Enemy Level Scaling

Enemy Level Scaling
Normal stat scaling for health, shields, and armor

All enemies encountered in WARFRAME have a certain level, which determines their strength by increasing some of their base statistics. The stats amplified by enemy level gain are Health, Armor, Shields, Damage dealt, and Affinity on death. The purpose of this article is to show how exactly these stats scale with level, how this translates to useful indicators such as effective health, and what implications this has towards player decision making such as Aura mods or damage type selection.

Note that enemy levels can only reach to a maximum of level 10000 with some edge cases (e.g. Eximus spawns).

Common Features of Stat Scaling

How scaling of fundamental enemy stats works in general is identical for all the stats: Each enemy type has a base value for this fundamental stat and a base level, the current value of the stat at the current level of the enemy is then calculated after a formula of the following structure:

${\text{Current Value}}={\text{Base Value}}\times (1+{\text{Coefficient}}({\text{Current Level}}-{\text{Base Level}})^{\text{Exponent}})$

Exponent and coefficient are determined by the specific stat in question but are equal across all enemy types. The base level and base value of the stat are determined by the enemy type. The current level is then the independent variable and the current value of the stat is the dependent variable of the formula.

At lower levels the coefficient is normally less than one, so growth is not easily noticed until mid-level ranges. For high levels, the exponent has the most impact when comparing different scaling stats against each other. If the exponent is 1, the scaling of the stat would be linear with level, which means the increase in value as level grows would be constant. For exponents higher than 1, each successive level-up grants a larger increase than the previous one, and for exponents lower than one, each successive level-up grants a smaller increase than the previous one.

The only exception of this common structure is Affinity scaling, where the current level is used instead of the difference between the current and base level.

Scaling of Fundamental Stats

As mentioned, all fundamental stats scale by the above formula structure and common features apply. A standardized graph is shown for each stat. When comparing the graphs, the different Y-axis scaling has to be considered. As of Update 27.2 (2020-03-05) health, shield, and armor scaling follow an "S"-like curve, where below a universal level range these stats grow "exponentially", and above this range, the stats grow slower and begin to plateau.

Showing scaling of health, shields, and armor between level 1-200. Note that shield scaling will surpass health above level 2025.

Showing scaling of Eximus health, shields, and armor between level 1-200.

Health, shields, and armor scaling formulae use two main functions to determine stat scaling at a particular level. One function is used when enemy level difference is below 70 and the other when enemy level difference is above 80. A common feature between the functions used is that they intersect at x=80. In other words, they produce the same value when the enemy level difference is 80.

Stat scaling between 70-80 inclusive is interpolated from the two functions using smoothstep.

$T(x)={\frac {x-{\text{Base Level}}-70}{10}}$

Finding out transition percentage from 70 to 80

$S_{1}(x)={\begin{cases}0,\;&x-{\text{Base Level}}<70\\3(T(x))^{2}-2(T(x))^{3},\;&70\leq x-{\text{Base Level}}\leq 80\\1,\;&x-{\text{Base Level}}>80\end{cases}}$

Smoothstep transitioning between functions

Note that while the growth at early levels is normally referred to as exponential by the community, it is actually a power growth of the form xⁿ, which is an order less than exponential growth (i.e. xⁿ ∈ O(n^x) v. n^x ∉ O(xⁿ)). For simplicity's sake however, it will still be referred to as exponential growth throughout the article.

Note that the following health, shield, and armor scaling formulae are derived from in-game testing and have not been confirmed or denied valid by Digital Extremes at this time. The accuracy of the following information is still under review.

Health

For health, the ranges of level differences from base to current level at which scaling transitions from exponential growth to a plateau is between 70 & 80. The formula by which enemy health scales is as follows:

$f_{1}(x)=1+0.015(x-{\text{Base Level}})^{2}$ (Original scaling pre-Update 27.2 (2020-03-05))

When Current Level - Base Level < 70

$f_{2}(x)=1+{\frac {24{\sqrt {5}}}{5}}(x-{\text{Base Level}})^{0.5}$

When Current Level - Base Level > 80

• Normal
• Eximus

${\begin{aligned}{\text{Health Multiplier}}=[f_{1}({\text{Current Level}})\times (1-S_{1}({\text{Current Level}})]\\+[f_{2}({\text{Current Level}})\times S_{1}({\text{Current Level}})]\end{aligned}}$

For Eximus enemies the same curves are used for scaling with smoothstep interpolation between level difference 70 and 80, but the base health is also increased between certain breakpoints:

${{\text{Health Multiplier}}={\begin{cases}f_{1}(x),\;&x\leq 25\\(1+0.05*(x-25))*f_{1}(x),\;&25<x\leq 35\\(1.5+0.1*(x-35))*f_{1}(x),\;&35<x\leq 50\\(3+0.02*(x-50))*[f_{1}(x)\times (1-S_{1}(x))+f_{2}(x)\times S_{1}(x)],\;&50<x\leq 100\\4*f_{2}(x),\;&x>100\\\end{cases}}}$

Where the Health Multiplier is the value that multiplies an enemy's base health to its current health.

Current health scaling at Base Level = 1.

Shields

“It's taking longer than I calculated.”

This page is actively being worked on and may not be completely correct. Please assist in making this page accurate.

Confirm increase in Eximus shield scaling by 50% as per https://forums.warframe.com/topic/1313506-echoes-of-the-zariman-update-316/

For shields, the ranges of level differences at which scaling transitions from exponential growth to a plateau is between 70 & 80. The formula by which enemy shields scale is as follows:

$f_{0}(x)=1+0.0075(x-{\text{Base Level}})^{2}$ (Original scaling pre-Update 27.2 (2020-03-05))

$f_{1}(x)=1+0.02(x-{\text{Base Level}})^{1.75}$

When Current Level - Base Level < 70

$f_{2}(x)=1+1.6(x-{\text{Base Level}})^{0.75}$

When Current Level - Base Level > 80

• Normal
• Eximus

${\begin{aligned}{\text{Shield Multiplier}}=[f_{1}({\text{Current Level}})\times (1-S_{1}({\text{Current Level}})]\\+[f_{2}({\text{Current Level}})\times S_{1}({\text{Current Level}})]\end{aligned}}$

For Eximus enemies the same curves are used for scaling with smoothstep interpolation between level difference 70 and 80, but the base shields are also increased between certain breakpoints:

${{\text{Shield Multiplier}}={\begin{cases}f_{1}(x),\;&x\leq 25\\(1+0.0325*(x-25))*f_{1}(x),\;&25<x\leq 35\\(1.325+0.065*(x-35))*f_{1}(x),\;&35<x\leq 50\\(2.3+0.013*(x-50))*[f_{1}(x)\times (1-S_{1}(x))+f_{2}(x)\times S_{1}(x)],\;&50<x\leq 100\\2.95*f_{2}(x),\;&100>x\\\end{cases}}}$

Where the Shield Multiplier is the value that multiplies an enemy's base shields to its current shields.

Current shield scaling at Base Level = 1.

Armor

For armor, the ranges of level differences at which scaling transitions from exponential growth to a plateau is between 70 & 80. The formula by which enemy armor scales is as follows:

$f_{1}(x)=1+0.005(x-{\text{Base Level}})^{1.75}$ (Original scaling pre-Update 27.2 (2020-03-05))

When Current Level - Base Level < 70

$f_{2}(x)=1+0.4(x-{\text{Base Level}})^{0.75}$

When Current Level - Base Level > 80

• Normal
• Eximus

${\begin{aligned}{\text{Armor Multiplier}}=[f_{1}({\text{Current Level}})\times (1-S_{1}({\text{Current Level}})]\\+[f_{2}({\text{Current Level}})\times S_{1}({\text{Current Level}})]\end{aligned}}$

For Eximus enemies the same curves are used for scaling with smoothstep interpolation between level difference 70 and 80, but the base armor is also increased between certain breakpoints. Note that because base armor changes with level, this also means that the number of  Shattering Impact hits needed to strip armor will change with level too.

${{\text{Armor Multiplier}}={\begin{cases}f_{1}(x),\;&x\leq 25\\(1+0.0125*(x-25))*f_{1}(x),\;&25<x\leq 35\\(1.125+0.06667*(x-35))*f_{1}(x),\;&35<x\leq 50\\(1.375+0.005*(x-50))*[f_{1}(x)\times (1-S_{1}(x))+f_{2}(x)\times S_{1}(x)],\;&50<x\leq 100\\1.625*f_{2}(x),\;&x>100\\\end{cases}}}$

Where the Armor Multiplier is the value that multiplies an enemy's base armor to its current armor.

Current armor scaling at Base Level = 1.

Overguard

Overguard is a unique health buffer to Eximus, though normal units can get overguard in unique sitations (like after a Overguard Exodamper is destroyed during Void Armageddon).

$f_{1}(x)=1+0.0015(x-{\text{Base Level}})^{4}$

When Current Level - Base Level < 45

$f_{2}(x)=1+260(x-{\text{Base Level}})^{0.9}$

When Current Level - Base Level > 50

Stat scaling between 45-50 inclusive is interpolated from the two functions using smoothstep.

$T(x)={\frac {x-{\text{Base Level}}-45}{5}}$

Finding out transition percentage from 45 to 50

$S_{2}(x)={\begin{cases}0,\;&x-{\text{Base Level}}<45\\3(T(x))^{2}-2(T(x))^{3},\;&45\leq x-{\text{Base Level}}\leq 50\\1,\;&x-{\text{Base Level}}>50\end{cases}}$

Smoothstep transitioning between functions

${\begin{aligned}{\text{Overguard Multiplier}}=[f_{1}({\text{Current Level}})\times (1-S_{2}({\text{Current Level}})]\\+[f_{2}({\text{Current Level}})\times S_{2}({\text{Current Level}})]\end{aligned}}$

Where the Overguard Multiplier is the value that multiplies an enemy's base overguard to its current overguard.

Current overguard scaling at Base Level = 1.

Damage

The formula by which enemy damage scales is as follows:

${\text{Damage Multiplier}}=1+0.015\times ({\text{Current Level}}-{\text{Base Level}})^{1.55}$

Current damage scaling at Base Level = 1.

Affinity

The formula by which enemy affinity scales is as follows:

${\text{Affinity Multiplier}}=1+0.1425\times {\text{Current Level}}^{0.5}$

${\text{Eximus Affinity Multiplier}}=3+0.1425\times {\text{Current Level}}^{0.5}$

Note that this is a special case: for the affinity scaling, base level is not subtracted from the current level. The base affinity multiplied by the Affinity Multiplier value is also rounded down to a whole number, e.g. 62.7 affinity will be rounded down to 62.

Current affinity scaling.

Scaling of Derived Stats

From these fundamental stats, more meaningful stats can be derived.

Effective Hitpoints

Effective Hit-points is a stat that indicates how much gross damage must be dealt to a target until the net damage thereby inflicted depletes its entire health pool. Effective Hit-points is not a fixed stat for any given enemy, it is heavily dependent on the damage type used against the target, as well as the various buffs and debuffs in effect for both the attacker and the enemy in question. For the following considerations, however, these influences are disregarded, as they do not alter the course of the graphs except for clinching or stretching them as a whole, which manifests as a scaling of the Y-axis.

For Enemies with Health only

For targets without shields and armor, the standardized effective hit-point scaling is synonymous with standardized health scaling, the health graph and formula apply.

For Enemies with Health and Shields

The standardized effective hit-points of shielded enemies are simply the sum of their shields and health, except for the case when the  Toxin damage portion of the gross damage depletes the target's health faster than the rest of the gross damage depletes its shield. Exact effective hit-point calculations considering damage types also become significantly more complex if  Toxin damage is involved, but this is disregarded here. The level scaling of standardized effective hit-points of shielded enemies is influenced by the ratio of base shields to base health:

${\text{EHP Multiplier}}={\text{Health Multiplier}}+{\text{Shield Multiplier}}\times {\frac {\text{Base Shields}}{\text{Base Health}}}$

In the cases where you are trying to one-shot shielded enemies without  Toxin damage, their effective hit-points will actually be higher due to their shield gate mechanic. Only 5% of total damage dealt will only damage the enemy's health when their shield gate is active. However, attacking enemy weakpoints ignores the shield gate.

Current EHP scaling with only Health and Shields at Base Level = 1.

For Enemies with Health and Armor

The standardized effective hit-points of armored enemies are simply the health divided by the compliment of the damage reduction granted from armor. Because armor adds damage reduction to incoming damage on health the level scaling of standardized effective hit-points of armored enemies is influenced by the base armor itself:

${\text{EHP Multiplier}}={\text{Health Multiplier}}\times \left(1+{\frac {{\text{Base Armor}}\times {\text{Armor Multiplier}}}{300}}\right)$

Current EHP scaling with only Health and Armor at Base Level = 1.

For Enemies with Health, Shields, and Armor

The standardized effective hit-points of enemies that are both armored and shielded are more complex than the simple EHP cases from the previous sections above. The level scaling of standardized effective hit-points of these enemies is influenced by the ratio of base shields to base health and base armor, making the formula at least 3 variable:

${\text{EHP Multiplier}}={\text{Health Multiplier}}\times \left(1+{\frac {{\text{Base Armor}}\times {\text{Armor Multiplier}}}{300}}\right)+{\text{Shield Multiplier}}\times {\frac {\text{Base Shields}}{\text{Base Health}}}$

Shielding Ratio

The shielding ratio of shielded, unarmored enemies is the ratio of their shield to their health. Since health and shield scale at different rates, this ratio changes with level. Pre-Update 27.2 (2020-03-05) this ratio used to converge towards a 1:2 ratio, where the higher the level the enemies, the closer they were to having twice as much health as shields, regardless of base stats. Currently, the ratio follows this original trend up until level 70, where it suddenly dips below 1:2 then diverges off towards infinity. This is because unlike before when health and shield scaling had same exponents (2), the current shield scaling has an exponent 50% larger than health scaling (0.75 vs 0.5) once past level 80, so it will grow at a faster rate despite having a smaller coefficient. This means the shield ratio will also grow larger over levels rather than converging.

The shielding ratio is relevant for evaluating and selecting damage types against shielded enemies, i.e. weighing benefits against shield types against benefits against health types. Eventually shielded enemies at high enough levels will have more shields than health, so assuming a lack of  Toxin or  True damage, effectiveness against shields may take more precedence in player builds than health effectiveness.

Current shield ratio scaling at Base Level = 1.

The shielding ratio of shielded, armored enemies is the ratio of their shield to their armored EHP. Like before, since health and shield scale at different rates, this ratio changes with level, though more complexly since armor scaling will also make an impact. This ratio converges towards a 0:1 ratio, where, as long as the enemy has a base armor of at least one, the higher the level the enemies the closer they are to having a negligible amount of shields relative to their EHP due to armor. Though as seen above, if no armor is present then the ratio will diverge towards infinity.

Current shield ratio scaling with Armor at Base Level = 1.

Affinity Density

The affinity density of an enemy is its affinity per effective hitpoints and a measure of its profitability for affinity farming.

Current affinity density scaling at Base Level = 1.

Current affinity density scaling accounting for Shields at Base Level = 1.

Current affinity density scaling accounting for Armor at Base Level = 1.

It is important to note the actual affinity farming profitability is significantly offset off the optimal area as implied by the affinity density function due to the two important practical influences of overkill and retargeting time, which both contribute to shifting the actual optimum from these implications towards higher levels.

Reflective Kill Rate

Reflective kill rate of an enemy is the ratio of its damage output and effective hit-points. This is inversely proportional to the amount of time or attacks an enemy would need to kill another of its kind. It's a measurement for the effectiveness of damage reflecting effects and abilities, such as the  Radiation damage proc, the  Reflection mod, and abilities such as  Link,  Shadows Of The Dead,  Absorb,  Chaos or  Mind Control.

Current reflective killing rate scaling at Base Level = 1.

Current reflective killing rate scaling accounting for Shields at Base Level = 1.

Current reflective killing rate scaling accounting for Armor at Base Level = 1.

Level Scaling During Endless Gameplay

“It's taking longer than I calculated.”

This page is actively being worked on and may not be completely correct. Please assist in making this page accurate.

During endless missions such as Survival, Defense, and Disruption, enemy spawn level will increase exponentially the more reward rotations are completed. Typically at around 8+ hours of in-mission time, players will reach the max enemy spawn level.

In Disruption missions, to calculate the approximate spawn level at a particular conduit number:

${{\text{Level Increase From Previous Round}}=L(x)=2.59e^{0.139({\text{Round Number}})}}$

${{\text{Spawn Level}}={\text{Starting Spawn Level}}+\sum _{x=1}^{\text{Round Number}}L(x)}$

External Links

Interactive calculator for most value multipliers

Patch History

Update 27.2 (2020-03-05)

Armor and Damage Changes (Enemy):

This section will go over before and after scenarios with our enemy Armor, Health, and Shield changes. Reading this section should give you a conceptual and on-paper understanding of what we’re changing and why, but practical experiences will tell the full story here. You may need to refresh some aspects of your Builds to truly optimize your power against your enemies.

Before: Armor, Shields and Health on an Exponential Curve
After: Armor Shields and Health on an S curve

Damage Changes:

Enemy Damage output should still be close to what is currently on the Live version of the game, but we have made a few changes that will affect how players take Damage in-game.

Infested Damage:

We did not want to overlook the Infested in our review. Infested are close-range enemies that telegraph most attacks - and now if one of those attacks hits you, it simply does more damage. Stay agile, stay moving, and the mission is as good as won!

Why: Having Infested simply deal more Damage encourages you to use mobility in ways that is not the norm for their ranged counterparts. Rewarding mobility is a key part of Warframe.

AI Aimbots

Up until now in Warframe, the higher the enemy level, the better their accuracy. High-level enemies would be pinned at the best Accuracy they are capable of - not quite 100%, but getting pretty close! Things like your movement and Mods would reduce accuracy, but the potential for bad ‘Aimbot’ moments was too high. We have spread this progression across a greater range of AI now We are decoupling enemy accuracy from level to reduce the overall ‘Aimbot’ like behaviours you face at higher levels.

Why: This change allows us more accurate balancing of foes at higher levels. This change alone would be noticed by simply sometimes ‘getting hit less’, but in conjunction with the numerous other changes we are making to enemies, it is part of a holistic Refresh to the underlying mechanics behind Warframe’s enemies.

Hotfix 25.0.7 (2019-05-30)

• Eximus enemies are now capped at Level 9999 like regular enemies.

Update 14.0 (2014-07-18)

• Enemies health is no longer capped at 65535.

Update 11.5 (2013-12-19)

• Armour/Shield/Health/Damage curves have been modified. We’ve lowered the “bullet sponge” to high level enemies, but they now deal more damage. The armour curve was radically dropped. The health and shields curves dropped slightly as well. However, damage output went up.

Update 11.0 (2013-11-20) Source: https://forums.warframe.com/topic/132366-information-on-damage-20/

Enemy Levels

Enemy levels now fall in a more compressed scale. Level 1 enemies are still the easiest, but the difficulty of a Level 40 enemy in Damage 2.0 will be comparable to a Level 100 enemy in Damage 1.0. Infinite mission types will still feature ever increasing enemy levels. Enemies will be wielding weapons that can inflict different types of damage and Procs on the Tenno, meaning the difficulty will come from a combination of their loadouts and their level.