Guide:Armour calculations: Difference between revisions
Jump to navigation
Jump to search
>TheFrz mNo edit summary |
>Illviljan mNo edit summary |
||
| Line 3: | Line 3: | ||
Let the following be: | Let the following be: | ||
{{math|formula=\begin{align} | {{math|formula= | ||
\begin{align} | |||
DR & \text{ the damage reduction factor} & DR & \in \mathbb{R}\\ | DR & \text{ the damage reduction factor} & DR & \in \mathbb{R}\\ | ||
A & \text{ the armor the player has} & A & \in \mathbb{N}^+ \\ | A & \text{ the armor the player has} & A & \in \mathbb{N}^+ \\ | ||
D_{raw} & \text{ the raw damage dealt} & D_{raw} & \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}^+\\ | D_{net} & \text{ the damage dealt after reduction} & D_{net} & \in \mathbb{R}^+\\ | ||
\end{align} }} | \end{align} | ||
}} | |||
==DR Formula== | ==DR Formula== | ||
{{math|formula=DR(A, D_{raw}) = {A \over A + 10 * D_{raw} } }} | {{math|formula= | ||
DR(A, D_{raw}) = {A \over A + 10 * D_{raw} } | |||
}} | |||
===Resolved for Raw Damage=== | ===Resolved for Raw Damage=== | ||
{{math|formula=\begin{align} | {{math|formula= | ||
\begin{align} | |||
DR & = {A \over A + 10 * D_{raw} } \\ | DR & = {A \over A + 10 * D_{raw} } \\ | ||
DR * (A + 10 * D_{raw}) & = A \\ | DR * (A + 10 * D_{raw}) & = A \\ | ||
| Line 22: | Line 27: | ||
D_{raw} & = { {A \over DR} - A \over 10} \\ | D_{raw} & = { {A \over DR} - A \over 10} \\ | ||
D_{raw} & = {A \over 10 * DR} - {A \over 10} | D_{raw} & = {A \over 10 * DR} - {A \over 10} | ||
\end{align} }} | \end{align} | ||
}} | |||
====Final result for raw damage==== | ====Final result for raw damage==== | ||
{{math|formula=D_{raw}(A, DR) = {A \over 10 * DR} - {A \over 10} }} | {{math|formula= | ||
D_{raw}(A, DR) = {A \over 10 * DR} - {A \over 10} | |||
}} | |||
===Resolved for Armour=== | ===Resolved for Armour=== | ||
{{math|formula=\begin{align} | {{math|formula= | ||
\begin{align} | |||
DR & = {A \over A + 10 * D_{raw} } \\ | DR & = {A \over A + 10 * D_{raw} } \\ | ||
DR * (A + 10 * D_{raw}) & = A \\ | DR * (A + 10 * D_{raw}) & = A \\ | ||
| Line 35: | Line 44: | ||
DR * 10 * D_{raw} & = A * (1 - DR) \\ | DR * 10 * D_{raw} & = A * (1 - DR) \\ | ||
{DR * 10 * D_{raw} \over 1 - DR} & = A | {DR * 10 * D_{raw} \over 1 - DR} & = A | ||
\end{align} }} | \end{align} | ||
}} | |||
====Final result for armour==== | ====Final result for armour==== | ||
{{math|formula=A(D_{raw}, DR) = {DR * 10 * D_{raw} \over 1 - DR} }} | {{math|formula= | ||
A(D_{raw}, DR) = {DR * 10 * D_{raw} \over 1 - DR} | |||
}} | |||
==Net Damage formula== | ==Net Damage formula== | ||
===Based on DR=== | ===Based on DR=== | ||
{{math|formula=D_{net}(A, D_{raw}) = D_{raw} - D_{raw} * DR(A, D_{raw})}} | {{math|formula= | ||
D_{net}(A, D_{raw}) = D_{raw} - D_{raw} * DR(A, D_{raw}) | |||
}} | |||
===Eliminating DR=== | ===Eliminating DR=== | ||
{{math|formula=\begin{align} | {{math|formula= | ||
\begin{align} | |||
D_{net}& = D_{raw} - D_{raw} * DR \\ | D_{net}& = D_{raw} - D_{raw} * DR \\ | ||
D_{net} & = D_{raw} - D_{raw} * {A \over A + 10 * D_{raw} } \\ | D_{net} & = D_{raw} - D_{raw} * {A \over A + 10 * D_{raw} } \\ | ||
| Line 51: | Line 66: | ||
D_{net} * (A + 10 * D_{raw}) & = 10 * {D_{raw} }^2 \\ | D_{net} * (A + 10 * D_{raw}) & = 10 * {D_{raw} }^2 \\ | ||
D_{net} & = {10 * {D_{raw} }^2 \over A + 10 * D_{raw} } | D_{net} & = {10 * {D_{raw} }^2 \over A + 10 * D_{raw} } | ||
\end{align} }} | \end{align} | ||
}} | |||
===Final result=== | ===Final result=== | ||
{{math|formula=D_{net}(A, D_{raw}) = {10 * {D_{raw} }^2 \over A + 10 * D_{raw} } }} | {{math|formula= | ||
D_{net}(A, D_{raw}) = {10 * {D_{raw} }^2 \over A + 10 * D_{raw} } | |||
}} | |||
==Defense Factor formula== | ==Defense Factor formula== | ||
===Base Formula=== | ===Base Formula=== | ||
{{math|formula=DF(D_{net}, D_{raw}) = {D_{raw} \over D_{net} } }} | {{math|formula= | ||
DF(D_{net}, D_{raw}) = {D_{raw} \over D_{net} } | |||
}} | |||
===Eliminating Net Damage=== | ===Eliminating Net Damage=== | ||
{{math|formula=\begin{align} | {{math|formula= | ||
\begin{align} | |||
DF & = {D_{raw} \over D_{net} } \\ | DF & = {D_{raw} \over D_{net} } \\ | ||
DF & = {D_{raw} \over {10 * {D_{raw} }^2 \over A + 10 * D_{raw} } } \\ | DF & = {D_{raw} \over {10 * {D_{raw} }^2 \over A + 10 * D_{raw} } } \\ | ||
| Line 68: | Line 89: | ||
DF & = {A + 10 * D_{raw} \over 10 * D_{raw} } \\ | DF & = {A + 10 * D_{raw} \over 10 * D_{raw} } \\ | ||
DF & = {A \over 10 * D_{raw} } + 1 \\ | DF & = {A \over 10 * D_{raw} } + 1 \\ | ||
\end{align} }} | \end{align} | ||
}} | |||
===Final result=== | ===Final result=== | ||
{{math|formula=DF(A, D_{raw}) = {A \over 10 * D_{raw} } + 1}} | {{math|formula= | ||
DF(A, D_{raw}) = {A \over 10 * D_{raw} } + 1 | |||
}} | |||
Revision as of 08:45, 3 July 2016
Calculating the formulas
Let the following be:
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/edac57ad5c2b8fab0a1031938de6d6b04f86bbee)
DR Formula
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}DR(A,D_{raw})={A \over A+10*D_{raw}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a2070d64eb84186b7daeb0ad85d506da9e77fe5b)
Resolved for Raw Damage
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a28faa7b356871f9c041eb0b6ee6bd651cb21990)
Final result for raw damage
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}D_{raw}(A,DR)={A \over 10*DR}-{A \over 10}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a6e3efba51fbf5757a6114539142a1d992de72a)
Resolved for Armour
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/36106a8e82d8213b4f681ad460e93622b34cb6ca)
Final result for armour
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}A(D_{raw},DR)={DR*10*D_{raw} \over 1-DR}](https://wikimedia.org/api/rest_v1/media/math/render/svg/185f3d0f5ff657139d76421fda396728e067dc15)
Net Damage formula
Based on DR
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}D_{net}(A,D_{raw})=D_{raw}-D_{raw}*DR(A,D_{raw})](https://wikimedia.org/api/rest_v1/media/math/render/svg/cead05459a4a83660f7bd8c0d98169ae7b99d4f6)
Eliminating DR
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/59865e6e59d9e4d8628053932b2d982d6883b1b8)
Final result
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}D_{net}(A,D_{raw})={10*{D_{raw}}^{2} \over A+10*D_{raw}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efe1afc6ade2b831bf87de0b1ef5372aa2d3ef9d)
Defense Factor formula
Base Formula
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}DF(D_{net},D_{raw})={D_{raw} \over D_{net}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0996cf556b7dcdb2d2710b7dd533aa83368dedb6)
Eliminating Net Damage
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c2b3ab1d422605401c57b18f7b8e6702a729d49)
Final result
![\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}DF(A,D_{raw})={A \over 10*D_{raw}}+1](https://wikimedia.org/api/rest_v1/media/math/render/svg/254641e6deab09498e9e958f142b6695380eb75a)