Calculating Bonuses

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. The same goes for temporary or conditional buffs and debuffs from abilities, mods, Arcane Enhancements, and enemies.

Last updated: Wed, 28 Jul 2021 08:13:54 +0000 (UTC) by User:Cephalon Scientia

Additive Stacking

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. For example, if a primary weapon has  Serration (+165% damage) and  Heavy Caliber (+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. Combining  Speed Trigger (+60% fire rate) and  Shred (+30% fire rate, +1.2 punch-through) will give a total of +90% bonus fire rate.

Multiplicative Stacking

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  Vex Armor additively stacking with base damage mods). This is commonly referred to as multiplicative stacking. For example, a primary weapon with  Serration (+165% damage) and  Bane of Grineer (+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  Bane of Grineer 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)
•  Cryo Rounds (1.9x  Cold elemental damage on top of base damage)
•  Viral procs (up to 4.25x damage on health)
•  Bane of Infested (1.3x damage against Infested)
•  Lasting Purity (1.6x damage on aiming)
•  Primed Chamber (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,  Arca Titron 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)

Flat Stat/Percentage Bonuses

Sources that grant flat percentage point increases are typically applied after all other bonuses are applied. For example, say a melee weapon with 20% critical chance and  True Steel equipped has 0.2 × (1 + 1.2) = 44% critical chance. Since a max ranked  Arcane Avenger 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's Eye buff triggers (adding a flat 60% critical chance), then the resultant critical chance will be 0.44 + 0.45 + 0.6 = 149%.

Exceptions

•  Piercing Navigator - applied before other bonuses are applied, effectively increasing the base stat
•  Ballistic Battery - applied after after the 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
•  Energy Channel - applied after after the critical damage multiplier

Diminishing Returns

Additive Stacking

Players may refer to additive stacking having "diminishing returns" (despite being linear increases), 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  Hornet Strike (+220%), it would deal 320 base damage, a  2.2 / 1 = 220% relative increase in base damage.
2. Adding a maxed rank  Magnum Force (+165%), it will deal 485 base damage, a  1.65 / (1 +  2.2) = 51.5625% relative increase in base damage over just equipping  Hornet Strike.
3. Adding a maxed rank  Augur Pact (+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  Hornet Strike and  Magnum Force.
4. Adding an unmodded Rank 3  Vex Armor 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  Hornet Strike,  Magnum Force, and  Augur Pact.
   • Notice that despite the larger base damage bonus of +275%,  Vex Armor only provided a smaller relative increase in base damage.
5. Adding a maxed rank  Anemic Agility (-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  Hornet Strike,  Magnum Force,  Augur Pact, and with  Vex Armor 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 (i.e. having "diminishing returns" relatively speaking) 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 gained per additional point of armor does not have diminishing returns.

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  Hornet Strike (+220%), it would deal 320 base damage, a 220% relative increase in base damage or 3.2x base damage.
2. Adding a maxed rank  Bane of Infested (+30%), it will deal 416 base damage (against Infested enemies), a 30% relative increase in base damage over just equipping  Hornet Strike 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  Hornet Strike and  Bane of Infested 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  Hornet Strike,  Bane of Infested, and on a headshot or 3x the previous damage.

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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, with an unmodded  Arca Titron 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  Heavy Caliber will additively stack separately from  Bane of Corrupted 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  Heavy Caliber will multiplicatively stack with the bonus from  Bane of Corrupted and  Rhino's  Roar
3. Bonuses that grant a flat number or percentage points, additively stacking with each other

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,  Hornet Strike and  Serration.
2. Some mods increase physical damage types:  Slash,  Impact, and  Puncture. For example,  Fanged Fusillade or  Piercing Caliber.
3. Some mods increase primary elemental damage types:  Heat,  Electricity,  Cold, and  Toxin. For example,  Pathogen Rounds or  Hellfire.
4. Some mods increase damage against enemies of a certain faction (i.e. faction damage bonuses). For example,  Bane of Corpus or  Bane of Infested

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  Bane of Corpus (+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  Cernos Prime, 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  Split Chamber, 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  Split Chamber 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,  Split Chamber's 90% multishot will cause each shot to randomly have a 90% chance to fire two projectiles instead of one. Since  Cernos Prime already fires 3 arrows per shot, adding  Split Chamber 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  Split Chamber 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  Fanged Fusillade 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  Fanged Fusillade 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  Cryo Rounds (+ 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  Thermite Rounds 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

Main article: Damage#Final Calculations

Modded Stats

$\begin{aligned} \text{Modded Stat} = \text{Base Stat} \cdot (1 + \text{Stat Bonuses}) \end{aligned}$

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

$\begin{aligned} \text{Modded Stat Time} = \frac{\text{Base Stat Time}}{(1 + \text{Stat Speed Bonuses})} \end{aligned}$

Formula for calculating modded reload time and charge time.

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Total Damage

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

${ \begin{aligned} \text{Average Total Damage} &= [ \text{Modded Base Damage}(1 + \text{Elemental Bonuses}) \\ &\qquad + \text{Modded Base Damage} \\ &\qquad \cdot (\text{Impact Distribution}(1 + \text{Impact Bonuses}) \\ &\qquad + \text{Puncture Distribution}(1 + \text{Puncture Bonuses}) \\ &\qquad + \text{Slash Distribution}(1 + \text{Slash Bonuses}) ) ] \\ &\qquad \cdot \text{Modded Multishot} \end{aligned} }$

For melee weapons, remove multishot from the equation

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

${ \text{Total Inflicted Damage} = \text{SD}_{1} \cdot \text{DM}_{1} + ... + \text{SD}_{N} \cdot \text{DM}_{N} }$

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

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Gun Damage Per Second

“It's taking longer than I calculated.”

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Burst-fire and mag-burst attacks (not simultaneous burst like  Quartakk which can be treated like semi-auto weapons) have a more complicated DPS calculation

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:

${ \text{Normal Shot} = \text{Total Damage} \cdot [1 + (\lfloor \text{Modded Crit Chance} \rfloor \cdot (\text{Modded Crit Multiplier} - 1) ) ] }$

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 $\lfloor \qquad \rfloor$ denotes a flooring function (rounding down)

${ \text{Critical Shot} = \text{Total Damage} \cdot [1 + (\lceil \text{Modded Crit Chance} \rceil \cdot (\text{Modded Crit Multiplier} - 1) ) ] }$

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 $\lceil \qquad \rceil$ denotes a ceiling function (rounding up)

${ \begin{aligned} \text{Average Shot} &= \text{Total Damage} \cdot (1 + \text{Modded Crit Chance} \cdot (\text{Modded Crit Multiplier} - 1)) \end{aligned} }$

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

${ \begin{aligned} \text{Effective Fire Rate} &= \frac{ 1 }{ \text{Modded Charge Time} + \frac{ 1 }{ \text{Modded Fire Rate} } } \end{aligned} }$

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.

${ \begin{aligned} \text{Number of Shots Per Magazine} &= \frac{ \text{Modded Mag Size} }{ \text{Ammo Cost Per Shot} } \end{aligned} }$

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

${ \begin{aligned} \text{Average Burst DPS} &= \text{Avg. Shot} \cdot \text{Effective Fire Rate} \end{aligned} }$

${ \begin{aligned} \text{Average Sustained DPS} &= \text{Avg. Burst DPS} \cdot \frac{ \text{Number of Shots Per Mag} }{ \text{Effective Fire Rate} \cdot \text{Modded Reload Time} + \text{Number of Shots Per Mag}} \end{aligned} }$

For the  Vectis and  Vectis Prime 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.

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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:

${ \text{Normal Hit} = \text{Total Damage} \cdot [1 + (\lfloor \text{Modded Crit Chance} \rfloor \cdot (\text{Modded Crit Multiplier} - 1) ) ] }$

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 $\lfloor \qquad \rfloor$ denotes a flooring function (rounding down)

${ \text{Critical Hit} = \text{Total Damage} \cdot [1 + (\lceil \text{Modded Crit Chance} \rceil \cdot (\text{Modded Crit Multiplier} - 1) ) ] }$

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 $\lceil \qquad \rceil$ denotes a ceiling function (rounding up)

${ \begin{aligned} \text{Average Hit} &= \text{Average Combo Damage Multiplier} \\ &\qquad \cdot \text{Total Damage} \cdot (1 + \text{Modded Crit Chance} \cdot (\text{Modded Crit Multiplier} - 1)) \end{aligned} }$

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

${ \begin{aligned} \text{Average DPS} &= \frac{\text{Avg Hit} \cdot \text{Modded Attack Speed}}{\text{Base Combo Length}} \end{aligned} }$

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

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Damage Over Time

${ \begin{aligned} \text{Modded Damage} &= \text{Modded Base Damage} \\ &\qquad \cdot \text{Modded Multishot} \\ &\qquad \cdot (1 + \text{Faction Damage Bonuses}) \end{aligned} }$

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

${ \begin{aligned} \text{Base Avg DoT} &= \text{Modded Damage} \\ &\qquad \cdot (1 + \text{Faction Damage Bonuses}) \\ &\qquad \cdot \text{Total Ticks} \end{aligned} }$

Without accounting multipliers of specific DoT.

${ \begin{aligned} \text{Avg Slash DoT} &= 0.35 \cdot \text{Base Avg DoT} \\ \text{Avg Electricity DoT} &= 0.5 \cdot (1 + \text{Electricity Bonuses}) \cdot \text{Base Avg DoT} \\ \text{Avg Heat DoT} &= 0.5 \cdot (1 + \text{Heat Bonuses}) \cdot \text{Base Avg DoT} \\ \text{Avg Toxin DoT} &= 0.5 \cdot (1 + \text{Toxin Bonuses}) \cdot \text{Base Avg DoT} \\ \text{Avg Gas DoT} &= 0.5 \cdot \text{Base Avg DoT} \end{aligned} }$

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

${ \begin{aligned} \text{Total Avg DoT} &= (\text{Slash DoT} \cdot \text{Slash Distribution}) \\ &\qquad + (\text{Electricity DoT} \cdot \text{Electricity Distribution}) + \dots \\ &\qquad + (\text{Gas DoT} \cdot \text{Gas Distribution}) \end{aligned} }$

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

${ \begin{aligned} \text{Normal Total Avg DoT} &= \text{Total Avg DoT} \\ &\qquad \cdot [1 + (\lfloor \text{Modded Crit Chance} \rfloor \cdot (\text{Modded Crit Multiplier} - 1) ) ] \end{aligned} }$

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 $\lfloor \qquad \rfloor$ denotes a flooring function (rounding down)

${ \begin{aligned} \text{Crit Total Avg DoT} &= \text{Total Avg DoT} \\ &\qquad \cdot [1 + (\lceil \text{Modded Crit Chance} \rceil \cdot (\text{Modded Crit Multiplier} - 1) ) ] \end{aligned} }$

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 $\lceil \qquad \rceil$ denotes a ceiling function (rounding up)

${ \begin{aligned} \text{Avg Total Avg DoT} &= \text{Modded Status Chance} \\ &\qquad \cdot \text{Total Avg DoT} \\ &\qquad \cdot (1 + \text{Modded Crit Chance} \cdot (\text{Modded Crit Multiplier} - 1)) \end{aligned} }$

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

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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.

${ \begin{aligned} \text{Average Lifetime Damage} &= \text{Average Shot} \cdot \text{Number of Shots Per Magazine} \cdot (1 + \frac{ \text{Modded Maximum Ammo} }{ \text{Modded Magazine} }) \end{aligned} }$

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