Damage Calculation

Process

Damage calculations in Dark Souls generally follow a simple pattern, where only the number and value of components varies by context. In general, to determine the Damage of an attack:

  1. A product is taken of different factors relating to physical or a specific elemental damage type
  2. Defense Calculations occurs using the above determined product and the opponent's defense, using the function described below
  3. The determined Damage is again multiplied with any applicable factors
  4. This process is repeated for all damage types and the sum of them is the final damage

One may also consider the inclusion of an earlier step, in which AR, Magic Adjustment or Physical Adjustment is determined. This would include the weapon base AR, upgrade multipliers and its Scaling, as well as miscellaneous thing such as the Gauntlets of Thorns effect on fist weapons.

Motion Values

"Motion Value" (MV) is a wider Video-Game term. In the case of Dark Souls, it refers to a multiplier every attack of each weapon and every spell has, that is applied before the Defense Calculation, that allows the developers to differentiate attacks in their damage potential. These are often given in their percent value1, e.g. almost all one-handed light attack have an MV of 100, a 1x multiplier, two-handed light-attacks have an MV of 120, a 1.2x multiplier, and two-handed jumping attacks an MV or 155, a 1.55x multiplier.

Due to the behavior of the Damage Function (Defense Calculation below), a multiplier on AR always results in a greater multiplier on the resulting Damage, which is not constant, e.g. depending on AR and Defense a two-handed light-attack will have a multiplier of 1.2, but might deal 1.3x to 1.4x more damage for a Katana.
As another consequence of the function, identical MVs will have a lesser multiplicative effect for attacks with higher AR, as such a two-handed light-attack of a Dagger might instead deal 1.6x more Damage.

A comprehensive list of motion values can be found here.

Defense Calculation

(1)
\begin{align} \textrm{DMG} =\, \begin{Bmatrix} \textrm{Atk}\cdot0.1 & \textrm{Atk}\leq\frac{1}{8}\cdot \textrm{Def} \\ \textrm{Atk}\cdot\left(\frac{19.2}{49}\cdot \left(\frac{\textrm{Atk}} {\textrm{Def}}-0.125\right)^2+0.1\right) &\textrm{Atk}\leq 1\cdot \textrm{Def}\\ \textrm{Atk} \cdot\left(\frac{-0.4}{3}\cdot \left(\frac{\textrm{Atk}} {\textrm{Def}}-2.5\right)^2+0.7\right) & \textrm{Atk}\leq2.5\cdot\textrm{Def}\\ \textrm{Atk}\cdot\left(\frac{-0.8}{121}\cdot\left(\frac{\textrm{Atk}}{\textrm{Def}} -8\right)^2+0.9\right) & \textrm{Atk}\leq8\cdot\textrm{Def}\\ \textrm{Atk}\cdot0.9 & \textrm{Atk}\geq8\cdot\textrm{Def}\\ \end{Bmatrix} \end{align}

Where DMG is only the unmodified, partial damage after defense calculations, Atk is result of step 2 and Def is the Defense of the Damage taking target (e.g. fire defense, thrust defense if the attack is physical and of that attack type etc.).23

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