Armour/math

This page explains how to calculate armour values.

Calculating the formulas
Let the following be:

$\begin{align} DR & \text{ the damage reduction factor} & DR & \in \mathbb{R}\\ A & \text{ the armour rating the defender has} & A & \in \mathbb{N}^+ \\ D_{raw} & \text{ the raw damage dealt} & D_{raw} & \in \mathbb{N}^+\\ D_{net} & \text{ the damage dealt after reduction} & D_{net} & \in \mathbb{R}^+\\ \end{align}$

DR Formula
$DR(A, D_{raw}) = {A \over A + 10 * D_{raw} }$

Resolved for Raw Damage
$\begin{align} DR & = {A \over A + 10 * D_{raw} } \\ DR * (A + 10 * D_{raw}) & = A \\ A + 10 * D_{raw} & = {A \over DR} \\ 10 * D_{raw} & = {A \over DR} - A \\ D_{raw} & = { {A \over DR} - A \over 10} \\ D_{raw} & = {A \over 10 * DR} - {A \over 10} \end{align}$

Final result for raw damage
$D_{raw}(A, DR) = {A \over 10 * DR} - {A \over 10}$

Resolved for Armour
$\begin{align} DR & = {A \over A + 10 * D_{raw} } \\ DR * (A + 10 * D_{raw}) & = A \\ DR * A + DR * 10 * D_{raw} & = A \\ DR * 10 * D_{raw} & = A - DR * A \\ DR * 10 * D_{raw} & = A * (1 - DR) \\ {DR * 10 * D_{raw} \over 1 - DR} & = A \end{align}$

Final result for armour
$A(D_{raw}, DR) = {DR * 10 * D_{raw} \over 1 - DR}$

Based on DR
$D_{net}(A, D_{raw}) = D_{raw} - D_{raw} * DR(A, D_{raw})$

Eliminating DR
$\begin{align} D_{net}& = D_{raw} - D_{raw} * DR \\ D_{net} & = D_{raw} - D_{raw} * {A \over A + 10 * D_{raw} } \\ D_{net} * (A + 10 * D_{raw}) & = D_{raw}*(A + 10 * D_{raw}) - D_{raw} * A \\ D_{net} * (A + 10 * D_{raw}) & = 10 * {D_{raw} }^2 \\ D_{net} & = {10 * {D_{raw} }^2 \over A + 10 * D_{raw} } \end{align}$

Final result
$D_{net}(A, D_{raw}) = {10 * {D_{raw} }^2 \over A + 10 * D_{raw} }$

Base Formula
$DF(D_{net}, D_{raw}) = {D_{raw} \over D_{net} }$

Eliminating Net Damage
$\begin{align} DF & = {D_{raw} \over D_{net} } \\ DF & = {D_{raw} \over {10 * {D_{raw} }^2 \over A + 10 * D_{raw} } } \\ DF & = {D_{raw} * (A + 10 * D_{raw}) \over 10 * {D_{raw} }^2} \\ DF & = {A + 10 * D_{raw} \over 10 * D_{raw} } \\ DF & = {A \over 10 * D_{raw} } + 1 \\ \end{align}$

Final result
$DF(A, D_{raw}) = {A \over 10 * D_{raw} } + 1$

Броня/подсчёт