Enemy Level Scaling

All enemies that you encounter 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, and Affinity. 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 or damage type selection.

Common Features of Stat Scaling Edit

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. Base level and base value of the stat are determined by the enemy type. The current level is then the independent variable and 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 easy to notice until mid-level ranges. For high levels, the exponent is the 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 current and base level.

This so far only applies to fundamental stats, i.e. health, armor, shields, damage, and affinity. Derived stats, such as effective health, are calculated by incorporating multiple of these fundamental stats, which is covered further below. Fundamental stats are stats in the narrower sense, so if "stats" is not specified, fundamental stats are meant.

Scaling of Fundamental Stats Edit

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

*Note that the following Health, Shield, and Armor scaling formula 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 Edit

For health, the level ranges at which scaling transitions from exponential growth to a plateau is 70-85. The formula enemy health scales at is as follows:

$ f_1(x) = 1 + 0.015(x - \text{Base Level})^2 $ (Original scaling pre-Update 27.2)

 

$ f_2(x) = 1 + 10.75(x - \text{Base Level})^{0.5} $

 

$ f_3(x) = min\left(1, \frac{max(x, 70 + \text{Base Level}) - (70 + \text{Base Level})}{15} \right) $

Where the $ min() $ and $ max() $ functions simply take the smallest or largest of the two values in their arguments, respectively.

$ \begin{align}\text{Health Multiplier} = 1 + (f_1(\text{Current Level}) - 1)\times(1 - f_3(\text{Current Level}))\\+ (f_2(\text{Current Level}) - 1)\times f_3(\text{Current Level})\end{align} $

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

Shields Edit

For shields, the level ranges at which scaling transitions from exponential growth to a plateau is 70-85. The formula enemy shields scale at is as follows:

$ f_1(x) = 1 + 0.0075(x - \text{Base Level})^2 $ (Original scaling pre-Update 27.2)

 

$ f_2(x) = 1 + 1.6(x - \text{Base Level})^{0.75} $

 

$ f_3(x) = min\left(1, \frac{max(x, 70 + \text{Base Level}) - (70 + \text{Base Level})}{15} \right) $

 

$ \begin{align}\text{Shield Multiplier} = 1 + (f_1(\text{Current Level}) - 1)\times(1 - f_3(\text{Current Level}))\\+ (f_2(\text{Current Level}) - 1)\times f_3(\text{Current Level})\end{align} $

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

Armor Edit

For armor, the level ranges at which scaling transitions from exponential growth to a plateau is 60-80. The formula enemy armor scales at is as follows:

$ f_1(x) = 1 + 0.005(x - \text{Base Level})^{1.75} $ (Original scaling pre-Update 27.2)

 

$ f_2(x) = 1 + 0.4(x - \text{Base Level})^{0.75} $

 

$ f_3(x) = min\left(1, \frac{max(x, 60 + \text{Base Level}) - (60 + \text{Base Level})}{20} \right) $

 

$ \begin{align}\text{Armor Multiplier} = 1 + (f_1(\text{Current Level}) - 1)\times(1 - f_3(\text{Current Level}))\\+ (f_2(\text{Current Level}) - 1)\times f_3(\text{Current Level})\end{align} $

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

Damage Edit

The formula enemy damage scales at is as follows:

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

Affinity Edit

The formula enemy affintiy scales at is as follows:

$ \text{Affinity Multiplier} = 1 + 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.

Scaling of Derived Stats Edit

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

Effective Hitpoints Edit

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 Edit

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 Shield Edit

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}} $

For Enemies with Health and Armor Edit

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) $

For Enemies with Health, Shield and Armor Edit

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 Edit

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 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 85, 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.

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.

Affinity Density Edit

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

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 Edit

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.

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