Difference between revisions of "Scaling"

Revision as of 14:20, 27 July 2014

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

This function is the archetype for both combatStatLimit and combatTalentLimit.

(cS) combatScale

This function is the archetype for both combatStatScale and combatTalentScale.

Example of talent description

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

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 as (Talent Level * Cunning) varies from 0–500 ^cS.

The resulting fit function is y = 5.59 * (Talent Level * Cunning) ^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

(cSS) combatStatScale

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

(cTMD) combatTalentMindDamage

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

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.

(this is all you need to know in the majority of cases)

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 fit parameters should be noted on the talent page if possible

If the talent description is: This skill has a range of 5–10^cTS:0.75P

then the fit parameter power = 0.75 will be used instead.

Logarithmic fits

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

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

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, they are generally rounded down to the nearest integer instead.

(cTSD) combatTalentStatDamage

(cTWD) combatTalentWeaponDamage