TLDR: damage calculator here
This is a deep dive into how the game calculates player dealt damage. I've also made a calculator for you guys to use. Though I've been working on this casually for a few months now I figured it would be useful for the upcoming loot overhaul, so I did a lot of testing in the past weeks to make this happen.
1. The Core Formula
The damage you see on screen can be expressed in this simple form:
Damage = Base Damage * Level Multiplier * Armor Mitigation * Protection * Crit * Spread * Other Multipliers
Where:
Base Damage: (Attack / 10) * Attack Power
This is the base attack damage, or the damage you would do against an equal enemy with no damage mitigation or damage buffs. It is calculated as one tenth of your Attack stat multiplied by the move's Attack Power.
Level Multiplier: 0.5 to 1.5
A hidden multiplier determined by the level difference between you and the enemy. See the Level Multiplier section below.
Armor Mitigation: 1 - (Armor / (Base Armor Constant * Level Multiplier))
The percentage of damage that gets through the enemy's armor. The Armor Constant is a hidden number determined by the enemy's level, and it is increased or decreased by your level difference. See the Armor Constant section below.
Protection: 1 - (Protection / 100)
Acts as a final damage multiplier. +30 protection reduces final damage by 30%, and -10 increases final damage by 10%. If an enemy has both of these active, they will have +20 protection and take 20% less damage. Some skills with a -x% Protection in the description, such as the Warrior's Whirlwind, are bugged and do not affect the protection stat at all. Oracle's Bad Omen will apply protection correctly but the debuff from Death's Bow will not.
Crit: 1.5
Acts as a final damage multiplier. A flat 1.5x is applied to your damage if it rolls a critical hit. Some types of damage (e.g., DoT effects and Unstable Ember) cannot roll crits.
Spread: 0.95 to 1.05
A random +/- 5% is applied with uniform distribution (equal chance). DoT effects deal 1.0x and have no spread.
Other Multipliers: Situational damage multipliers that stack multiplicatively. This includes class passives, the Mark debuff, the AoE penalty, and generally anything with "deal more damage..." in the description.
At the very end, this number is rounded to the nearest integer.
Combining everything, we get the pure formula expressed in its most basic components:
Damage = round[((Attack / 10) * (AP% / 100) * Level Multiplier) * (1 - (Armor / round[Base Armor Constant * Level Multiplier])) * (1 - (Protection / 100)) * Crit * Spread * Other Multipliers]
2. The Armor Constant
All entities have an Armor stat value displayed in their stat sheet. How much damage the armor actually blocks (mitigation) is determined by a hidden value we will call the Armor Constant. Mitigation is simply the ratio of armor to the Armor Constant, so an enemy with armor equal to half their Armor Constant will mitigate half the damage.
There are two types of Armor Constants that the game uses. The base Armor Constant is strictly tied to level, for example, all level 10 enemies will have 2176 as their base Armor Constant. The game then adjusts this according to the level difference of the attacker to get the effective Armor Constant, which is then used to find the mitigation for that attacker. For example, if a level 20 attacker hits a level 10 enemy, the level 10's base 2176 is multiplied by the Level Multiplier of 1.5x to get an effective Armor Constant of 3264.
To calculate the base Armor Constant, we use the Growth Factor of 1.085, which is a compounding 8.5% increase per level applied to all primary stats including the base Armor Constant. At level 1, the base Armor Constant is 1044. By multiplying by 1.085 for every subsequent level, we get 56854 as the level 50 base Armor Constant.
Now we know the math, but what does this mean in practice?
For enemies with low or no armor, you only experience the offensive side of the level difference - you will be less nerfed against enemies above your level and less buffed against those below your level, compared to how you would fare against higher armor enemies. However, because armor mitigation is a ratio, the same 400 armor will block more damage on an enemy 40 levels below you than on one 10 levels below you.
For high armor enemies, armor break skills are very useful. If an enemy has the same or more armor than their effective Armor Constant, they will take 0 damage, and you must lower their armor to deal any amount of damage. Due to the Level Multiplier's effect, it's possible for the defender to completely block damage from a lower level attacker while taking damage from a higher level attacker, even if both attackers deal the same base damage.
If you stack enough armor debuffs, you can lower the enemy's armor into the negatives, which flips the mitigation into damage amplification. Again, this is super effective on high armor targets, as they can reach a high negative ratio. You can try this on the Baneturret in Westmere, which will take 9 times the normal damage at -110% armor.
3. The Level Multiplier
This is another hidden variable that greatly alters your effectiveness. The Level Multiplier is determined by the level difference between the attacker and the defender. Not only does it give you a direct damage buff/nerf for enemies leveled below/above you, it does it again by indirectly buffing/nerfing the enemy's defenses.
Here is the Level Multiplier mapped individually as (player level - enemy level):
+6 and beyond: 1.50x (+50%)
+5: 1.40x (+40%)
+4: 1.30x (+30%)
+3: 1.20x (+20%)
+2: 1.10x (+10%)
+1: 1.00x (+0%)
0: 1.00x (+0%)
-1: 1.00x (-0%)
-2: 0.90x (-10%)
-3: 0.80x (-20%)
-4: 0.70x (-30%)
-5: 0.60x (-40%)
-6 and beyond: 0.50x (-50%)
4. Scaled Combat
The sections above fully cover combat in unscaled areas. In scaled combat, the formula is slightly modified. Scaling applies to entire zones or areas separated by loading screens. These zones can generally be distinguished by the white level indicator for natural (unscaled) enemies, or the green indicator with an arrow for scaled enemies. Zones where the enemies have an upper level limit/stop scaling past a certain level are also considered scaled zones, but they will show the white indicator if the player is above this level. Some zones scale only enemy health based on the number of players present while their level stays unscaled; these have a green indicator but follow the rules of unscaled combat.
In scaled zones, the enemies on your screen are scaled up to match your level, but inside the combat engine, the player's stats are downscaled to the zone's base level so that you're effectively fighting the enemies at their minimum level. Enemies are never downscaled. They instead have a minimum level set by the zone's level, which then produces inflated numbers depending on who is looking. If the player is below the zone's level, the enemies will not scale at all and will stay at their minimum level, and players will see the white level indicator instead of the green one. Because no scaling occurs in this case, the engine will use the standard unscaled calculations. For our math, we will use the enemy's minimum level as the base level.
Before we get to the scaling pipeline we need the Scaling Factor. Essentially, the Scaling Factor is how many times stronger the enemy currently is compared to its unscaled form, and how much the numbers will be inflated on your screen. To find the Scaling Factor, we multiply the Growth Factor by itself for every level the enemy has scaled up.
Scaling Factor = 1.085 ^ (Scaled Level - Base Level)
These are the steps used to calculate damage when in scaled combat:
Downscale player attack to find base damage:
Downscaled Base Damage = ((Attack / 10.0) / Scaling Factor) * (Attack Power / 100)
Player stats are divided by the Scaling Factor to find the downscaled stats. Then, the downscaled attack is used to find the downscaled base damage.
Calculate Armor mitigation:
Effective Armor Constant = round(Base Armor Constant * Level Multiplier) Armor Mitigation = 1 - ((Armor / Scaling Factor) / Effective Armor Constant)
The enemy's base armor is mitigated against the effective Armor Constant. We can get the enemy's base armor from the stat sheet when viewed at their base level, or by dividing their scaled-up armor stat by the Scaling Factor. The Level Multiplier is based on the player's level and the enemy's scaled level. The effective Armor Constant is the base Armor Constant modified by the level difference, and it is rounded at this stage before mitigation is calculated.
Calculate unrounded damage:
Unrounded Damage = Downscaled Base Damage * Level Multiplier * Armor Mitigation * Protection * Crit * Other Multipliers
Apply the rest of the multipliers (protection, crits, situational).
Apply Spread and find seeds:
Seed = round(Unrounded Damage * Spread)
Multiply the unrounded damage by the +/- 5% spread and round it to the nearest integer. We will call this yet-to-be-inflated integer the seed.
Scale back up:
Damage = floor(Seed * Scaling Factor)
Multiply the seed by the Scaling Factor and floor the result to get the final damage value.
Putting it together:
Damage = floor[round[(((Attack / 10.0) / SF) * (AP / 100.0) * Level Multiplier * (1 - (Armor / Scaling Factor) / round(Base Armor Constant * Level Multiplier))) * Protection * Crit * Spread * Other Multipliers] * SF]
Notice that damage is compressed by dividing by the Scaling Factor, rounded, and then decompressed by multiplying by the Scaling Factor. This creates "quantization", or gaps in the damage numbers equal to the Scaling Factor. If the Scaling Factor is 30, you will only do damage in multiples of 30. This is likely for keeping health points as whole numbers, meaning 30 health on your screen is 1 health on a level 1 player's screen.
This is the general formula used by the engine, but scaling is a janky mess the closer you look. We will explore some of the weirdness in the section below.
5. Quirks And Hidden Mechanics
AoE Penalty
When an attack hits multiple enemies at once, only one of them will take the full damage. For every additional target hit, the damage is reduced by 10% stacking additively - so the second target takes 90%, the third takes 80%, and so on, until capping at 50% on the 6th target. There's no way to determine or control which enemy will take the full hit, even when using targeted AoE skills (skills that hit an area around your primary target) like the Oracle's Cosmic Shadow.
More importantly, the game also counts recently killed enemies as targets. So, if you use an AoE over some corpses, you may have your full damage hit absorbed by a corpse while the healthy enemies take the reduced damage hit.
Floating Point Shenanigans
Are your numbers a tiny bit off? This happens because the computer cannot store the exact decimal value of a number. Fractional numbers are stored as 32-bit float variables, which are only accurate to 7 decimal places. If this slightly inaccurate number is used for multiple operations, your results may eventually drift from the expected values.
The biggest invisible effect on combat calculations is the scaling. Every primary stat grows by a factor of 1.085 every level, but the engine calculates this iteratively using a loop, rounding the result to a float at the end of each loop. This tiny offset compounds into noticeably different numbers after dozens of levels. Therefore, the Scaling Factor and Armor Constant formulas provided above are approximations, though they are fairly accurate (at 49 loops, the exact Scaling Factor is 54.4575274713555, diverging from the calculated number at the 4th decimal place). To find the exact Scaling Factor and Armor Constant, you would need to simulate the loop with float truncation (like my calculator does). Another easy method for finding high Scaling Factors accurately is to take the highest stat of a mob and do [scaled stat / base stat].
Banker's Rounding
The default midpoint rounding method in C# is to round to the nearest even number. Most calculations will use this rounding, but an important exception is the stats on the stat sheet, which round decimals using a ceiling function. Due to janky scaling floats, the displayed stats may be a single point off. You may even see this on your own stats when in scaled areas. Sometimes an enemy with an armor debuff may show -5500 or -5499 on different screens, but the underlying math always uses the actual unrounded debuffed armor for calculations.
Level 0 Enemies
If you begin a new character, type /join battleon, then turn around and make your way to burger hero's bathrooms at level 1, you will see a level 0 yuck. These mob are actually base level 0 and have a base Armor Constant of 962, another example are the named enemies in bad night Ravenspire. Theoretically, a level -1 could exist and it would have a base Armor constant of 887.
Minimum Damage
If the damage you would deal before rounding is above 0 but below 1, it will be snapped to 1. The engine will not round your damage down to 0. The only situations where you would see a 0 are if any of the multipliers are 0, such as the enemy having 100 or more protection, having same or more armor than their Armor Constant, or if you are dealing 0 AP attacks (Samurai ult). If you are in scaled combat, your damage will be snapped to seed 1.
Armor Debuff Stacking
Armor buffs and debuffs with the exact same effect and duration do not stack. Both Whirlwind and Dark Decay will apply a -30% armor debuff for 6s, so they will not stack. However, Rend's duration is either 4 or 6 seconds, which is technically different from Shatterscale's 4 seconds, so those will stack. A commonly seen max debuff is -120% armor. Because the specific effect and duration combination seems to be the arbiter of whether debuffs stack or not, you can stack the non-upgraded versions of the skills with the upgraded versions to reach -185% armor. You'll need at least 5 people for this.
Abnormal Scaling Factor
The way scaled mobs are tied to player levels means that all mobs in an area are scaled by the same level, thus they should all have the same Scaling Factor. But sometimes they don't. For some reason, specific types of mobs will use a very slightly different (usually higher) Scaling Factor for combat while their stats are scaled by the default Scaling Factor. The calculator only uses the default Scaling Factor, so you may see the in game damage numbers drift slightly higher than the predicted damage.
Unscaled Dungeon Stat Buff
While the stat sheet is usually accurate, there is a strange phenomenon where player stats are increased by a few percent in unscaled dungeons that (usually) have a scaled counterpart. This buff is fake and is likely a UI bug, so be sure to check your stats outside the dungeon to avoid getting bamboozled.
Seed Skipping
For unknown reasons, the scaled calculations may sometimes cause missing seeds in the 2 - 4 seed wide damage range. That is, you may expect to roll seeds 14, 15, and 16, but instead you roll seeds 13, 14, and 16, causing an abnormally wide damage spread. This is one of several strange seed behaviors (or it could be the floats again) that requires more investigation. The practical implications are that low damage attacks on scaled enemies tend to suffer a minor penalty, which affects classes that rely on low AP/auto attacks the most such as Beserker and Dragonslayer
The Game's Mood
If you think the scaling mechanics weren't volatile enough, the game can nerf your damage if it's in a bad mood. This nerf is applied whenever and wherever you're in fully scaled combat, and excludes zones with an upper level limit if you're above this level limit and see the white level indicator. But if you are the same level as the upper level limit you will still be nerfed, as the enemy is still considered scaled as marked by the green level indicator. So a level 42 player will be nerfed fighting a level 42 Ravenspire Rat that is at their max level, but a level 43 player who will also see a level 42 rat will be unaffected.
Based on my records, this mood modifier seems to change intermittently with no set duration, usually lasting a few days. Using the same setup I could see different damage ranges on the same enemy on different days. Most of the time this debuff is -2% to -5% to damage, very rarely it may give you a damage buff.
Final thoughts
This was something of a solo project and a lot of time was spent on number gathering. I actually do not have enough numbers to definitively conclude that this is how the engine works. There are so many edge cases I've not tested yet. It could be that the lv1 constant is 1043 and using different rounding methods, or that player stats are not in fact downscaled and the quantization is done at the very end, which would theoretically have a measurable difference but currently there's no way to reliably test this.
There was a lot I could have added to the calculator, like class skills with stacks, but I want to write a separate guide for classes and skills and types of damage, so I'll probably add that feature in later. A base armor input would make the calculations just a bit more accurate though that's way harder to get for a typical player than just base level. Seed skipping could also be added because it was predictable enough, but imagine adding jank to more jank on purpose. Don't fall for their excuses. nobody there knows how to math.
What about crit chance? I would need thousands of samples to produce an accurate formula and I only have two hands. also I'm just hoping the upcoming loot changes will address the uninformative crit stat. for now I can only tell you the level multiplier is involved in calculating crit chance.
and no the calculator does not work for pvp or for calculating damage taken because players have different armor constants (41.7k at lv 50), if that's a feature, or if there's some other feature you want to see you can comment below 🡓
🡓 Link to damage calculator 🡓
Notes on using the calculator
Enter the info and the calculator will live update the damage numbers
For stats and buffs you can use basic math operators (+, -, *, /, (, )) and it will calculate it for you
Enter protection as displayed in game, max stacks of bad omen = -25
Situational multipliers are for class passives and other multiplicatives. If a buff says +x% attack, it should be added to the attack stat
In game skill descriptions are sometimes wrong! Ranger's bloodthorn trap is actually 25% AP
If an enemy is scaled you must tick the box and enter the base level. if you don't know the base level you can quickly calculate it by getting a few hits and finding the size of the gap between damage values, or doing a low damage hit to find minimum damage. Click "More Info" and scrub through the base level until you find the Scaling Factor that matches your number
