Relationship between Attack, Defense, and PEN and the amount of damage (damage calculation formula)


In this article, I will explain how damage is calculated in Hero Wars.

For the sake of clarity, I’ll use the following notation for this article.

Offensive Power: Physical/Magic Attack
Defensive Power: Armor / Magic Defense
PEN: Armor/Magic Penetration

The idea of damage calculation is the same for physical and magical attacks.So, I”ll make the notation consistent with Offensive Power, Defensive Power and PEN.

“Physical damage” only relate to “Physical attack” and “Armor , and “Magic damage” only relate to “Magic attack” and “Magic defense“.
The combination of Physical attack and Magic defense has no relevance to the damage calculation, and similarly, the combination of Magic attack and Armor has no relevance to the damage calculation too.

The relationships are as follows

Physical damage: Physical AttackArmorArmor Penetration
Magic damage: Magic AttackMagic DefenseMagic Penetration

I’ve created a calculator that you can use to input amount of Offensive Power, Defensive Power, and PEN to calculate actual damage. I think the formula will be easier to understand if you input your own hero’s stats into this calculator and test actual damages in Guild Battles(on fb/web) or Trainings(on mobile).
Hero Wars Damage Calculator

Damage calculations are not calculated by subtraction

*To make it easier to understand, I will start the explanation without the PEN

The damage calculation in Hero Wars is not simple.
Maybe you are thinking of it as simple as the below, but the actual method of calculating damage is quite different.

This formula is wrong
Damage = Offensive PowerDefensive Power

Defensive power does not reduce your opponent’s offensive power by subtracting it, but rather reduces damage by a percentage based on your Defensive power
The actual damage calculation formula is as follows

This formula is correct
Damage Reduction = 1 – 1 / (1 + Defensive Power / 3000 ) * 100%

Damage Reduction Rate (excerpt)

Defensive PowerDamage Reduction Rate
Maybe you are thinking like “What the heck is this?”. For now, just imagine like “If you have 3,000 Defensive power(Armor/Magic Defense), the damage you take is reduced by 50%, regardless of your opponent’s Offensive power”.
Likewise, 4000 Defensive Power reduces damage by 57% and 8000 reduces damage by 72%.

For example, if the attacker’s Offensive Power is 20,000 and the defender’s Defensive Power is 3,000, the damage is not 17,000, but 10,000, which is 50% of 20,000.
If the Defensive Power is 8,000, the damage is reduced by 72%, so the damage will be 5,600.

This is what I mentioned earlier, that damage calculations are not calculated by subtraction. Again, Defensive power does not reduce your opponent’s Offensive power by subtracting it, but rather reduces damage by a percentage based on your Defensive power!

When the attacker's Offensive Power is 20,000

Defensive PowerActual damageReduction Rate

When an Attacker has 20,000 Offensive power and a Defender has 20,000 Defensive power, the damage taken is not 0. Even if the Defender has 50,000 Defensive power, it just reduce the damage by percentage(94.3396%), so the Defender still takes 5.6604%(1,132) damage.
As such, the damage reduction from Defensive Power is just by a percentage.

Here’s a link to the full version of the damage amount percentage list.
I put the numbers up to 100,000, and up to 12,000 is in increments of 100.
hero-wars-(Damage-Reduction-Investment-Efficiency-per-100-Armor-Magic-DefenseDamage Reduction rate by Armor/Magic Defense ( per 100, up to 100k )

Penetration (PEN) changes the power balance

Maybe you’re thinking “You’re a liar! My heroes have over 3,000 Armor/Magic Defense, but they are taking a lot of damage!
That’ s because of the Penetration (PEN). The Attackers’ PEN will reduce the Defender’s Defensive Power.
Let’s modify the previous formula to include the existence of a PEN.

The actual formula used in the game
1 – 1 / ( 1 + ( Defender’s Defensive PowerAttacker’s PEN ) / 3000 ) * 100%

The Defender’s Defensive power is subtracted by the Attacker’s PEN and that is the actual Defensive power used in the damage calculation. PEN is subtracted from Defensive power and is not a percentage reduction.

For example, if a Defender has 3000 Armor

and The Attacker has 300 Armor PEN

In the battle,Defender’s Armor is calculated as 2,700.(3,000300)

So in game battle, damage will be calculated like this

Damage Reduction = 1 – 1 / (1 + 2700 / 3000 ) * 100%

By this calculation, the damage is reduced by 47.3684%.

In this case, if the Attacker had 10,000 Offensive power, the damage would be 5263, which is reduced by 47.3684% from 10,000.

Important: Armor/Magic Defense will never go below 0
If the Attacker’s PEN is greater than the Defender’s Defensive power, meaning it is less than or equal to 0, Defender’s Defensive power will be calculated as 0. Note that no matter how much you raise your hero’s PEN, your opponent’s Defensive power will not go below 0!

Now, as a case study, let’s assume that the Attacker has 20,000 Offensive power(Physical/Magic Attack) and 5,000 PEN(Armor/Magic Penetration), and look at the following table

Case 1: Attacker has 20,000 Offensive power and 5,000 PEN

Defensive Power
(Armor/Magic Defense)
Defensive power
(After subtracting PEN)
DamageReduction ratio

This is the actual damage you take in the game, as it is. If an Attacker with 20,000 Physical/Magic Attack and 5,000 Penetration attacks to a hero with 12,000 Armor/Magic Defense, it will do exactly 6,000 damage. (Armor/Magic Defense become 7,000(12,0005000) and it reduces the damage by 70%)

Now you understand how important it is to raise your DPS’s Penetration.Conversely, when your hero’s Defensive Power are subtracts by your opponent’s PEN, if they have even 3,000 Defensive Power left, the damage your heroes taken is reduced by 50%.

Furthermore, you’ll appreciate #1 Artifacts that increases Armor/Magic Defense or Penetrations to 32,040.

Examples of actual damage in battle

I know it’s hard to get an idea of what’s going on if I just list the numbers, so let’s take a look at an example from an actual battle.
I’ve set K’arkh to Attacker, so let’s check it out.

※I tested with the fb/web version at max status. Note that the maximum status is different on the mobile but damage calculation formula is the same.

  • Physical Attack: 67,020
  • Armor Penetration: 34,600
  • Artifact#1: Physical attack +21,357
SKILLS: Karkh’s third skill is a passive skill that deals massive damage (100% of Physical attack in stats) to enemies thrown in the air during battle, plus double damage if the opponent’s level is below the skill level.
The first skill throws the enemy into the air.

case1: K’arkh va Aurora

  • Aurora’s Armor: 15,813
  • Actual armor(After subtracting Karkh’s PEN):
    15,81334,600 = 0 (it can’t be below 0)
  • Damage Reduction by Armor: 0%

Aurora only has 15,813 armor even with her status max status, so subtracting K’arkh’s PEN(34,600) is a negative.
Defensive power cannot be negative, so it is calculated as 0.

Let’s look at the normal attack. The damage reduction by Armor is 0%, so K’arkh’s Physical Attack 67,020 becomes damage.

Once 1st skill is activated, the damage by K’arkh’s attack is calculated as follows.
The default Physical Attack (67,020) + 1st artifact’s bonus (Physical Attack + 21,367)
= 88,377 is the Physical Attack after artifact activation

Skill #1 + #3 deals damage of 100% Physical Attack, so the damage is 88,377.
It doubles the damage, depending on the skill level, so the damage becomes 176,754.

The damage reduction rate is 0%, so this damage will go directly to Aurora.
hero wars damage vs karkh

case1: K’arkh va Galahad

  • Galahad’s Armor: 37,426
  • Actual armor(After subtracting Karkh’s PEN):
    37,42634,600 = 2,826
  • Damage Reduction by Armor: 48.507%

The normal attack deals 34,510 damage at a damage reduction rate of 48.507% on 67,020 Offensive power.

When he activates the first skill, his Offensive power will be 176,754, just like last case.
K’arkh’s artifact#1 is not a PEN, so the damage reduction rate of 48.507% remains the same. 48.507% of the damage is reduced from 176,754 damage, resulting in a damage of 91,016.

How far should Armor and Magic Defense be boosted?

Now you understand the relationship between Offensive Power (Physical/Magic Attack), Defensive Power (Armor/Magic Defense), and PEN (Armor/Magic Penetration), but how much should you boost your Defensive Power to?
As for this matter, it’s all dependent on your server’s competitors, so it’s hard to say “just get it up to this number”.
Personally, for beginners, I think it’s a good idea to make it at least 3,000 or so and then boost it depending on strength of other player’s DPS on your server.
If you feel that the enemy’s attack is too powerful, you should grow your Offensive Power, and conversely, if your attack doesn’t deal good damage to the enemy, you should boost your hero’s PEN.

Damage Reduction Rate (click to enlarge)

The investment efficiency for every 100 Defensive Power, in percent, is as follows (Click to enlarge)

Take a look at those graphs.
Once your Defensive power exceeds 2500, the damage reduction increase per 100 defensive power drops to less than 1%.

For specific investment efficiency numbers, please refer to this article.
hero-wars-(Damage-Reduction-Investment-Efficiency-per-100-Armor-Magic-DefenseDamage Reduction rate by Armor/Magic Defense ( per 100, up to 100k )

Perhaps you’re thinking, “What do I do in case opponent’s Artifact#1 is a PEN! If your opponent’s Artifact#1 is Maximum and has PEN+32,040, there’s nothing you can do to deal with it by raising the stats.
Almost all of your heroes will exceed their max defensive stats, so you can’t deal with it by raising their stats. With the exception of a some of tanks, it exceeds the max stats of almost every hero’s Armor/Magic Defense, so raising a hero’s stats won’t deal with it.
If you want to handle your opponent’s maxed out Artifact #1 that boost PEN, you’ll have to team up with a Heroes who have Defensive power on Artifacts#1 instead of increasing each hero’s Defensive status.
In the case of handling enemy’s Armor Pen, you have to take on Tanks or someone like Helios who have Armor on Artifacts#1. In the case of handling enemy’s Magic Pen, it’s Maya, Peppy, Cornelius etc who have Magic Defense on Artifacts#1.

Pure damage is unaffected by Armor / Magic Defense

pure-damage in Hero Wars
In addition to Physical damage (orange) and Magic damage (purple), Hero Wars also has a silver damage called “pure damage”. Pure damage ignores the Defensive Power(Armor / Magic Defense).
Note that regardless of your Defensive Power value, you will take full damage. Pure damage is completely skill-dependent. The damage taken will be the same value as the amount on the skill screen.

Pure damage is indicated by a green color on the skill screen.
Both Pure Damage and Heal are shown in green on skill screen, so beginners should take care not to confuse them.

This is pure damage skill.

This is heal skill.

The green color in battle is “Heal” not “Pure Damage”, so don’t get confused.

Some examples

Lastly, I’ll give you some examples to help you understand from specific numbers.

Offensive Power: 10000
PEN: 2500
Defensive Power
(Armor/Magic Defense)
Defensive power
(After subtracting PEN)
DamageReduction rate
Offensive Power10000PEN2500

Offensive Power: 25000
Defensive Power
(Armor/Magic Defense)
Defensive power
(After subtracting PEN)
DamageReduction rate
Offensive Power25000PEN4000

Offensive Power: 40000
Defensive Power
(Armor/Magic Defense)
Defensive power
(After subtracting PEN)
DamageReduction rate
Offensive Power40000PEN8000

Offensive Power: 60000
Defensive Power
(Armor/Magic Defense)
Defensive power
(After subtracting PEN)
DamageReduction rate
Offensive Power60000PEN12000

K’arkh’s maximum status in the fb/web version
High defensive heroes’ max status

Offensive Power: 67,020

 Defensive Power
(Armor/Magic Defense)
Defensive power
(After subtracting PEN)
DamageReduction rate
Physical Attack67,020PEN34,600