Defense is calculated as:

\( {\text{DEF}}={\text{DEF}}_{\text{Character}}\times (1+\%{\text{ DEF Bonus}})+{\text{DEF Flat Bonus}}\)

For both characters and enemies, defense reduces incoming damage based on this formula:^[1]

\( {\text{DEF DMG Reduction}}={\frac {\text{DEF}}{{\text{DEF}}+5\times {\text{Level}}_{\text{Attacker}}+500}}\)

The incoming damage will then be multiplied by

\({\text{DEF Multiplier}}=1-{\text{DEF DMG Reduction}}\)

Enemy Defense

File:Damage vs defense graph.png

Characters have defense attributes based on their base stats, levels, weapons, artifacts, and any buffs (e.g. Food).

Enemy defense is given as:

\( {\text{DEF}}_{\text{Enemy}}=5\times {\text{Level}}_{\text{Enemy}}+500 \)

Defense reduces incoming damage, but its effectiveness is dependent on the attacker's level:^[2]

\( {\text{DEF Multiplier}}={\frac {{\text{Level}}_{\text{Character}}+100}{{\text{Level}}_{\text{Character}}+{\text{Level}}_{\text{Enemy}}+200}}\)

• In general this means that damage received is half (50%) of the attack power (also Incoming Damage used in the equations) at equal foe levels.
• The change in damage due to differences in level is relatively small, less than a 10% relative difference for a level difference of 20 (and far less at high levels).

For enemies with debuffed defense:

\( {\text{DEF Multiplier}}_{\text{(Debuffed)}}={\frac {{\text{Level}}_{\text{Character}}+100}{\left[1-\%{\text{ DEF Reduction}}\right]({\text{Level}}_{\text{Enemy}}+100)+{\text{Level}}_{\text{Character}}+100}}\)

Intermediate Equations

The DEF Multiplier formula from above:

Given the expression for damage reduction as:

\( {\text{DEF DMG Reduction}}={\frac {{\text{DEF}}_{\text{Enemy}}}{{\text{DEF}}_{\text{Enemy}}+5\times {\text{Level}}_{\text{Character}}+500}}\)

Plug in enemy defense to produce the damage reduction for enemies:

$$\begin{aligned} {\text{DEF DMG Reduction}}&={\frac {\left[5\times {\text{Level}}_{\text{Enemy}}+500\right]}{\left[5\times {\text{Level}}_{\text{Enemy}}+500\right]+5\times {\text{Level}}_{\text{Character}}+500}}\\ &={\frac {{\text{Level}}_{\text{Enemy}}+100}{{\text{Level}}_{\text{Enemy}}+100+{\text{Level}}_{\text{Character}}+100}}\\ &={\frac {{\text{Level}}_{\text{Enemy}}+100}{{\text{Level}}_{\text{Enemy}}+{\text{Level}}_{\text{Character}}+200}} \end{aligned}$$
Subtract the damage reduction from 1 to get a defense multiplier for incoming damage.

$$\begin{aligned} {\text{DEF Multiplier}}&=1-{\text{DEF DMG Reduction}} \\&=1-\left[{\frac {{\text{Level}}_{\text{Enemy}}+100}{{\text{Level}}_{\text{Enemy}}+{\text{Level}}_{\text{Character}}+200}}\right] \\&={\frac {{\text{Level}}_{\text{Character}}+100}{{\text{Level}}_{\text{Enemy}}+{\text{Level}}_{\text{Character}}+200}} \end{aligned}$$

File:Damage vs defense debuff graph.png

To consider debuffs that decrease an enemy's defense, multiply the enemy defense accordingly.

$$\begin{aligned} {\text{DEF}}_{\text{Enemy (Debuffed)}}&=(1-\%{\text{ DEF Reduction}})\times {\text{DEF}}_{\text{Enemy}}\\ {\text{DEF Multiplier}}_{\text{Enemy (Debuffed)}} &={\frac {{\text{Level}}_{\text{Character}}+100} {\left[1-\%{\text{ DEF Reduction}}\right]({\text{Level}}_{\text{Enemy}}+100)+{\text{Level}}_{\text{Character}}+100}} \end{aligned}$$