The theory of Electro-charged procs GU consumption and a unified shield theory

This is an attempt to explain a number of inconsistencies regarding Electro-charged reaction shields and armor breaking capabilities.

First, what we know so far about Abyss shields and Fatui armor. The table below has Gauge Unit values listed required to break the shield from the corresponding elemental reactions. For example, 12U Pyro vs Hydro shield means it requires 6 Amber charged shots (each has 2U value) on the Hydro shield (resulting in Vaporize reactions) or 12 Xiangling Guoba (1U each) Vaporize procs. 6U Pyro vs Cryo shield requires 3 Amber shots or 6 Guoba attacks.

EDIT: there were some inaccurate values in the table below. Please refer to this table for accurate values
https://docs.google.com/spreadsheets/d/1GZHd0eLAv8364QKnwtUpraqWmKipXeWQ7S-lsgi69hw/edit?usp=sharing

As we can see, all elements and shields line up with each other pretty nicely. All the data (excluding EC reaction) suggests that all Abyss mage shields have exact same GU values vs all reactions (excluding Freeze vs Cryo Abyss mage). Vaporize/Melt reactions are known to have a mechanic that multiplies GU values by 2 which explains the Hydro vs Pyro and Pyro vs Cryo lower GU values. So in fact, Abyss mages have shield durability of 12U. Note: this is not the case for Fatui armor. There is no multiplication going on. 2U Kaeya’s Es destroy Electro Fatui armor, 2U Amber’s charged shots destroy Cryo Fatui armor.

Electro-charged reaction seems to work a bit differently and inconsistently. 1U of Electro application results in 2EC procs which suggests that EC procs consume 0.5U each tick. However, it takes 10 EC procs to take down the Fatui Hydro armor which suggests that EC procs consume 0.4U. As for the shields, sometimes it takes 26 EC procs (with a total of 13U Electro applied to it) to take down the Abyss mage shield, sometimes it takes up to 30 EC procs (with a total of 15U Electro applied to it).

The evidence:

• Lvl 70 Lisa with lvl 1 weapon, no artifacts and lvl 2 normal attack talent results in a total 26 EC procs: https://streamable.com/f7hv46
• Lvl 30 Beidou with lvl 1 weapon, no artifacts and lvl 1 elemental skill results in a total 30 EC procs: https://streamable.com/3y9n7z 

The explanation for the difference in the number of EC procs seems to be the difference in damage they deal.

Now, here we assume that each EC damage proc does two things at the same time: 1) Deals a certain amount of % HP damage corresponding to a certain amount of GU consumption; 2) Deals EC damage directly to the shield corresponding to level and EM of the character.

Additional evidence:

• Lvl 80 fully geared Kaeya destroys Pyro shield with 10 Es: https://streamable.com/suebyx
• Lvl 80 ungeared Kaeya destroys Pyro shield with 12 Es: https://streamable.com/xhwhr1

From here we will assume that 30 EC ticks indeed correspond to the total shield durability since Beidou does minimal damage to the shield. Here is the spreadsheet with some additional calculations and estimation of the total HP of the WL6 Abyss mage:

https://docs.google.com/spreadsheets/d/167gv0GWLu5HFLGCXZW3mBY0S2nimPv3dm5mGsxSiJME/edit?usp=sharing

Now, the fact that it takes 30 EC ticks to destroy a shield suggests that each EC tick consumes 12/30 = 0.4U. This correlates with the data that Fatui Hydro armor requires 10 ticks to destroy it (4/10 = 0.4U).

The problem is that 0.4U per tick may suggest that there have to be 3 ticks instead of 2 when you apply 1U Electro to the Hydro shield since after two ticks there is still 0.2U left to consume. The same goes for 0.4U left after 4 ticks of 2U application and 1.2U left after 7 ticks of 4U application.

In order to explain this, let’s take at the graph provided by BowlSoldier#3528 with some additional graphs by me to model what exactly happens each time an EC tick occurs.

https://www.desmos.com/calculator/bebuiwuqt0

The decay rate depends on the GU value of the first aura applied to the target. The problem is that we don’t actually know the GU value of the shield/armor since it stays on the target until it destroys. We may be able to measure it precisely by applying an Electro aura and measuring the time it stays on the enemy (taking into consideration EC ticks consumption) but for now we will consider 3 possibilities: 1U, 2U and 4U decay rate. Note that there might be a different decay rate that we don’t know of yet.

How to use the graphs:

• Click on the folder graph to show all the lines for this case
• Green, red and purple graphs are the dependence of the elemental gauge left on time.
• The horizontal black dash lines represent EC ticks GU consumptions. For example, at t = 0 the first EC tick consumes 0.4U which is represented by the line y = 1 - 0.4
• The vertical black dash lines represent the GU natural decay that occurs in 1 second between two EC ticks. For example, to plot the first line in the image, we found the intersection of the last horizontal line (y = 1 - 0.4) with the red graph; the intersection is (1.725, 0.6). Then the equation for the line is x = 1.725 + 1.
• The next horizontal line is found by looking at the intersection of the last vertical line (x = 1.725 + 1) with the red graph; the intersection is (2.725, 0.4596). Then the equation for the line is y = 0.4596 - 0.4.
• We continue until all gauge is depleted. In the example, we stop right here at the second EC tick. As we can see, the graph reaches zero in the next second. In order to account for the phenomenon of an early EC tick (which happens if gauge is depleted between 0.5 and 1 seconds), we plot an additional line representing 0.5 seconds passed. In the example this line is x = 5.725 + 0.5. Here we can see that the gauge is depleted before 0.5 seconds has passed which means that 3rd EC tick should not occur.

I have made the demos for all 3 cases of GU decay rates and all 3 cases of GU application, 9 demos in total. Here is the result of the analysis:

Both 2U and 4U decay rates explain the evidence we have on the number of EC ticks observed depending on the strength of GU applied. Even though from this analysis we can’t determine the GU rate of the shields, the most important point is that the theory that EC ticks consumption is 0.4U is valid (with the assumption that these decay rate graphs are true).