This page explains how to calculate armour values.
Calculating the formulas
Let the following be:
D
R
the damage reduction factor
D
R
∈
R
A
the armour rating the defender has
A
∈
N
+
D
r
a
w
the raw damage dealt
D
r
a
w
∈
N
+
D
n
e
t
the damage dealt after reduction
D
n
e
t
∈
R
+
\color[RGB]{163,141,109} \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
D
R
(
A
,
D
r
a
w
)
=
A
A
+
10
∗
D
r
a
w
\color[RGB]{163,141,109} DR(A, D_{raw}) = {A \over A + 10 * D_{raw} }
Resolved for Raw Damage
D
R
=
A
A
+
10
∗
D
r
a
w
D
R
∗
(
A
+
10
∗
D
r
a
w
)
=
A
A
+
10
∗
D
r
a
w
=
A
D
R
10
∗
D
r
a
w
=
A
D
R
−
A
D
r
a
w
=
A
D
R
−
A
10
D
r
a
w
=
A
10
∗
D
R
−
A
10
\color[RGB]{163,141,109} \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
r
a
w
(
A
,
D
R
)
=
A
10
∗
D
R
−
A
10
\color[RGB]{163,141,109} D_{raw}(A, DR) = {A \over 10 * DR} - {A \over 10}
Resolved for Armour
D
R
=
A
A
+
10
∗
D
r
a
w
D
R
∗
(
A
+
10
∗
D
r
a
w
)
=
A
D
R
∗
A
+
D
R
∗
10
∗
D
r
a
w
=
A
D
R
∗
10
∗
D
r
a
w
=
A
−
D
R
∗
A
D
R
∗
10
∗
D
r
a
w
=
A
∗
(
1
−
D
R
)
D
R
∗
10
∗
D
r
a
w
1
−
D
R
=
A
\color[RGB]{163,141,109} \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
r
a
w
,
D
R
)
=
D
R
∗
10
∗
D
r
a
w
1
−
D
R
\color[RGB]{163,141,109} A(D_{raw}, DR) = {DR * 10 * D_{raw} \over 1 - DR}
Net Damage formula
Based on DR
D
n
e
t
(
A
,
D
r
a
w
)
=
D
r
a
w
−
D
r
a
w
∗
D
R
(
A
,
D
r
a
w
)
\color[RGB]{163,141,109} D_{net}(A, D_{raw}) = D_{raw} - D_{raw} * DR(A, D_{raw})
Eliminating DR
D
n
e
t
=
D
r
a
w
−
D
r
a
w
∗
D
R
D
n
e
t
=
D
r
a
w
−
D
r
a
w
∗
A
A
+
10
∗
D
r
a
w
D
n
e
t
∗
(
A
+
10
∗
D
r
a
w
)
=
D
r
a
w
∗
(
A
+
10
∗
D
r
a
w
)
−
D
r
a
w
∗
A
D
n
e
t
∗
(
A
+
10
∗
D
r
a
w
)
=
10
∗
D
r
a
w
2
D
n
e
t
=
10
∗
D
r
a
w
2
A
+
10
∗
D
r
a
w
\color[RGB]{163,141,109} \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
n
e
t
(
A
,
D
r
a
w
)
=
10
∗
D
r
a
w
2
A
+
10
∗
D
r
a
w
\color[RGB]{163,141,109} D_{net}(A, D_{raw}) = {10 * {D_{raw} }^2 \over A + 10 * D_{raw} }
Defense Factor formula
Base Formula
D
F
(
D
n
e
t
,
D
r
a
w
)
=
D
r
a
w
D
n
e
t
\color[RGB]{163,141,109} DF(D_{net}, D_{raw}) = {D_{raw} \over D_{net} }
Eliminating Net Damage
D
F
=
D
r
a
w
D
n
e
t
D
F
=
D
r
a
w
10
∗
D
r
a
w
2
A
+
10
∗
D
r
a
w
D
F
=
D
r
a
w
∗
(
A
+
10
∗
D
r
a
w
)
10
∗
D
r
a
w
2
D
F
=
A
+
10
∗
D
r
a
w
10
∗
D
r
a
w
D
F
=
A
10
∗
D
r
a
w
+
1
\color[RGB]{163,141,109} \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
D
F
(
A
,
D
r
a
w
)
=
A
10
∗
D
r
a
w
+
1
\color[RGB]{163,141,109} DF(A, D_{raw}) = {A \over 10 * D_{raw} } + 1