# Redux

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This article is a work in progress!

Redux, also known as Total Damage Reduction, is the ability of a character to resist physical damage more effectively, resulting in less health loss, as well as reducing or even negating what should have inflicted a wound. This is not to be confused with Defensive Strength (DS), which reduces the endroll in the combat formula. Redux does not activate until the character is successfully hit by an AS-based or Unarmed Combat attack at which point it will then reduce the ensuing damage correspondingly.

The following is a player-generated theory.

## Redux Points

Redux is initially achieved by training in physical skills, and the total reduction is increased by additional training in these skills. Some skills provide more redux benefit than others, and are divided into primary, secondary, and tertiary skills. Primary skills provide 10 "points" towards redux, secondary skills provide 4 points, and tertiary provide 3 points.

The threshold for achieving redux is approximately $\displaystyle \mathrm{1060 + \frac{2000}{level}}$ redux points. For example, a level 27 character with 1134 redux points did not have sufficient points to gain redux but did with 1135 points $\displaystyle \mathrm{1060 + \frac{2000}{27}}$ .

Characters will receive the following message when checking out of a local inn indicating that they do not have redux. If this message is not displayed then the character does have redux.

Current skills bonus is insufficient to gain DF reduction.


## Redux Factor

There are three elements that determine a character's redux factor:

1. Redux Points
2. Character Level (RF increases with higher level)
3. Spell Ranks (RF decreases when spell ranks known increases)

Two methods of calculating the redux factor are shown below. The first one uses redux points while the second uses the quadratic formula in standard form. The first formula will generally be more accurate.

### Redux Factor Formula (Points)

It must be stated that this formula is incomplete but should still have an accuracy of +99%.

 $\displaystyle \mathrm{Redux \ Factor=\frac{(Redux \ Points - T)}{(2 * Redux \ Points) - X + Y}}$

Important note: The Y value only applies when redux points are >3600

$\displaystyle \mathrm{T = 1060 + \frac{2000}{level}}$ This is the redux threshold
$\displaystyle \mathrm{X = \frac{4472}{level}}$
$\displaystyle \mathrm{Y = (60 * \sqrt{redux \ points}) - 3600}$ (only use when redux points are >3600)

The $\displaystyle \mathrm{X}$ value $\displaystyle \mathrm{4472}$ is derived from $\displaystyle \mathrm{\sqrt{2000} * 100}$

#### Examples (all examples assume 0 spell ranks)

1. Level 66 w/3000 redux points

Numerator (RP - T): $\displaystyle \mathrm{3000 - (1060 + \frac{2000}{66}) = 1909}$
Denominator (2RP - X): $\displaystyle \mathrm{6000 - \frac{4472}{66} = 5932}$
Redux Factor (Num/Den): $\displaystyle \mathrm{\frac{1909}{5932} = .3218138}$

2. Level 38 w/1700 redux points

Numerator: $\displaystyle \mathrm{1700 - (1060 + \frac{2000}{38}) = 587}$
Denominator: $\displaystyle \mathrm{3400 - \frac{4472}{38} = 3282}$
Redux Factor: $\displaystyle \mathrm{\frac{587}{3282} = .1788543}$

3. Level 74 w/4250 redux points

Numerator: $\displaystyle \mathrm{4250 - (1060 + \frac{2000}{74} = 3163}$
Denominator (2RP + Y): $\displaystyle \mathrm{8500 + (60 * \sqrt{4250}) - 3600 = (8500 + 3912 - 3600) = 8812}$
Redux Factor: $\displaystyle \mathrm{\frac{3163}{8812} = .358942}$

4. Level 100 w/12000 redux points

Numerator: $\displaystyle \mathrm{12000 - (1060 + \frac{2000}{100}) = 10920}$
Denominator: $\displaystyle \mathrm{24000 + (60 * \sqrt{12000}) - 3600 = (24000 + 6573 - 3600) = 26973}$
Redux Factor: $\displaystyle \mathrm{\frac{10920}{26973} = .4048492}$

5. Level 81 w/4784 redux points

Numerator: $\displaystyle \mathrm{4784 - (1060 + \frac{2000}{81}) = 3700}$
Denominator: $\displaystyle \mathrm{9568 + (60 * \sqrt{4784}) - 3600 = (9568 + 4150 - 3600) = 10118}$
Redux Factor: $\displaystyle \mathrm{\frac{3700}{10118} = .3656849}$

### Redux Factor Formula (Quadratic Formula)

An approximate redux factor can be also be calculated by using the coefficients and constant of a quadratic equation in the standard form:

 $\displaystyle \mathrm{ax^2 + bx + c = 0}$

An understanding of this formula is not necessary to calculate the redux factor. The only requirements are determination of raw and critical damage values for a given attack. Averaging the results of multiple attack resolutions is recommended for greater accuracy. Avoid using damage weighted weapons and damage padded armor since they will cause erroneous results.

Where:

$\displaystyle \mathrm{x = redux factor}$
$\displaystyle \mathrm{a = raw damage}$
$\displaystyle \mathrm{b = (raw damage * 2) + crit damage}$
$\displaystyle \mathrm{c = raw damage + crit damage + 0.5 - actual damage taken}$

Note: $\displaystyle \mathrm{Raw damage = (endroll - 100) * weapon damage factor}$

Once the a, b, c values have been calculated, they can be entered into a quadratic equation calculator. The b value must be entered as a negative.

An online calculator can be found at:

http://www.math.com/students/calculators/source/quadratic.htm

#### Example

You swing a gleaming rune-scribed maul at Drangell!
AS: +803 vs DS: +520 with AvD: +41 + d100 roll: +68 = +392
... and hit for 91 points of damage!
A mighty hit turns Drangell's insides to outsides!

Weapon damage factor: $\displaystyle \mathrm{.450}$ (perfect maul vs scale)
Raw damage: $\displaystyle \mathrm{131.4 (292 * .450)}$
Crit damage: $\displaystyle \mathrm{75}$ (R9 crush - abdomen)
Actual damage: $\displaystyle \mathrm{91}$
$\displaystyle \mathrm{a = 131.4}$ (raw damage)
$\displaystyle \mathrm{b = 337.8}$ (raw damage * 2) + crit damage (entered as negative)
$\displaystyle \mathrm{c = 115.9}$ (raw damage + crit damage + 0.5 - actual damage)

$\displaystyle \mathrm{Redux Factor: ~.408}$ (0.4077873841171237 is the X2 value from the online calculator).

## Order of Operations

This section contains a detailed explanation of the procedure (order of operations) used to calculate damage reduction as it applies to AS-based attacks. (see Unarmed Combat section below for UAC damage reduction formula).

In the previous redux model, DFredux, the weapon damage factor (DF) was effectively reduced by a redux factor (RF) using the formula: .ceil((DF * (1-RF)) = DFr, where DFr is the reduced weapon DF and (DFr * endroll success margin) determined actual raw damage taken. The critical rank with corresponding damage was based on the reduced raw damage but there was no critical damage reduction. It has remained an open question whether or not there is just 1 or 2 redux factors used in the current model (answer is 1) and the order of operations for reducing damage.

The current model, Total Damage Reduction, consists of two parts. Part I functions similarly to DFredux: the weapon damage factor is reduced by the redux factor and the resulting reduced raw damage determines the maximum critical rank. Part II includes an additional raw damage reduction plus critical damage reduction.

### Part 1 (weapon damage factor reduction)

Formula for calculating the reduced weapon damage factor (designated DFr)

DFr = .ceil((DF * (1-RF))

For example, a broadsword has a normal damage factor of .200 vs plate armor. Against a character with RF .315 the broadsword's damage factor is reduced to .137

.ceil((.200 * (1 - .315) = .137

### Part 2 (total damage reduction)

Formula for calculating total damage taken

Total damage taken = (reduced raw damage + crit damage) - trunc((redux factor *(reduced raw dmg + crit dmg))

Formula for calculating reduced raw damage taken

Reduced raw damage taken = round(DFr * (endroll - 100))

Example

You swing a gleaming rune-scribed maul at Drangell!
AS: +803 vs DS: +520 with AvD: +41 + d100 roll: +68 = +392
... and hit for 91 points of damage!
A mighty hit turns Drangell's insides to outsides!


Weapon DF: .450 (perfect maul vs scale)
Redux factor: .408
Reduced weapon DF (DFr): .267 [.ceil((1 - .408) * 450)]
Endroll - 100: 292
Reduced raw damage: 78 [round(.267 * 292)]
Critical damage: 75 (Rank 9 Crush, Abdomen)

Total damage taken = (78 + 75) - trunc(.408 * (78 + 75)) = 91 total damage taken

## Unarmed Combat

 UAC Damage Taken = [1 - Redux Factor * (Total Calculated Damage)]

## Weighting and Padding

• Critical weighting/padding is added to or subtracted from reduced raw damage. This adjusted value is used for maximum critical rank determination only.
• Damage weighting/padding is added to or subtracted from the total calculated damage.

## Spell Penalty

This section is due for a rewrite when further calculations are done.

Training in spells will reduce a character's redux. This is a gradual reduction based on the number of spell ranks trained, but the exact formula is not currently known. There is some research which indicates that at one spell rank per level the penalty is approximately 34-38%. At two ranks per level the penalty is 100%.

Example: A level 100 character with a redux factor of .360 decides to train 100 spell ranks. This character can expect that the spell penalty will lower their redux factor from .360 to approximately .225. With 200 spell ranks or greater they will lose their redux entirely.

Note: Training in magic skills other than spells has no effect on redux.