Elemental Gauge Theory/Advanced Mechanics

This page contains advanced mechanics related to elemental Auras, such as the calculation of the gauges and durations of special Auras created as a result of elemental reactions, and the behaviors of Self Auras.
==Aura Tax==
If an aura is created from an elemental attack, there will be an Aura Tax, which reduces 20% of the gauge.
\text{Gauges}_\text{Aura} = 0.8 \times \text{Gauges}_\text{Elemental Attack}
==Calculating Origin Aura Decay==
In the following sections, many calculations will involve the gauge of the Origin Aura at the moment of triggering a reaction, which should consider the aura's natural decay if it was applied by an external source. This step is not necessary for innate auras.
For calculating the gauge units of a decayed attack-inflicted aura, the following formula can be used:
:
\text{Gauge}_\text{Decayed Origin Aura} = (0.8 \times \text{Gauge}_\text{Origin Element}) \times (1 - \frac{\text{Time Between Applications of Origin and Trigger Elements}}{2.5 \times \text{Gauge}_\text{Origin Element} + 7})
Derivation of formula: this accounts for the aura tax (multiply by 0.8) and assumes linear decay of the initial aura for the time between Origin and Trigger application. {2.5 \times \text{Gauge}_\text{Origin Element} + 7} is the duration for attack-inflicted Origin Auras. Dividing the time between Origin and Trigger application by the duration gives the portion of the gauge depleted. The portion of the gauge remaining is 1 minus that (assuming a linear decay model).
==Swirl Elemental Application==
===Swirl Application Gauges===
There is a special feature for the gauges of swirl attack:
\text{Gauges}_\text{Swirl Attack} = (\text{Gauges}_\text{Reaction} - 0.04) \times 1.25 + 1
\text{Gauges}_\text{Reaction} =
 \begin{cases}
 \text{Gauges}_\text{Anemo} & \text{Gauges}_\text{Origin Aura} \ge 0.5 \times \text{Gauges}_\text{Anemo} \\
 \text{Gauges}_\text{Origin Aura} & \text{Gauges}_\text{Origin Aura} < 0.5 \times \text{Gauges}_\text{Anemo}
 \end{cases}
*Origin Aura means the Pyro/Hydro/Electro/Cryo aura considering the gauge decay.
As a regular elemental attack, Swirl-inflicted auras are affected by Aura Tax.
\text{Gauges}_\text{Swirl Aura} = 0.8 \times \text{Gauges}_\text{Swirl Attack}
===Swirl-Inflicted Aura Duration===
As a regular elemental attack, the duration for Swirl-inflicted auras follows the regular aura duration formula:
\text{Duration (Seconds)}_\text{Swirl Aura} = 2.5 \times \text{Gauges}_\text{Swirl Attack} + 7 
==Frozen==
The state created by the Frozen reaction is maintained by the Freeze Aura.
The Freeze Aura is a sibling aura to Cryo and Frozen, but it has certain special properties:
#Freeze doesn't react with Hydro
#An enemy with the Freeze Aura can be Shattered by Blunt or Geo attacks.
Note that the Freeze Aura is not the same as the regular Cryo aura or the Frozen aura caused by elemental shields or innate auras, and can coexist with them. Certain reaction priorities will be followed if another element is applied. See Elemental Gauge Theory/Simultaneous Reaction Priority for more details.
===Freeze Aura Gauges===
\text{Gauge}_\text{Freeze Aura} = 2 \times \text{Gauge}_\text{Reaction}
\text{Gauge}_\text{Reaction} =
\min(\text{Gauge}_\text{Origin Aura}, \text{Gauge}_\text{Trigger Element})
* Origin Aura means the Hydro or Cryo aura initially applied to the target. It considers the gauge decay.
===Freeze Aura Duration===
:\text{Freeze Duration (Seconds)} = 2\sqrt{5\times \text{Gauge}_\text{Freeze Aura} \times (1 - \text{Freeze Resistance}_\text{Target}) + 4} - 4
====Freeze Resistance====
Freeze Resistance reduces the Freeze Aura's duration. Currently, the following enemies have Freeze Resistance:
* (While Shielded): 80%
* (Revival Phase): 40%
* : 80%
* : 50%
* Most Land Local Legends: 90%
===Blunt Attack Poise DMG Cost===
When a target with the Freeze Aura is hit by a Blunt Attack, it will reduce the Freeze Aura's gauge based on a convesion ratio of 0.006U Per Poise DMG. For example, the hold version of Razor's Elemental Skill, which deals 300 Poise DMG, will consume 1.8U from the Freeze Aura.
After this consumption has been applied, if there is still leftover Freeze Aura, Shatter will trigger.
===Shatter===
When a target with the Freeze Aura is hit by a Blunt or attack, Shatter will be triggered.
Note that the shatter check occurs after the Poise DMG Cost has been applied. If the Freeze Aura is fully depleted through Poise DMG Cost, Shatter will not trigger.
When Shatter occurs, the gauge of Freeze Aura will decrease by 8. When the Freeze Aura gauge hits 0, the target will no longer be frozen.
\text{Gauge}_\text{Freeze Aura} =
(\text{Initial Gauge}_\text{Freeze Aura} - 8)_+
* The + denotes the positive part of the expression (it is 0 if the expression is non-positive).
* Initial Gauge considers the gauge decay.
==Quicken==
The Quicken Aura is applied by triggering the Quicken reaction that decays over time. The Quicken Aura can react with and be consumed by and .
Applying Electro or Dendro on a Quicken Aura will trigger Aggravate or Spread which add Additive Base DMG Bonus to the attacks that trigger them. However, this does not consume the Quicken Aura.
The Quicken Aura can coexist with Electro and Dendro auras. Certain reaction priorities will be followed if another element is applied. See Elemental Gauge Theory/Simultaneous Reaction Priority for more details.
===Quicken Aura Gauges===
\text{Gauge}_\text{Quicken Aura} = \min(\text{Gauge}_\text{Origin Aura}, \text{Gauge}_\text{Trigger Element})
===Quicken Aura Duration===
\text{Duration (Seconds)}_\text{Quicken Aura} = \text{Gauge}_\text{Quicken Aura} \times 5 + 6
If Quicken is triggered again on a target with an existing Quicken aura:
* If the resulting Quicken Aura has a higher gauge than the remaining Quicken Aura, the resulting Quicken Aura will replace the existing one, and the duration and decay rate will be recalculated based on the new Quicken gauge.
* If the resulting Quicken Aura has a lower gauge than the remaining Quicken Aura, the existing aura will not change.
==Electro-Charged==
Shock is a state created by Electro-Charged. Shock is maintained by Electro Aura and Hydro Aura. Once one of auras is depleted, the shock state will not exist.
During the Shock state, Electro and Hydro will coexist and decay at their regular rates. Certain reaction priorities will be followed if a third element is applied. See Elemental Gauge Theory/Simultaneous Reaction Priority for more details.
===Special Decay===
Besides the normal decaying, there is a special decaying for both auras in Shock State. Both auras will lose 0.4U gauges per tick of DoT.
==Burning==
The Burning reaction produces a 2U Burning Aura (unaffected by Aura Tax) regardless of the gauges of Pyro/Dendro used to trigger it, which can react with and be consumed by Hydro/Electro/Anemo/Geo. The Burning Aura does not decay.
While Burning, all three auras will coexist. The Burning state appears to require both the Burning Aura and the Dendro Aura to maintain, and will end if either is depleted. If the Dendro Aura is depleted, the Burning Aura will be automatically removed. Note that the Pyro Aura is not required for maintaining Burning: Depleting the Underlying Pyro Aura without depleting the Burning Aura will not extinguish the Burning state, and it is possible to extinguish the Burning state without removing the Pyro Aura.
Burning DMG also applies 1U of Pyro. This application follows an Internal Cooldown of 2 seconds.
===Burning Refresh===
While a target is already in the Burning state, if Dendro or Pyro is applied again:
* The Burning Aura will not be altered.
* Burning DMG from this point on will be calculated based on the stats of the character responsible for the latest instance of Dendro or Pyro application.
* If Dendro is reapplied, the new Dendro gauge will overwrite the existing aura, even if the existing aura has a higher gauge.
===Special Decay===
While Burning, the Pyro aura will decay at its regular rate, while the Dendro Aura will be consumed at a special rate and will not use natural decay.
The special Dendro consumption rate (gauge units/second) is:
:
\text{Dendro Consumption} = \max(0.4, \text{Natural Decay Rate}_\text{Dendro Aura} \times 2)
==Self Aura==
Self Auras or Elemental Effect Auras refer to elements applied to a target without an elemental attack. These include the Pyro Aura from Bennett's Burst, the Hydro Aura from water, the Cryo Aura from Condensed Ice, etc. Elemental Shields used by enemies are also a form of Self Aura.
These auras have some different features from the auras of elemental attacks:
# Their decay rates are fixed and are not determined by gauges.
# Some self auras may not decay at all, like the auras from most Elemental Shields and Elemental Nodes.
# There is no Aura Tax on them.
Moreover:
* When a self aura application triggers a reaction, if it has a higher gauge unit value than the existing aura, excess gauges will not be lost, and the aura will transition directly to the self aura.
* Self Auras can serve as sources for Elemental Absorption.
Below is a non-exhaustive list of Self Auras:
Source 	Element	Gauge Units 	Duration (Seconds)
 	 	1 	0.2
 	 	1 	0.1
Dendro Field 	 	1.6 	8
Toxic Seeds 	 	4 	5
Electro Seelie 	 	4 	10
Thunder Sphere 	 	2.4 	10
ThunderwoodApplies a status lasting 10 seconds that applies Electro every second.	 	1 	2
Electro Mark 	 	1 	∞GU does not decay, but is forcibly removed when the mark's duration ends.
Electro Riptide Mark 	 	2 	∞
 	 	1 	2.1
 	 	1 	2
Cryo Mark 	 	1 	∞
 	 	2 	0.1
 	 	1 	0.1
Pyro Mark 	 	1 	∞
Arena Barrier 	 	2 	0.5
 	 	1 	1
 	 	1 	2.1
 	 	1 	1
 	 	1 	0.2
Water 	 	0.4–2Increases by 0.4GU every 0.25s, maximum 2GU. 	8
Rain 	 	0–1.2Increases by 0.32GU every 0.5s, maximum 1.2GU; Aura will remain even if Hydro GU is fully consumed.	15Forcibly removed when exiting rain.
Hydro Amber 	 	1 	3
Hydro Mark 	 	1 	∞
Hydro Riptide Mark 	 	1 	∞
Soothing Rain 	 	2 	8
application to nearby targets when attacked 	 	1 	10
application to nearby targets when attacked 	 	2 	10
 	 	1 	0.5
 	 	1 	0.5
 	 	1 	0.2
 	 	1 	0.3
idle animation 	 	1 	2.5If idle animation is not interrupted, reapplies once every 2s, up to 3 times.
Note that Dori's self Electro application is special and not a Self Aura. Instead, it is an elemental attack on the active character, which is affected by Aura Tax and uses standard decay.
==Weapon Aura==
Weapon Auras are applied to Swords, Claymores, and Polearms in the process of Elemental Infusions. They have similar properties to Self Auras.
==Immutable Aura==
Some enemies or objects can have an immutable aura. Immutable auras cannot be consumed by Elemental Reactions, but still have a set gauge unit value that will be taken into account when triggering Elemental Reactions.
When an element is applied to a target with an immutable aura, if the applied element still has leftover gauge units after reacting with the immutable aura, the remaining gauge units can continue to react with a coexisting aura, while the immutable aura stays unaffected.
For example, if coexists with a 2U immutable aura on a Cryo Slime, and 4U of is applied using Beidou's Elemental Burst, 2U of the applied Electro will be consumed first to cause Superconduct with the immutable Frozen aura, and the remaining 2U Electro will continue to react with the underlying Dendro aura to cause Quicken. However, the same will not occur on a Cryo Hypostasis, as it has a higher 4U immutable Frozen aura, which will fully consume the Electro applied and prevent further reactions with underlying Dendro.
 Immutable Aura Data
Source 	Element	Gauge Units
Water Bodies 	 	3.2
Petrification Geo Aura 	 	0.04
Innate Aura 	 	2
Innate Aura 	 	1
Innate Aura 	 	2
Infused State Innate Aura	/// 	4
Exposed Core Innate Aura 	 	4
Exposed Core Innate Aura 	 	4
Exposed Core Innate Aura 	 	4
Exposed Core Innate Aura 	 	4
Exposed Core Innate Aura 	 	4
Exposed Core Innate Aura 	 	1
Innate Aura 	 	4
Parts While Repairing 	 	4
Innate Aura 	 	4
Innate Aura 	 	4
Innate Aura 	 	4
Innate Aura 	 	4
Innate Aura 	 	1
==Reaction Coefficient Exceptions==
When certain special states are activated, such as Fatui Skirmishers' elemental shields, Reaction Coefficients may change. This may also include reactions that do not involve the shield's element.
The following tables list the special Reaction Coefficients under different special states. Reactions not listed either retain their normal Reaction Coefficients, or are impossible to trigger.
 Shielded State
Reaction Type 	Special Reaction Coefficient
Cryo SwirlCryo CrystallizeElectro Superconduct 	0.1
Hydro SwirlHydro CrystallizeHydro BloomDendro BloomPyro Vaporize	1
 Shielded State
Reaction Type 	Special Reaction Coefficient
Electro SwirlElectro CrystallizePyro OverloadedDendro Quicken	0.1
Cryo Superconduct 	2
Hydro BloomDendro Bloom 	1
 Shielded State
Reaction Type 	Special Reaction Coefficient
Hydro SwirlHydro CrystallizePyro VaporizeCryo FrozenDendro Bloom	0.05
Electro SwirlElectro CrystallizePyro Melt 	1
 Shielded State
Reaction Type 	Special Reaction Coefficient
Pyro SwirlPyro CrystallizeElectro OverloadedCryo Melt	0.1
For example, if 1.6U of is applied onto a Cryogunner Legionnaire's shield to coexist with the element, then 1U of is applied, the Dendro application will not be able to fully clear the Hydro aura, as the reaction coefficient for Dendro Bloom under the effect of the Cryogunner's shield is 1, instead of the usual 2.
==Notes==
Category:Elemental Gauge Theory
vi:Thuyết Định Lượng Nguyên Tố/Cơ Chế Nâng Cao