Guide:Armour calculations

Cacluating the formulas

Let the following be:

${\begin{aligned}DR&{\text{ the damage reduction factor}}&DR&\in \mathbb {R} \\A&{\text{ the armor the player has}}&A&\in \mathbb {N} ^{+}\\D_{raw}&{\text{ the raw damage dealt}}&D_{raw}&\in \mathbb {N} ^{+}\\D_{net}&{\text{ the damage dealt after reduction}}&D_{net}&\in \mathbb {R} ^{+}\\\end{aligned}}$

DR Formula

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

Resolved for Raw Damage

${\begin{aligned}DR&={A \over A+10*D_{raw}}\\DR*(A+10*D_{raw})&=A\\A+10*D_{raw}&={A \over DR}\\10*D_{raw}&={A \over DR}-A\\D_{raw}&={{A \over DR}-A \over 10}\\D_{raw}&={A \over 10*DR}-{A \over 10}\end{aligned}}$

Final result for raw damage

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

Resolved for Armour

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

Final result for armour

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

Net Damage formula

Based on DR

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

Eliminating DR

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

Final result

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

Defense Factor formula

Base Formula

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

Eliminating Net Damage

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

Final result

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