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 majority of these functions can be found in tome.team/mod/class/interface/Combat.lua.

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.

(CFD) Cursed Form Damage

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

This function is defined in tome.team/data/talents/cursed/cursed-form.lua as combatTalentDamage and is only used for Cursed Form talents

Example of talent description

The value is _[min]max^cTSpD

What the game actually does

The value will be identical to _[min]max^cTSpD, except it uses (1.2 * (Character Level + Willpower) ) as your effective spellpower.

(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 parameter x 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

Example of talent description

The value is low–high^{cSL:limit,stat}

What the talent description means

The value will be low when the stat is 10, and high when the stat is 100, with some diminishing returns and will never exceed limit.

(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.

(cTID) combatTalentIntervalDamage

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

Example of talent description

The value is min–max^{cTID:stat_weight *stat}

What the talent description means

The value will be max when stat is 100 and the talent level is 6.5.

What the game actually does

Calculate Base Value = min + (max - min) * ( (stat_weight * stat / 100) + (1 - stat_weight) * Talent Level / 6.5 )

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

The stat_weight parameter

The stat_weight parameter determines the relative weight between stats and talent level. It defaults to 0.5 to indicate equal contributions.

(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.

Paradox modifier

With a talent description of: Value is low–high^cTL:limit,PM

the game will multiply your talent level by a Paradox Modifier when calculating the value, where

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

(cTMD) combatTalentMindDamage

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

Example of talent description

The value is _[base]max^cTMD

What the talent description means

The value will scale with respect to both mind power and talent level, returning max at 100 mind power and talent level 5.

What the game actually does

The actual value will be ( max * Mind Power Factor * Talent Factor )^1.04, where

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

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

Notice that base is not actually the minimum possible value.

(cTPD) combatTalentPhysicalDamage

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

Example of talent description

The value is _[base]max^cTPD

What the talent description means

The value will scale with respect to both physical power and talent level, returning max at 100 physical power and talent level 5.

What the game actually does

The actual value will be ( max * Physical Power Factor * Talent Factor )^1.04, where

Physical Power Factor = (base + Physical Power) / (base + 100),

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

Notice that base is not actually the minimum possible value.

(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 low–high^cTS

What the talent description means

The value will be low at talent level 1, and 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 m and b that produce the best fit to the two points y(1) = low and y(5) = high,

then return y(x) as the desired value using the fitted function and 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, the final value will be rounded up or down, though no convention has yet been set to indicate how this rounding will be expressed.

(cTSpD) combatTalentSpellDamage

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

Example of talent description

Value is _[base]max^cTSpD

What the talent description means

The value will scale with respect to both spell power and talent level, returning max^1.04 at 100 spell power and talent level 5.

What the game actually does

The actual value will be ( max * Spell Power Factor * Talent Factor )^1.04, where

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

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

Paradox modifier

With a talent description of: Value is _[base]max^cTSpD:PM,

the game will multiply the final value by your Paradox Modifier, which is defined as

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

Value is _[base]max^cTStD:stat

What the talent description means

The value before diminishing returns will scale with respect to both stat and talent level, returning max at 100 stat and talent level 5.

What the game actually does

Calculate Base Value = ( max * Stat Factor * Talent Factor ), where

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

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

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

(cTWD) combatTalentWeaponDamage

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

Example of talent description

Value is base–max^cTWD

What the talent description means

The value will be max at talent level 5.

What the game actually does

The value is (base + (max - base) * √ (Talent Level / 5) )

The t2 Parameter

An extra t2 parameter can sometimes be provided (e.g. Shield Pummel), in which case

the value is (base + (max - base) * √ ((Talent Level + t2 / 2 ) / 5) )

Although the CTWD template will accept an extra parameter for t2, it is probably best to just explain its effects directly in a talent's description instead.