Long read- How Damage is Calculated?

Update 3/3/2018: added items section and true damage/damage reduction section.
Update 2/13/2018: added counterargument to diminishing returns on armor, 3rd example on pierce, and the abilities section

Arena of Valor’s Damage Reduction Formula

Damage Reduction Formula

An understanding of how damage is calculated in game can give players a better sense of their capabilities in battle as well as the effectiveness of different items. We will use Violet to demonstrate some of the formulae Arena of Valor uses to calculate damage.

Damage is calculated by subtracting the enemy’s resistance from the attacker’s base damage. Armor and Magic resistance use the following formula:
Damage Reduction = Armor/(Armor + 600) or Magic Defense/(Magic Defense + 600)

Example

By looking at the stats section, you can see all heroes’ current stats. The second stat from the right is armor. The enemy Thane is currently at 259 armor. Violet’s Attack Damage is 172, attack being the second stat from the left and indicated by a sword icon. Using the previously mentioned formula, we can find exactly how much damage we will do when attacking.

Armor Value = 259/(259 + 600) = 0.3015 (30.15%)
Damage Reduction = 172 x 0.3015 = 51.86
Actual Damage = 172 – 51.86 = 120.14 (note: damage numbers are rounded down to the nearest 1)

We can see that this is correct in the image below.

Diminishing Returns?

The formula ensures that armor and magic defense have diminishing returns, as can be seen with the following examples.

If the defensive stat is 300:
Damage Reduction = 300/(300 + 600) = 33.33%

If the defensive stat is 600:
Damage Reduction = 600/(600 + 600) = 50%

If the defensive stat is 900:
Damage Reduction = 900/(900 + 600) = 60%

Since the amount of damage blocked per point drops as the point total increases, it’s better to have a mix of resistance items and HP boosts than focusing completely on a single thing.

Update: Though the percentage displayed shows diminishing returns, the effective HP of the hero goes up linearly when buying armor items, so take that into consideration as well when buying defense items.

Calculating Armor and Magic Defense Pierce

Armor and Magic Pierce

If the enemy hero has high Armor or Magic Defense, buy items that increase Armor Pierce or Magic Pierce.
For example, if you attack an enemy with 259 Armor (Damage Reduction: 30.1%) after buying an item that increases Armor Pierce by 60:

Enemy’s Armor = 259 – 60 = 199
New Damage Reduction = 199/(199 + 600) = 24.91%

And if you buy an item with +45% Armor Pierce:

Enemy’s Armor = 259 – 259 x 45% = 142.45
New Damage Reduction = 142.45/(142.45 + 600) = 19.19%

This formula also corresponds to damage dealt to towers and neutral monsters, each having their own defense stats.

If you buy two items, one with 60 raw damage pierce, and one with 45% pierce, the percentage is calculated from the reduced armor amount:

Enemy’s Armor = 259 – 60 – ((259 – 60) x 45%) = 109.45
New Damage Reduction = 109.45/(109.45+600) = 15.4%

Calculating Critical Damage

Calculation of critical damage:
Critical Damage = Actual Damage Dealt x 2

Some items and Arcana increase the amount of critical damage dealt. Using the item Slikk’s Sting as an example:
Critical Damage = Actual Damage Dealt x 2.5

Critical damage applies to buffs related to the attacker’s base AD, like Fenrir’s Tooth, but does not apply to damage buffs based on the opponent’s health, like Fafnir’s Talon.

Critical Damage does not apply to towers.

True Damage and Damage Reduction

True damage will ignore all armor or magic defense and deal the exact amount of damage listed in the description (unless you’re Maloch and you land a critical hit; see below). True damage will also penetrate any shields the opponent has, reducing their HP and not the shield amount.

The only exception to the true damage rule is when an ability or item description states that it reduces incoming damage. For example, Omen gains 50%-70% damage reduction with Untouchable, meaning even the amount of true damage taken is reduced. Similarly, Asterion’s Buckler reduces the damage from all sources, including true damage.

What About Abilities? Does Pierce Apply? Critical?

Normal (armor) pierce applies to all abilities that deal physical damage, while magic pierce obviously applies to abilities that deal magic damage. Critical damage, however, only applies to abilities that enhance attacks. Yorn, for instance, can crit on all of the attacks from his Fierce Shot passive (albeit at 70% normal damage) so investing in items and Arcana that enhance his critical chance and damage is a wise choice.

Most heroes who have an ability that enhance a basic attack only have the AD portion of their attack doubled. If the ability multiplier is greater than 1, then only the portion of AD up to 1 is multiplied. As an example, let’s take a look at Violet’s Tactical Fire:

Though Violet’s attack damage is multiplied by 1.15 when she uses Tactical Fire, a normal (200% damage) critical hit would only double up 100% of her AD, and not the remaining 15%. So a normal critical hit on Violet’s Tactical Fire at level 15 would deal AD x 2 + AD x .15 + 475 = 2.15 x AD + 475 damage, as opposed to doubling the AD multiplier or the entire damage amount.

Exceptions

Exceptions to the rule just mentioned are Jinnar (though his AD isn’t part of the ability that’s multiplied), Moren (just 25 damage extra), Slimz (passive and 2nd ability) and Wukong (passive). It is a particularly big deal for Wukong and Slimz: Wukong naturally picks up 540 extra crit damage at level 15 just off of his base kit, while Slimz’ critical damage stacks off both his passive and 2nd ability to deal 2.6AD + 260 damage on third attacks after using Leap of Vitality.

Crit and Deal Magic Damage

Currently, the only heroes who can crit and deal magic damage are Valhein (with his 3rd attack), Kahlii, and Jinnar (on his fourth spirit orb). Each of their passives have some peculiar nuances to them, which we’ve tested and listed on their attributes pages.

Crit and Deal True Damage

The only hero who can crit and deal true damage is Maloch, when Plunder is activated. Zanis is an example of a hero whose true damage portion does not multiply on a critical hit. A general (but not steadfast) rule is if the description says “additional damage,” then that damage does not multiply on a crit, while increasing the hero’s attack damage (eg. Tel’Annas or Slimz) allows for the full damage to multiply.

The same rule applies for life steal – any “additional” damage is not included in the calculation for life steal, while effects like critical hits and pierce are included.

Damage Rules For Items

Similar to abilities, any “additional damage” listed in items is not considered when calculating the damage from critical hits or including damage from attack-enhancing effects. For example, Fafnir’s Talon‘s passive is not included when calculating critical damage, and is also not part of the true damage Maloch deals when Plunder is active. In addition, the 8% damage is reduced by the opponent’s armor, meaning pierce will increase the additional damage dealt by Dragon’s Breath. Everything just mentioned applies to the unique passives of Shuriken, Omni Arms, Trick Blade, Apocalypse, and Frost Cape.

In contrast, Fenrir’s Tooth reads “Increases all damage,” meaning that the 30% bonus is included in all critical damage multipliers as well as Maloch’s Plunder. Hercules’ Madness functions in the same manner.

The one item whose functionality rests between the items above is Blitz Blade. The damage from Chain Lightning is treated as an entirely separate attack, meaning it can benefit from critical hits (and additional critical damage from Slikk’s Sting). Chain Lightning is subject to reduction due to the opponent’s armor, even when Plunder is active. It is possible to deal a critical hit with Chain Lightning and not with your normal attack, and vice versa.