Toughness

Toughness is an enemy-only stat in Honkai: Star Rail.
In combat, the Toughness gauge is displayed above the HP gauge of enemies. It can be reduced by attacks of a Type that the enemy is weak to. Once fully depleted, the enemy will suffer a Weakness Break which has the following effects:
* Deals an instance of Break DMG
* Delays the enemy's action by 25%
* Has a 150% base chance to apply a debuff corresponding to the Type used to inflict Weakness Break
* Enters the Weakness Broken state
In the enemy's next turn, they will recover from the Weakness Broken state and fully restores their Toughness gauge.
As long as the enemy is not Weakness Broken, all incoming DMG will be multiplied by 0.9, including the Break DMG from Toughness depletion.
==Multi-Layered Toughness==
Some enemies have multiple Toughness Bars. Fully depleting any Toughness Bar before the final one will only deal Break DMG without any other Weakness Break effects (action delay, Type-specific debuffs, entering the Weakness Broken state).
==Exo-Toughness==
Exo-Toughness is an additional Toughness bar applied by certain effects, appearing as a purple bar behind the initial white Toughness. The initial Toughness needs to be depleted first (which triggers Weakness Break effects) before the Exo-Toughness can be reduced. Then, the Exo-Toughness can be reduced with any Type of attack regardless of Weaknesses, triggering Weakness Break again if depleted, which is equal to when depleting the original Toughness. Like the original Toughness, the Exo-Toughness can only be depleted once before recovering from Weakness Break.
==Toughness Value and Reduction==
Different enemies have varying amounts of Toughness. The base Toughness value of most enemies is a multiple of 10, with the exception of some enemies with modified Toughness value in a certain phase. Sometimes, 10 Toughness Reduction on display is also referred to as 1 Toughness Unit.
Different character skills will also deal varying amounts of Toughness Reduction. Currently, characters may deal 2, 2.5, 3.333..., 5, 10, 15, 20, 30 or 40 Toughness Reduction with their attacks.
Attacking an enemy in the overworld will deal 10 Toughness Reduction to all enemies weak to that attack's type upon entering battle. Certain Techniques can attack the enemy in the overworld and deal 20 Toughness Reduction to all enemies weak to that attack's type upon entering battle.
Some enemies have the ability to make themselves immune to Toughness Reduction.
===Toughness Reduction Formula===
For calculating Toughness Reduction:
\begin{align} \text{Toughness Reduction} ={} & \text{Base Toughness Reduction} \times (1 + \text{Toughness Reduction Increase}) \\ & \times (1 + \text{Weakness Break Efficiency} + \text{Toughness Vulnerability}) \end{align}
Note that currently Weakness Break Efficiency has a cap of 200%.
==Weakness Break==
===Type-Specific Effects===
Depending on the Type that caused the Weakness Break, the Base DMG of the Break DMG and the debuff applied will differ:
\text{Max Toughness Multiplier} = 0.5 + \frac{\text{Max Toughness}_\text{Target}}{40}
 Break Properties
Type 	Break Base DMG 	Applied Debuff
Physical 	2 \times \text{Level Multiplier} \times \text{Max Toughness Multiplier}_\text{Target} 	Bleed
Fire 	2 \times \text{Level Multiplier} \times \text{Max Toughness Multiplier}_\text{Target} 	Burn
Ice 	1 \times \text{Level Multiplier} \times \text{Max Toughness Multiplier}_\text{Target} 	Freeze
Lightning	1 \times \text{Level Multiplier} \times \text{Max Toughness Multiplier}_\text{Target} 	Shock
Wind 	1.5 \times \text{Level Multiplier} \times \text{Max Toughness Multiplier}_\text{Target}	Wind Shear
Quantum 	0.5 \times \text{Level Multiplier} \times \text{Max Toughness Multiplier}_\text{Target}	Entanglement
Imaginary	0.5 \times \text{Level Multiplier} \times \text{Max Toughness Multiplier}_\text{Target}	Imprisonment
 Debuff Properties
Debuff 	Debuff Base DMG 	Turns	Additional Effects 	Is DoT
Bleed 	Normal: 0.16 \times \text{Max HP}_\text{Target}Elite/Boss: 0.07 \times \text{Max HP}_\text{Target} 	2 	There is a max cap for Bleed Base DMG:2 \times \text{Level Multiplier} \times \text{Max Toughness Multiplier}_\text{Target}	
Burn 	1 \times \text{Level Multiplier} 	2 	— 	
Freeze 	1 \times \text{Level Multiplier} 	1 	Upon unfreezing, skips the target's current turn but advances their next turn forward by 50% 	
Shock 	2 \times \text{Level Multiplier} 	2 	— 	
Wind Shear 	1 \times \text{Stack Count} \times \text{Level Multiplier} 	2 	Applies 1 stack to Normal, 3 stacks to Elite/Boss Enemies (Max 5 Stacks) 	
Entanglement	\begin{align} & 0.6 \times \text{Stack Count} \times \text{Level Multiplier} \\ & \times \text{Max Toughness Multiplier}_\text{Target} \end{align}	1 	Delays action by 20 \% \times (1 + \text{Break Effect})Applies 1 stack when the Entangled target is hit (Max 5 Stacks) 	
Imprisonment	— 	1 	Delays action by 30 \% \times (1 + \text{Break Effect})Reduces the speed of the Imprisoned target by 10% 	—
===Damage Formula===
For calculating Break DMG, DoT, and Delayed DMG caused by Weakness Breaks:
\begin{align} \text{DMG} ={} & \text{Base DMG} \times \text{Ability Multiplier} \times (1 + \text{Break Effect}) \\ & \times \text{DEF Multiplier}_\text{Target} \times \text{RES Multiplier}_\text{Target} \\ & \times \text{Vulnerability Multiplier}_\text{Target} \times \text{DMG Mitigation Multiplier}_\text{Target} \\ & \times \text{Broken Multiplier}_\text{Target} \end{align}
Where:
\text{Ability Multiplier} = \begin{cases}
\text{Ability Attribute} & \text{if specified}\\
100% & \text{if not specified}\\
\end{cases}
\text{DEF Multiplier} = \frac{\text{Level}_\text{Attacker} + 20}{(\text{Level}_\text{Enemy} + 20) \times (1 - \% \text{DEF Reduction} - \% \text{DEF Ignore}) + \text{Level}_\text{Attacker} + 20}
\text{RES Multiplier} = 1 - (\text{RES}_\text{Target} - \text{RES PEN}_\text{Attacker})
\begin{align} \text{Vulnerability Multiplier} ={} & 1 + \text{Type Vulnerability} + \text{All Type Vulnerability} \\ & + \text{Break DMG Vulnerability} + \text{DoT Vulnerability} \end{align}
\begin{align} \text{DMG Mitigation Multiplier}_\text{Total} ={} & (1 - \text{DMG Mitigation}_\text{1}) \times (1 - \text{DMG Mitigation}_\text{2}) \\ & \times (1 - \text{DMG Mitigation}_\text{3}) \times \text{. . .} \end{align}
\text{Broken Multiplier} = \begin{cases}
0.9 & \text{if enemy has Toughness (affects Toughness depletion Break DMG)}\\
1.0 & \text{if enemy Toughness is broken}\\
\end{cases}
Break-related DMG is also not affected by Weaken.
====Super Break DMG====
Super Break DMG is a special variation of Break DMG dealt by certain abilities. Super Break DMG is dealt only when enemy targets are attacked in the Weakness Broken state, and the Toughness Reduction of hits dealt in the Weakness Broken state will be converted into 1 instance of Super Break DMG.
For calculating Super Break DMG:
\begin{align} \text{Super Break DMG} ={} & \text{Level Multiplier} \times \frac{\text{Toughness Reduction}}{\text{10}} \times \text{Ability Multiplier} \\ & \times (1 + \text{Break Effect}) \times (1 + \text{Super Break DMG Increase})\\ & \times \text{DEF Multiplier}_\text{Target} \times \text{RES Multiplier}_\text{Target} \\ & \times \text{Vulnerability Multiplier}_\text{Target} \times \text{DMG Mitigation Multiplier}_\text{Target} \end{align}
===Level Multiplier===
Level Multiplier is determined by the attacker's level (Level 81 to Level 95 stats are enemy-exclusive when their Weakness is Broken due to non-character effects):
Level	Level Multiplier
1 	54.0000
2 	58.0000
3 	62.0000
4 	67.5264
5 	70.5094
6 	73.5228
7 	76.5660
8 	79.6385
9 	82.7395
10 	85.8684
11 	91.4944
12 	97.0680
13 	102.5892
14 	108.0579
15 	113.4743
16 	118.8383
17 	124.1499
18 	129.4091
19 	134.6159
20 	139.7703
21 	149.3323
22 	158.8011
23 	168.1768
24 	177.4594
25 	186.6489
26 	195.7452
27 	204.7484
Level	Level Multiplier
28 	213.6585
29 	222.4754
30 	231.1992
31 	246.4276
32 	261.1810
33 	275.4733
34 	289.3179
35 	302.7275
36 	315.7144
37 	328.2905
38 	340.4671
39 	352.2554
40 	363.6658
41 	408.1240
42 	451.7883
43 	494.6798
44 	536.8188
45 	578.2249
46 	618.9172
47 	658.9138
48 	698.2325
49 	736.8905
50 	774.9041
51 	871.0599
52 	964.8705
53 	1056.4206
54 	1145.7910
Level	Level Multiplier
55 	1233.0585
56 	1318.2965
57 	1401.5750
58 	1482.9608
59 	1562.5178
60 	1640.3068
61 	1752.3215
62 	1861.9011
63 	1969.1242
64 	2074.0659
65 	2176.7983
66 	2277.3904
67 	2375.9085
68 	2472.4160
69 	2566.9739
70 	2659.6406
71 	2780.3044
72 	2898.6022
73 	3014.6029
74 	3128.3729
75 	3239.9758
76 	3349.4730
77 	3456.9236
78 	3562.3843
79 	3665.9099
80 	3767.5533
Level	Level Multiplier
81 	3957.8618
82 	4155.2118
83 	4359.8638
84 	4572.0878
85 	4792.1641
86 	5020.3833
87 	5257.0466
88 	5502.4664
89 	5756.9667
90 	6020.8836
91 	6294.5654
92 	6578.3734
93 	6872.6823
94 	7177.8806
95 	7494.3713
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