Let the following be:
D R the damage reduction factor D R ∈ R A the armor the player 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 + {\displaystyle {\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}}}
D R ( A , D r a w ) = A A + 10 ∗ D r a w {\displaystyle DR(A,D_{raw})={A \over A+10*D_{raw}}}
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 {\displaystyle {\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}}}
D n e t ( A , D r a w ) = D r a w − D r a w ∗ D R ( A , D r a w ) {\displaystyle D_{net}(A,D_{raw})=D_{raw}-D_{raw}*DR(A,D_{raw})}
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 {\displaystyle {\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}}}
D n e t ( A , D r a w ) = 10 ∗ D r a w 2 A + 10 ∗ D r a w {\displaystyle D_{net}(A,D_{raw})={10*{D_{raw}}^{2} \over A+10*D_{raw}}}
D F ( D n e t , D r a w ) = D r a w D n e t {\displaystyle DF(D_{net},D_{raw})={D_{raw} \over D_{net}}}
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 {\displaystyle {\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}}}
D R ( A , D r a w ) = A 10 ∗ D r a w + 1 {\displaystyle DR(A,D_{raw})={A \over 10*D_{raw}}+1}