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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 <span id="cL"></span>==

''This function is the archetype for both [[#cSL|combatStatLimit]] and [[#cTL|combatTalentLimit]].''

==(cS) combatScale <span id="cS"></span>==

''This function is the archetype for both [[#cSS|combatStatScale]] and [[#cTS|combatTalentScale]].''

;Example of talent description
:The value is '''''y<sub>low</sub>'''''– '''''y<sub>high</sub>''''' as the parameter varies from '''''x<sub>low</sub>'''''– '''''x<sub>high</sub>''''' <sup>[[Scaling#cS|cS]]</sup>

;What the talent description means
:The value will be '''''y<sub>low</sub>''''' when the parameter is '''''x<sub>low</sub>''''', and '''''y<sub>high</sub>''''' when the parameter is '''''x<sub>high</sub>''''', with some diminishing returns.

;What the game actually does
:Using the function '''''y(x) = m * (t + shift) <sup>power</sup> + b + add''''',
:find the values of '''''m''''' and '''''b''''' that produce the best fit to the two points '''''y( x<sub>low </sub>)''''' = '''''y<sub>low</sub>''''' and '''''y( x<sub>high </sub>)''''' = '''''y<sub>high</sub>''''',
: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 (talent)|Heightened Senses]] is 0–125 as (Talent Level * Cunning) varies from 0–500 <sup>[[Scaling#cS|cS]]</sup>.
:The resulting fit function is '''''y = 5.59 * (Talent Level * Cunning) <sup>0.5</sup>''''' and will, for example, produce the following results:
:{|class = "wikitable"
!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 <span id="cSL"></span>==

==(cSS) combatStatScale <span id="cSS"></span>==


''This function is almost identical to [[#cS|combatScale]] except that it sets '''''x<sub>low</sub> = 10''''' and '''''x<sub>high</sub> = 100''''' to represent the stat that the scaling is based on. [[Prodigies]] will typically use '''''x<sub>low</sub> = 50''''' instead.''

==(cTL) combatTalentLimit <span id="cTL"></span>==


==(cTMD) combatTalentMindDamage <span id="cTMD"></span>==

;Example of talent description
:Talent deals '''''d<sub>1</sub>'''''– '''''d<sub>2</sub>'''''<sup>[[Scaling#cTMD|cTMD]]</sup> damage.

;What the talent description means
:The talent's damage will scale with respect to both mind power and talent level, dealing '''''d<sub>2</sub>''''' damage at 100 mind power and talent level 5.

;What the game actually does
:The actual talent damage will be ( '''''d<sub>2</sub>''''' * '''Mind Power Factor''' * '''Talent Factor''' )<sup>1.04</sup>, where
:'''Mind Power Factor''' = ('''''d<sub>1</sub>''''' + '''Mind Power''') / ('''''d<sub>1</sub>''''' + 100),
:'''Talent Factor''' = (0.2 + 0.8 * √ '''Talent Level''') / (0.2 + 0.8 * √ 5)

==(cTS) combatTalentScale <span id="cTS"></span>==

''This function is almost identical to [[#cS|combatScale]] except that is sets '''''x<sub>low</sub> = 1''''' and '''''x<sub>high</sub> = 5''''' to represent the talent level that the scaling is based on.

;Example of talent description
:Value is '''''y<sub>low</sub>'''''– '''''y<sub>high</sub>'''''<sup>[[Scaling#cTS|cTS]]</sup>

;What the talent description means
:The talent parameter will have value '''''y<sub>low</sub>''''' at talent level 1, and value '''''y<sub>high</sub>''''' 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) <sup>power</sup> + b + add''''',
:find the values of '''''m''''' and '''''b''''' that produce the best fit to the two points '''''y(1)''''' = '''''y<sub>low</sub>''''' and '''''y(5)''''' = '''''y<sub>high</sub>''''',
: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<sup>[[Scaling#cTS|cTS:0.75P]]</sup>
: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<sup>[[Scaling#cTS|cTS:log]]</sup>
:then the game will use a logarithmic fit with the function '''''y(x) = m * Log<sub>10</sub>(x + shift) + b + add''''' instead

;Example of calculation
:If the description of a talent is: This skill has a range of 5–10<sup>[[Scaling#cTS|cTS]]</sup>
:then the game will use default values to produce the fit function
:'''''y(x) = 4.045 * x <sup>0.5</sup> + 0.955'''''
:which would return the following values for the talent's range
:{|class = "wikitable"
!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 <span id="cTSD"></span>==

==(cTWD) combatTalentWeaponDamage <span id="cTWD"></span>==

[[Category:Game Mechanics]]