Asayre wrote: »

In the Thieves Guild update, the Scathing Mage set was buffed. In this post, I’ll compare Scathing Mage to Law of Julianos.

There are several approaches in determining when Scathing Mage is preferred over Julianos. I suggest looking at the number of attacks required to proc Scathing Mage. From there we can estimate the uptime of Scathing Mage and then it is a straightforward comparison to Julianos. I’ll show some example calculations based on my sorcerer.
The proc chance per attack with Scathing Mage is quite simplistically

Assuming that all attacks are independent we can model the resulting distribution of required attacks to proc Scathing Mage with a geometric distribution. In order to demonstrate that the geometric distribution is a suitable model I did some in-game testing. I counted the number of hits required to proc Scathing Mage. I only did 50 trials but I was reasonably convinced by the results. I trial here is defined as the number of hits needed to proc Scathing Mage. The image bellow summarises my in-game testing as well as the theoretical model. I was reasonably convinced with validity of the model despite the low number of trials.

The median of this distribution is

The median corresponds to the point where 50% of the time you’ll need less than X attacks to proc Scathing Mage and equivalently 50% of the time you’ll need more than X attacks to proc Scathing Mage. From this, it is reasonably straightforward to calculate the median amount of time required to proc Scathing Mage

From this the uptime of Scathing Mage is expected to be

where there is an implicit assumption that the internal cooldown of Scathing Mage is the duration of the proc, which is based on personal testing during the IC PTS. The effective spell damage of Scathing Mage is then

Or to simplify it in a single equation

Let us consider a magicka Sorcerer using the Thief mundus (6 pieces of Legendary divines) and with a precise staff. The spell critical of this character is 71.2% or 74.2% with Minor Prophecy active. I timed myself doing 50 Force Pulse/LA weaves and could do it in 1.16 seconds per weave or equivalently 3.45 attacks per second. Since this is probably close to the upper limit of attacks per second, I would estimate that the upper limit of the Scathing Mage 5 piece bonus for the magicka Sorcerer in question is

A more practical approach to estimating SM SD equivalence is by looking at a parse and determining the number of non-DoT attacks per second. In the example parse below, I estimate the number of non-Dot attacks to be 84 (Force Pulse + Crystal Fragments + Light Attack) which means that the number of non-DoT attacks in this example is 2.37 (parse duration 35.5s).

This is 97 SD greater than the 5 piece bonus of Julianos. Since this character has 43486 Max Magicka and 3189 Spell Damage, the 80 spell damage corresponds to an average tooltip damage increase of ~1.7%

So based on the example parse above, if I were to use Scathing Mage instead of Julianos I would expect a DPS increase of around 425 (1.7%*25000). There is a slight simplification here since Light Attacks depend more strongly on Spell Damage than abilities so in fact my Light Attacks will do more than 1.7% damage with Scathing Mage.
However most Sorcerers rely quite a bit on Overload so the SM SD equivalence during Overload needs to evaluated. The magicka Sorcerer is using Nirnhoned swords (Spell Critical of 64.2%) for Overload and does 0.862 non-Dot attacks per second

This is 38 SD less than the 5 piece of Julianos and corresponds to an average damage loss of ~0.6% during Overload or around 200 DPS (0.6%*32000).

During Overload, I use about 18 Ultimate per second. It takes 6 seconds of non-Overload time to generate 18 Ultimate. Thus on average Scathing Mage provides an increase of 336 DPS.

This is based on the assumption that you Overload all things equally.

To Precise or not?
An additional question that arises when using Scathing Mage is whether a Precise or Sharpened/Nirnhoned weapon should be used.
Percentage penetration can be converted into equivalent spell damage with the following equation

where the variables Mit_pen and Mit_Base are defined as

For simplicity, b is assumed to be 10.5. Using some typical values, 14% penetration (Sharpened) is worth about

Additional Spell Critical from Precise can be converted into equivalent spell damage with the following equation

Again using typical values, 7% Spell Critical (Precise) is worth about

This means that for mobs with 13k resistance which is a typical value for bosses debuffed with Major Breach, Sharpened/Nirnhoned is preferred over Precise. However, going with Precise will increase the uptime of Scathing Mage and the question is whether the increased uptime will compensate for the difference. Using my first parse with Force Pulse, the spell damage equivalence of Scathing Mage is expected to be 418 with a Sharpened Staff

While the spell damage equivalence with Precise is

Thus the average Spell Damage gain from using a Precise weapon with Scathing Mage compared to Sharpened is 9 base spell damage which is increased to around 11 by Major Sorcery and Expert Mage. However, the spell damage equivalent difference between Sharpened and Precise on a PvE monster with 13000 resistance is 93 which is larger thus a Sharpened weapon is still preferred even when Scathing Mage is used.