HeavyCaliber (+165% damage) installed, it will receive a total of +330% bonus base damage or 4.3x the base damage.

This is true of all percent bonuses, not just damage. For example, combining SpeedTrigger (+60% fire rate) and Shred (+30% fire rate, +1.2 punch-through) will give a total of +90% bonus fire rate.

Flat Value and Percentage Point Bonuses[]

Generic formula for additive stacking flat value and percentage point bonuses.

Sources that grant flat value or percentage point increases are typically applied after all other bonuses are applied (internally represented as ADD operation type). For example, say a melee weapon with 20% critical chance and TrueSteel equipped has 0.2 × (1 + 1.2) =44% critical chance. Since a max ranked ArcaneAvenger grants a flat 45% critical chance when triggered, the melee weapon will have 0.44 + 0.45 =89% critical chance as a result.

Note that flat bonuses are additive with each other. Using the previous example, if the player's Adarza Kavat's Cat'sEye buff triggers (adding a flat 60% critical chance), then the resultant critical chance will be 0.44 + 0.45 + 0.6 =149%.

Exceptions

• PiercingNavigator - applied before other bonuses are applied, effectively increasing the base stat
• BallisticBattery - applied after base damage bonuses but before other bonuses/multipliers
• Volt's passive - applied after base damage and elemental bonuses but before critical damage multiplier and Sniper Rifle combo counter
• EnergyChannel - applied after the critical damage multiplier

Multiplicative Stacking[]

Generic formula for multiplicative stacking bonuses.

Sources that affect the same fundamental stat but have different conditions for granting its bonuses will typically have their bonuses multiplied together (but not always such as Chroma's VexArmor additively stacking with base damage mods). This is commonly referred to as multiplicative stacking. For example, a primary weapon with Serration (+165% damage) and BaneofGrineer (+30% damage to Grineer) would result in a [(1 + 1.65) × (1 + 0.3) - 1] =244.5% bonus in base damage against Grineer enemies. Note that multiplicative stacking effects grant greater bonuses than additive stacking. For example, if Serration and BaneofGrineer were to additively stack, it would only grant 1.65 + 0.3 =195% bonus base damage.

Examples of sources of damage bonuses/multipliers that will multiplicatively stack with each other:

• Serration (2.65x base damage in all situations)
• CryoRounds (1.9x Cold elemental damage on top of base damage)
• Viral procs (up to 4.25x damage on health)
• BaneofInfested (1.3x damage against Infested)
• LastingPurity (1.6x damage on aiming)
• PrimedChamber (2x damage on first shot)
• Eclipse (3x damage in brightest environmental lighting)
• Headshots (2x damage on headshot)
• Damage Reduction from Armor

Exponential Stacking[]

In rare instances, some bonuses are applied to itself multiplicatively and is multiplicative with all other bonuses. This is often referred to as exponential stacking. For example, ArcaTitron has a unique mechanic where each successive kill adds a charge that multiplies the next slam radial damage bonus by 2 using the following equation:

Total Radial Damage = Base Radial Damage × 2ⁿ (where n is the number of charges)

Opportunity Cost In Modding[]

Additive Stacking[]

Players may refer to additive stacking having "diminishing returns" (despite being linear increases; a more accurate term would be "opportunity cost"), meaning that at higher percent bonuses, the additional value gained per additional percent bonuses is less, relatively speaking. For instance, if one were to equip a secondary that dealt 100 base damage:

1. Adding a maxed rank HornetStrike (+220%), it would deal 320 base damage, a 2.2 / 1 =220% relative increase in base damage.
2. Adding a maxed rank MagnumForce (+165%), it will deal 485 base damage, a 1.65 / (1 + 2.2) =51.5625% relative increase in base damage over just equipping HornetStrike.
3. Adding a maxed rank AugurPact (+90%), it will deal 575 base damage, a 0.9 / (1 + 2.2 + 1.65) =18.5567% relative increase in base damage over just equipping HornetStrike and MagnumForce.
4. Adding an unmodded Rank 3 VexArmor at max buff (+275%), it will deal 850 base damage, a 2.75 / (1 + 2.2 + 1.65 + 0.9) =47.8261% relative increase in base damage over just equipping HornetStrike, MagnumForce, and AugurPact.
   • Notice that despite the larger base damage bonus of +275%, VexArmor only provided a smaller relative increase in base damage.
5. Adding a maxed rank AnemicAgility (-15%), it will deal 835 base damage, a -0.15 / (1 + 2.2 + 1.65 + 0.9 + 2.75) =−1.7647% relative increase (or 1.7647% relative decrease) in base damage over just equipping HornetStrike, MagnumForce, AugurPact, and with VexArmor active.
   • Notice that base damage bonus penalties are also relatively low at higher base damage bonuses.

Because of this, sometimes it is better to not equip mods that provide relatively lower additive bonuses due to opportunity cost. That mod slot is better reserved for bonuses that multiplicatively stack with other bonuses.

Armor[]

Although most Armor bonuses are percentage based (thus having "diminishing returns" strictly speaking on relative armor point increases) and that the relative increase of Damage Reduction percentage is smaller at higher armor values (e.g. the difference between 100 and 200 armor is 15% while the difference between 400 and 500 is 5.3571%), the actual number of effective health points (EHP) gained per additional point of armor does not have diminishing returns and remains constant (linear change). Every 300 armor points added will provide an additional 100% nominal health to EHP. This means that at higher armor values, the difference between EHP and nominal health is greater as seen in the above graph.

Nominal health refers to listed health points as displayed in-game; in other words, it is the total health after mods and buffs are applied

Simplified EHP calculation to demonstrate how damage reduction from armor can be expressed as a multiplier to nominal health. Every 300 armor points gained will increase the health multiplier by 1.

Multiplicative Stacking[]

Note that multiplicative stacking does not have "diminishing returns". For example, for a secondary that deals 100 base damage:

1. Adding a maxed rank HornetStrike (+220%), it would deal 320 base damage, a 220% relative increase in base damage or 3.2x base damage.
2. Adding a maxed rank BaneofInfested (+30%), it will deal 416 base damage (against Infested enemies), a 30% relative increase in base damage over just equipping HornetStrike or 1.3x the previous damage.
3. On a headshot (2x), it will deal 832 base damage, a 100% relative increase in base damage over just equipping HornetStrike and BaneofInfested or 2x the previous damage.
4. Adding a Rank 3 Eclipse at max buff (3x), it will deal 2,496 base damage, a 200% relative increase in base damage over just equipping HornetStrike, BaneofInfested, and on a headshot or 3x the previous damage.

Like multiplicative stacking, exponential stacking also has no "diminishing returns" since the next stat bonus always give the same relative additional value gained per additional percent bonuses as the previous bonus. For instance, the ArcaTitron has a unique passive where kills increases the damage of the next Slam Radial Attack by 100%, stacks multiplicatively with itself up to 10 times. With an unmodded ArcaTitron with a base radial damage of Electricity 360:

• At one charge, the total radial damage will be Electricity 720, a 2 / 1 =2x increase in base radial damage.
• At two charges, the total radial damage will be Electricity 1440, a (2 * 2) / (1 * 2) =2x increase in base radial damage over one charge.
• At three charges, the total radial damage will be Electricity 2880, a (2 * 2 * 2) / (1 * 2 * 2) =2x increase in base radial damage over two charges.
• And so on.

Order of Operations[]

To summarize, the order in which bonuses for the same fundamental stat applies as follows:

1. Bonuses that additively stack with each other
   • For example, Serration and HeavyCaliber will additively stack separately from BaneofCorrupted and Rhino's Roar despite affecting the same damage stat.
2. Bonuses that multiplicatively stack with each other and the previous additive bonuses
   • For example, bonus from Serration and HeavyCaliber will multiplicatively stack with the bonus from BaneofCorrupted and Rhino's Roar
3. Bonuses that grant a flat number or percentage points, additively stacking with each other

Example equation demonstrating the above order.

Expressing above equation as a product of summations since multiplicatively stacking bonuses can have additively stacking components.

Weapons[]

Types of Damage Bonuses[]

Mods primarily increase damage in one of four different ways:

1. Some mods increase the base damage of the weapon. This is usually written as simply "+X% damage". For example, HornetStrike and Serration.
2. Some mods increase physical damage types: Slash, Impact, and Puncture. For example, FangedFusillade or PiercingCaliber.
3. Some mods increase primary elemental damage types: Heat, Electricity, Cold, and Toxin. For example, PathogenRounds or Hellfire.
4. Some mods increase damage against enemies of a certain faction (i.e. faction damage bonuses). For example, BaneofCorpus or BaneofInfested

The Damage Application Order[]

1. When calculating damage, first base damage bonuses are added together and applied. For example, the Karak has a base damage of 29. Equipping a max rank Serration (+165% base damage) adds 1.65 × 29 =47.85 additional damage for a total of 76.85 damage (the arsenal will round this number to 76.9). The added damage will be of the same damage type distribution the weapon innately deals.
2. Then, all elemental and physical damage bonuses are calculated based on the modified base damage. For example, adding a Hellfire (+90% Heat damage) to a Karak that already has Serration equipped will add 90% of 76.85 for a total of 69.165 Heat damage. This damage is added to the base, and the Karak now deals a total of 146.015 damage if you add together all damage types.
3. After that, faction damage bonuses are applied to all damage types. Note that faction damage bonuses will not be accounted for in the arsenal stats. A Karak equipped with Serration, Hellfire, and BaneofCorpus (+30% damage against Corpus) will deal an extra 0.3 × 76.85 =23.055 physical damage and an extra 0.3 × 69.165 =20.7495 Heat damage for a total of 189.8195 damage of all types.

Once damage is calculated, it may be affected by Critical Hit mechanics or modified based on the opponent's armor or sources of damage reduction. For detailed calculations of how various damage types affect different types of enemies, see the Damage page.

Multishot[]

For weapons that fire multiple projectiles like shotguns or CernosPrime, the damage calculated is the damage dealt by each projectile. In other words, if the weapon only fires one projectile at a time, all of the damage is the base damage per projectile.

If the weapon has multishot from a mod like SplitChamber, it will have a percent chance to fire additional projectiles per shot, each of which will deal the full modded damage as if one projectile was shot. The arsenal will display multishot bonuses as percent increases in total damage when in fact this is not true in reality. The total damage stat shown in the arsenal actually reflects the average damage dealt per shot in this case. For example, a Karak with only SplitChamber equipped will see a 29 × 0.9 =26.1 increase in damage for an average of 55.1 damage per shot.

For weapons that only fire a single projectile, SplitChamber's 90% multishot will cause each shot to randomly have a 90% chance to fire two projectiles instead of one. Since CernosPrime already fires 3 arrows per shot, adding SplitChamber will make it fire 3 × 0.9 =2.7 additional arrows, so each shot will fire at least 5 arrows, and 70% of shots will fire 6.

On continuous beam weapons like the Glaxion, multishot adds a chance to increase damage on a tick. For example, adding SplitChamber to a Glaxion will give a 90% chance for a damage tick to double as if two projectiles were shot.

Calculating Physical Damage[]

Physical damage mods apply only to base damage of the same type. For example, at max rank FangedFusillade increases Slash damage by +120%. The Karak does 29 damage split into 13 Impact, 8.7 Puncture, and 7.3 Slash. A Karak equipped a max rank Fanged Fusillade will gain 7.3 × 1.2 =8.76 additional Slash damage for a total of 16.06 Slash and 37.76 total damage.

If a physical damage mod is added to a weapon that does no physical damage of the corresponding type, the mod will have no effect. For example, the Amprex does entirely Electricity damage when unmodded, so FangedFusillade will provide no Slash damage bonuses.

Calculating Elemental Damage[]

Elemental damage mods apply to all damage done by a weapon. For example, a max rank Hellfire adds 90% Heat damage to a rifle. If a Karak was equipped with a max rank Hellfire, it would gain 29 × 0.9 =26.1 Heat damage.

Each two different elemental mods will be added up into a secondary element, with has different damage type modifiers against certain enemy health, shields, and armor classes. For combined elements, the slots are ordered from left to right, top row then bottom row, with any inherent elemental damage (from the weapon) added last.

For example, if both Hellfire (+Heat damage) and CryoRounds (+Cold damage) are equipped on an Amprex, they will combine to add Blast damage to the weapon's base Electricity damage. If only Hellfire is used, it will combine with the Amprex's base Electricity damage to make Radiation damage instead.

If multiple mods of the same element are added, only the first is used when making combinations. For example, if Hellfire, Cryo Rounds, and ThermiteRounds are added to an Amprex, no matter what the order is the weapon will deal Blast and Electricity damage since the Heat element has already combined with Cold, so the second Heat mod simply increases the amount of Blast damage dealt.

Combining Physical and Elemental Damage[]

Both physical and elemental damage are combined in the same step and are based only on the weapon's base damage and any mods that effect base damage.

In terms of raw damage, this makes a +90% elemental damage bonus superior to +90% physical damage bonus unless the weapon deals all of its damage as a single physical damage type. In reality, the total effect varies based on the health, shields, abd armor classes of enemy being damaged due to damage type vulnerabilities and resistances.

Damage Calculations[]

Modded Stats[]

Basic formula for calculating modded stats (e.g. critical chance) with the exception of accuracy, reload time, and charge time.

Formula for calculating modded reload time and charge time.

Total Damage[]

The damage numbers displayed in the in-game arsenal calculates total weapon damage as such:

For melee weapons, remove multishot from the equation

Theoretical total inflicted damage against an enemy can be calculated as such (ignoring quantization for simplification):

Where SD represents the modded value of a particular damage type and DM represents the damage modifier for a particular damage type using the generalized damage modifier formula

Gun Damage Per Second[]

When comparing the performance of non-melee weapons, it may be useful to calculate their theoretical damage per second (DPS) (without accounting for status effects) using the following formulas:

In the case where modded critical chance is over 100%, the lowest crit tier possible will be considered a normal shot. (e.g. if a weapon has 250% crit chance, the 100% for an orange crit will be considered a normal shot)

Note that denotes a flooring function (rounding down)

In the case where modded critical chance is over 100%, the next crit tier possible will be considered a critical shot (e.g. if a weapon has 250% crit chance, the 50% for a red crit will be considered a critical shot)

Note that denotes a ceiling function (rounding up)

The average damage dealt on a single button input if all projectiles hit an enemy.

The lower the Fire Rate, the more delay between charge shots. If attack is not a charge trigger type (charge time is 0), then effective fire rate equals modded fire rate.

Not all weapons consume one ammo per shot; this is to account for cases such as Continuous Weapons

For the Vectis and VectisPrime specifically, one (1) should be subtracted from the denominator to account for their lack of a reload delay.

For Epitaph specifically, ignore Modded Reload Time since it draws ammo directly from the full ammo pool similar to bows, but does not "reload" between shots like them.

Assumes that damage ramp up is at max for Continuous Weapons.

Reload time is in seconds.

Reload time includes reload delay which is more prevalent for Battery Weapons. Reload delay for most weapons are negligible if not non-existent.

Melee Damage Per Second[]

When comparing the performance of melee weapons, it may be useful to calculate their theoretical damage per second (DPS) (without accounting for status effects) using the following formulas:

In the case where modded critical chance is over 100%, the lowest crit tier possible will be considered a normal hit. (e.g. if a weapon has 250% crit chance, the 100% for an orange crit will be considered a normal shot)

Note that denotes a flooring function (rounding down)

In the case where modded critical chance is over 100%, the next crit tier possible will be considered a critical hit (e.g. if a weapon has 250% crit chance, the 50% for a red crit will be considered a critical shot)

Note that denotes a ceiling function (rounding up)

The average damage dealt on the first enemy hit by melee attack, not accounting Follow Through

See individual stance pages for average combo damage multipliers or go to Stance#Comparison

See individual stance pages for average base combo lengths or go to Stance#Comparison

Damage Over Time[]

Total modded damage calculations used for DoT ignores elemental and physical damage bonuses.

Without accounting multipliers of specific DoT.

Individual calculations for each DoT proc. Keep in mind Slash DoT deals True damage, ignoring armor.

Multiply each DoT with the respective damage distribution (i.e. damage type / total damage) and add them together

In the case where modded critical chance is over 100%, the lowest crit tier possible will be considered a normal shot. (e.g. if a weapon has 250% crit chance, the 100% for an orange crit will be considered a normal shot)

Note that denotes a flooring function (rounding down)

In the case where modded critical chance is over 100%, the next crit tier possible will be considered a critical shot (e.g. if a weapon has 250% crit chance, the 50% for a red crit will be considered a critical shot)

Note that denotes a ceiling function (rounding up)

Accounting for critical hits, non-crits, and status chance for an average of total DoT averages.

Lifetime Damage[]

Lifetime damage is a derived damage stat that is based on the total amount of damage that a weapon can deal before it depletes its ammo reserve. Melee weapons, Battery Weapons or rechargable weapons, and Exalted Weapons (assuming Energy is always restored) will deal infinite damage over their in-game use since they are always available and are not reliant on ammo pickups or Squad Ammo Restores.

The average total damage dealt by a weapon without switching weapons or replenishing ammo.

Patch History[]

Game System Mechanics Edit
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	Mathematical	Calculating Bonuses (Additive Stacking, Multiplicative Stacking) • Condition Overload (Mechanic) • Damage Reduction • Enemy Level Scaling • Maximization • User Research