Scaling

This page will list some of the scaling functions that are frequently used in game to calculate talent parameters. The sections below are named after the actual function names used in the game's Lua files. The goal here is to provide a very basic understanding of how various talent parameters are scaled so that talent pages do not need to be filled with a plethora of unknown X's. Instead, the actual range of values can be displayed on each talent page with a footnote linking to this article for further details.

(cL) combatLimit

Talent parameters that scale by this function should be noted with the CL template

This function is the archetype for both combatStatLimit and combatTalentLimit.

(cS) combatScale

Talent parameters that scale by this function should be noted with the CS template

This function is the archetype for both combatStatScale and combatTalentScale.

Example of talent description

The value is y_low–y_high^cS as parameter x varies from x_low–x_high

What the talent description means

The value will be y_low when the parameter is x_low, and y_high when the parameter is x_high, with some diminishing returns.

What the game actually does

Using the function y(x) = m * (t + shift) ^power + b + add,

find the values of m and b that produce the best fit to the two points y( x_low ) = y_low and y( x_high ) = y_high,

then return the value y(x) with the fitted function given the actual parameter x of the character

Default values for the fit parameters are

power = 0.5

shift = 0

add = 0

Example calculation

The trap detection power of Heightened Senses is 0–125^cS as (0.25 * Cunning * Talent Level) varies from 0–125

The resulting fit function is y = 11.18 * (0.25 * Cunning * Talent Level) ^0.5 and will, for example, produce the following results:

Talent Level	Cunning	Detection Power
1	10	18
1	20	25
1	40	35
5	40	79
5	100	125
5	150	153

(cSL) combatStatLimit

Talent parameters that scale by this function should be noted with the CSL template

(cSS) combatStatScale

Talent parameters that scale by this function should be noted with the CSS template

This function is almost identical to combatScale except that it sets x_low = 10 and x_high = 100 to represent the stat that the scaling is based on. Prodigies will typically use x_low = 50 instead.

(cTL) combatTalentLimit

Talent parameters that scale by this function should be noted with the CTL template

Example of talent description

The value is low–high^cTL:limit

What the talent description means

The value will be low at talent level 1, and high at talent level 5, with some diminishing returns and will never exceed limit.

(cTMD) combatTalentMindDamage

Talent parameters that scale by this function should be noted with the CTMD template

Example of talent description

Talent deals d₁– d₂^cTMD damage.

What the talent description means

The talent's damage will scale with respect to both mind power and talent level, dealing d₂ damage at 100 mind power and talent level 5.

What the game actually does

The actual talent damage will be ( d₂ * Mind Power Factor * Talent Factor )^1.04, where

Mind Power Factor = (d₁ + Mind Power) / (d₁ + 100),

Talent Factor = (0.2 + 0.8 * √ Talent Level) / (0.2 + 0.8 * √ 5)

(cTS) combatTalentScale

Talent parameters that scale by this function should be noted with the CTS template

This function is almost identical to combatScale except that is sets x_low = 1 and x_high = 5 to represent the talent level that the scaling is based on.

Example of talent description

Value is y_low– y_high^cTS

What the talent description means

The talent parameter will have value y_low at talent level 1, and value y_high at talent level 5, with some diminishing returns.

What the game actually does

Using the function y(x) = m * (x + shift) ^power + b + add,

find the values of m and b that produce the best fit to the two points y(1) = y_low and y(5) = y_high,

then return the value of y(x) with the fitted function given the actual talent level x of the character

Default values for the fit parameters are

power = 0.5

shift = 0

add = 0

Custom power

With a talent description of: Value is 5–10^cTS:0.75P

the fit parameter power = 0.75 will be used instead.

Higher power suppresses the effects of diminishing returns.

Custom shift

With a talent description of: Value is 5–10^cTS:2S

the fit parameter shift = 2 will be used instead.

Higher shift basically acts as a direct bonus to your talent level.

Logarithmic fits

With a talent description of: Value is 5–10^cTS:log

the game will use a logarithmic fit with the function y(x) = m * Log₁₀(x + shift) + b + add instead

Paradox modifier

With a talent description of: Value is 5–10^cTS:PM

the game will multiply your talent level by a Paradox Modifier and return y ( x * Paradox Modifier ), where

Paradox Modifier = (0.5 + Paradox / 600)^0.5

Example of calculation

If the description of a talent is: This skill has a range of 5–10^cTS

then the game will use default values to produce the fit function

y(x) = 4.045 * x ^0.5 + 0.955

which would return the following values for the talent's range

Talent Level x	Range y(x)
1	5
2	6.68
3	7.96
4	9.05
5	10
6	10.86
7	11.66

In cases such as this where non-integer values are not meaningful, talent ranges are typically rounded down, while durations are rounded up.

(cTSpD) combatTalentSpellDamage

Talent parameters that scale by this function should be noted with the CTSPD template.

Example of talent description

Damage is d₁– d₂^cTSpD

What the talent description means

The talent's damage will scale with respect to both spell power and talent level, dealing d₂ damage at 100 spell power and talent level 5.

What the game actually does

The actual talent damage will be ( d₂ * Spell Power Factor * Talent Factor )^1.04, where

Spell Power Factor = (d₁ + Spell Power) / (d₁ + 100),

Talent Factor = (0.2 + 0.8 * √ Talent Level) / (0.2 + 0.8 * √ 5)

Spell power override

With a talent description of: Damage is d₁– d₂^cTSpD:50SP,

the game will calculate the damage assuming 50 spellpower instead.

Paradox modifier

With a talent description of: Damage is d₁– d₂^cTSpD:PM,

the game will multiply the final damage by your Paradox Modifier

Paradox Modifier = (0.5 + Paradox / 600)^0.5

(cTStD) combatTalentStatDamage

Talent parameters that scale by this function should be noted with the CTSTD template

Example of talent description

Damage is d₁– d₂^cTStD:Stat

What the talent description means

The talent's base damage before diminishing returns will scale with respect to both stat and talent level, dealing d₂ base damage at 100 stat and talent level 5.

What the game actually does

Calculate Base Damage = ( d₂ * Stat Factor * Talent Factor ), where

Stat Factor = (d₁ + Stat) / (d₁ + 100),

Talent Factor = (0.2 + 0.8 * √ Talent Level) / (0.2 + 0.8 * √ 5),

then return Final Damage = Base Damage * ( 1 - Log₁₀(2 * Base Damage) / 7 )

(cTWD) combatTalentWeaponDamage

Talent parameters that scale by this function should be noted with the CTWD template