Lets figure out how our total DPS will change when one skill damage output changes. Check the ESO rotation choice article to recall the denotations and formulas.
General case
List of denotations
- $N$ - number of different sources of damage
- $X$ - amount of parse dummy target health points
- $T_a$ - time required to kill dummy target with the first skill version
- $T_b$ - time required to kill dummy target with the second skill version
- $R_a=X/T_a$ - summary damage per second (dps) with the first skill version
- $R_b=X/T_b$ - summary damage per second (dps) with the second skill version
Initial scenario math
$X_i$ will be the amount of damage caused by a separate i-th source. $R_i$ will be DPS of a separate i-th source.
\[X=\sum_{i=1}^{N} X_i\] \[X_i=R_i T_a\] \[X=\sum_{i=1}^{N} R_i T_a = T_a \sum_{i=1}^{N} R_i\] \[R_a=\sum_{i=1}^{N} R_i\]Let’s assume that our changing skill has index 1, so:
\[R_a=R_1 + \sum_{i=2}^{N} R_i\]Let’s denote that summ as $R_s$:
\[R_s=\sum_{i=2}^{N} R_i\] \[R_a=R_1+R_s\]Target scenario
DPS of a single skill (we’ve chosen it as the first skill) changes. Time required to kill dummy target changes to $T_b$.
\[X=\sum_{i=1}^{N} Y_i\] \[Y_i=R_{i}^{*} T_b\] \[X=\sum_{i=1}^{N} R_{i}^{*} T_b = T_b \sum_{i=1}^{N} R_{i}^{*}\] \[R_b=\sum_{i=1}^{N} R_{i}^{*}\]As we set peviously, only first skill DPS changes, so:
\[R_{i}^{*}=R_i, \quad\text{$\nabla i \in [2,N]$}\]And taking into account initial scenario:
\[R_b = R_{1}^{*} + R_s\]Let’s assume that skill damage output increases in $K$ times, so:
\[\frac{R_{1}^{*}}{R_1}=K\]So our formula will be:
\[\begin{cases} R_a = R_1 + R_s \\ R_b = K R_1 + R_s \end{cases} \tag{1}\label{1}\]As we get our parse log we have contribution of each damage source as fractional part.
\[\frac{X_i}{X}=\frac{R_i}{R_a}=f_i\]We need only the first (changing) skill fractional part contribution $f$:
\[\frac{R_1}{R_a}=f\] \[\frac{R_s}{R_a}=1-f\] \[\begin{cases} R_1=f R_a \\ R_s=(1-f) R_a \end{cases} \tag{2}\label{2}\]Push results into the $\eqref{1}$:
\[R_b = K f R_a + (1-f) R_a\] \[\frac{R_b}{R_a}=1+(K-1)f \tag{3}\label{3}\]There are two cases:
1) Skill damage increases, $K>1$ 2) Skill damage decreases, $K<1$
Our practical research
As we get from PTS (public test server) patch notes, the arcanist skill Cephaliarch’s Flail will lose execute capability after game update 43.
Skill DPS change calculation
- $D_1$ - skill damage before change
- $D_2$ - skill damage after change
Base skill damage:
\[D_{base} = D n\]Skill with execute damage increase:
\[D_{exec} = D \frac{n}{2} + \frac{3}{2} D \frac{n}{2} = \frac{5}{4} D n\]As in upcoming update there will be no execute component, DPS change will be
\[\frac{D_2}{D_1}=\frac{D_{base}}{D_{exec}}=\frac{4}{5}\] \[K=\frac{4}{5} \tag{4}\label{4}\]Summary DPS change calculation
According to typical arcanist parsers, Cephaliarch’s Flail has 7.6% of total damage output, so $f$ will be:
\[f=0.076 \tag{5}\label{5}\]So let’s put equations $\eqref{4}$ and $\eqref{5}$ into $\eqref{3}$:
\[\frac{R_b}{R_a}=1+(K-1)f=0.9848\]With typical arcanist parser DPS of 130k, the DPS after update 43 will be 128k. So DPS loss will be 2k. That’s not critical. Arcanist still will rock! :)