Damage, Critical Hit, Defense/HP Balance Calculations

[Zanémarossi]

This topic incorporates elements from articles published on the old forum. A few elements have been added.

 

Thanks to the players who contributed to these previous articles: Solemnwolf, Guvnor, Yelnats24

Thanks to the players who helped update and proofread this thread: Fox, Maryj, Heyalexa

 

1. Damage Calculation

Author: SolemnWolf
Date: May 2018

After several months of statistical analysis of Raid and Alliance War battles, the conclusion is clear: **damage can be estimated using an Attack/Defense ratio combined with a power function.**

  A. The Formula

The general estimation for damage follows this equation:

B. Key Variables & Adjustments

Damage ≈ 100 x ( θ x Att / Def ) ^ 1.35

Tile damage is divided by three
The defense of the team managed by the AI is increased by 20% (certainly only concerns PvP fights)
θ is a random parameter between exp(-.5)=0.606 and exp(.5)=1.649.

C. Analysis & Observations

While the game's exact internal algorithm remains hidden, these estimates proved reliable across 1,047 studied cases. Here are the strategic takeaways:

The "Compression" Threshold

- If Attack < Defense: 
Damage is "compressed." Tiles will generally deal between 1 and 33 damage, while Special Skills and defender hits range between 1 and 100.
- If Attack > Defense: 
Damage scales significantly with no known maximum.
This explains the "plateau" feeling on the Map or against Titans. Once your heroes evolve enough for their Attack to surpass the enemy Defense, the difficulty drops sharply.

Multi-Color Stacking

Bringing multiple heroes of the same color only increases tile damage.
This is calculated by summing the Attack stats of all heroes of that color before applying the formula.

Strategic Optimization

Defense reduction (debuffing the enemy) is mathematically more effective than increasing your own Attack.

The Ultimate Combo: Combining defense debuffs with attack buffs produces a devastating exponential effect on total damage.

D. Documents

• Watch SpyCenturion's explanatory video on damage calculation (November 2019):

 2. Critical Damage

Original Author: Guvnor 
March 2020
Updated: January 2026

Critical damage is the most powerful lever to boost your offensive output without relying solely on your raw attack stat.

A. What is a Critical Hit?

A critical hit is an amplified attack. Since the 2025-2026 updates, they apply to three distinct categories:

• Normal Attacks: Includes tile damage (shields) when attacking and "Slash Attacks" from defenders.
• Mega-Minions: Unlike standard small minions, Mega-Minions now inherit the ability to land critical hits.
• Specific Special Skills: Historically excluded, some recent heroes possess skills capable of triggering critical hits directly.

B. Multiplier and Base Odds

• Base Chance: Since January 2025, all heroes benefit from a 10% base critical hit rate.
• The Multiplier: A critical hit applies a 2.0x multiplier to the base damage (doubling the impact).
• Strong Hit (Elemental): A 200 damage hit will become 300.
• Weak Hit: A 50 damage hit will become 150.
• Weak Spot (Titans): Hitting a Titan's weak spot guarantees a 100% critical chance.

C. Sources to Increase Critical Chance

Special Skills (Active Buffs)
Many heroes apply a temporary bonus to the team via the activation of their special skill as:

• Motsognir: +55% chance.
• Char'kai C1: +44% chance.
• Melia: +36% chance.

Passives (including Family Bonuses)
These bonuses are intrinsic to the heroes or their group. They are added to your stats without requiring the activation of a special skill:

• Untold Tales 1 (Abyss/Coral): Passives that increase the critical rate based on specific combat conditions.
• Wonderland & Avalon Families: Passive critical rate bonus based on the number of family members present in the team.
• 2025 HOTM Family: Direct and permanent critical rate increase for relevant allies.

Special Case: Outlaw Family (Langshian)
This family features a unique mechanic: their special skills have their own chance to trigger critical hits, which then deal +50% additional damage compared to a standard critical hit.

Troops & Emblems

• Troops: Only certain troops grant a critical bonus. This is notably the case for 5-Star Troops (Legendary), which offer a massive +15% bonus, as well as specific 4-star "Critical" type troops.
• Emblem Grid: Certain specific nodes add +2% or +4%.

D. Critical Damage in the Damage Calculation

Essentially every normal "hit" that is successful (i.e. not reflected or misses) has a check done on it first to see if "Critical Damage" will apply.

Essentially an "If" statement with a "Yes" & "No" outcome; the "roll" for critical damage is governed (like everything else) by RNG using your cumulative applying Critical Chance.

If the outcome of the "Does Critical Damage Apply?" question is "Yes" the damage calculation essentially becomes:

▼ Normal Damage Calculation for Reference

 

3. Talent Optimization Guide: HP vs. Defense

Original Author : Yelnats24 (may,2019)

The objective is to determine which talent node to choose to maximize a hero's survival. 

Please note that this calculation is intended to find the optimal balance between Defense and HP. While the ratio maximizes raw durability, it is not a mandatory rule: depending on the hero's specific role, their position in your defense team, or a deliberate choice to over-stack one stat for tactical reasons, you may choose to deviate from this path.

Using the durability formula derived from standard damage calculations:

The ideal balance point (crossover point) is reached when your Defense stat equals 0.675 times your HP.

Illustration by calculation: 
To make it simpler, let just say:
a = defense
b = hp
c = durability
d = total point

c = (d - 2a) × a^1.35
c = (d x a^1.35) - (2 × a^2.35)

We have c as a function of a, to find what a result in maximum c, we use derivative:

1.35d x a^(1.350-1) - (2.35 × 2) × a^(2.35-1) = 0
1.35d × a^0.35 - 4.7 × a^1.35 = 0
1.35d × a^0.35 = 4.7 × a^1.35
(1.35d × a^0.35) / 4.7 = a^1.35
a^1.35 / a^0.35 = (1.35d x a^0.35) / (4.7 × a^0.35
a = (1.35/4.7) × d

b = d - 2a
b = d - (2 × 1.35 / 4.7) × d
b = (2/4.7) × d675

a /b = (1.35/4.7) × d / (2/4.7) × d = 0.675

A. The Mathematical Logic

In the talent tree, a standard choice is between +36 HP or +18 Defense. This means a defense point "costs" twice as much as an HP point in terms of allocation.

By using differential calculus to maximize the durability function under this point constraint, we derive the following golden rule:

• Priority to Defense: If your current defense is lower than 0.675 times your HP, the Defense node is more cost-effective.
• Priority to HP: If your current defense is higher than 0.675 times your HP, the HP node becomes more advantageous.

B. Proof by Simulation

To verify this theory, let’s compare three hero configurations with different point distributions:

• Configuration A (The Optimum): With 675 Defense and 1000 HP (exact ratio of 0.675), the calculated durability is 660.02.
• Configuration B (Defense-Oriented): Taking 18 extra defense points but losing 36 HP (693 Def / 964 HP), durability drops to 659.27.
• Configuration C (HP-Oriented): Taking 36 extra HP but losing 18 defense points (657 Def / 1036 HP), durability drops to 659.28.

The result is clear: Configuration A, which respects the 0.675 ratio, offers the best survival. This proves that Small Giant's balancing (+18 Def for +36 HP) is mathematically consistent.

C. Special Cases: Defense Team and % Bonuses

The Defense Team Bonus (+20% Defense):
This bonus applied by the AI does not change the ideal ratio. Mathematically, it acts as a multiplying constant  (1.2^{1.35} ≈ 1.279), meaning it increases the durability of all heroes by 27.9% without shifting the 0.675 crossover point.

Concrete Example with Boldtus
Boldtusk naturally has high defense. Depending on the chosen talent paths:

• An HP-oriented path (Ratio 0.640) results in a durability of 1115.14.
• The balanced path (Ratio 0.674) results in the maximum durability of 1116.03.
• A path too heavily oriented toward defense (Ratio 0.710) brings durability back down to 1115.22.

Important Note: This specific 0.675 crossover point applies only because an HP node provides exactly double the points of a Defense node.