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Damage formula, modifier types and how they interact


vegax87
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Huge copy-pasta from the official forums: https://forum.treeofsavior.com/t/damage-guide-the-big-formula-modifier-types-and-how-they-interact/118950

The Formula

The exact formula, after much testing, and kindly simplified by user Tarocha here on the forums, and another user by the name of KDBA on reddit, is the following :

(((((Skill Attack + (Attack + Attack Modifier)) + (random(0% ... 100%) * Magic Amplification)) * (100% + T0)) - (((Defense + Defense Modifier) * (100% + Level Penalty)) + Elemental Resistance)) * (100% + (0 or 50% if crit)) + (0 or Critical Attack) + (Extra Elemental Attack) + (Enemy Specific Damage)) * (100% + T1) * (100% + T2) * (100% + T3) * (100% + Enhance) + Bonus Damage

All modifiers are converted from total figures to additive figures for the formula. For example, Meteor is 400%, so the additive value is +300%. All modifiers within a same tier are additive to one another and are added to the default value of "100%". The tiers are as follows:

Attack Modifiers
These alter the base attack stat in some way. They can both be flat values or percentual modifiers. Examples are Pommel Beat on stunned targets, Cloaking's attribute, or Shield Charge.

Magic Amplification
This is a very simple stat. It acts like a "Maximum attack" range for magic attacks and that's pretty much it (on top of, of course, existing "Maximum Attack" increases. It's still a different stat). It randomly adds between 0% and 100% of your Magic Amplification to your attack.

T0 : Base Damage Modifiers
These modify the total damage a skill would do before defense is subtracted. They are quite potent, as they can cause your damage to vastly exceed an enemy's defense and create a much larger number for the rest of the formula to calculate with.
Modifiers like this include Split Arrow's "Bounced Arrow Attack" and Sky Liner's damage on Bleeding targets.

Defense Modifiers
Effects that alter an enemies defense, wether it be raising or lowering it. These can be both flat values or percentual modifiers, though the order in which a flat and percentual modifier apply is currently not yet known. (eg. 100 Def - 5 Def -20% Def = 76 Def, but 100 Def - 20% Def - 5 Def = 75 Def. Testing required.)

Level Penalty
When you're more than 5 levels below an enemy, a penalty will start increasing the defense of the enemy you hit by 10% per level. Because a monster wont know if you're lower level until you actually hit it, any defense debuffs it is suffering from are subtracted from its base defense and not the increased defense from the penalty. At 5 levels below a monster, the penalty is 10%. It goes up by 10% by every level after that, so at 6 levels it's 20%, at 7 levels it's 30%, and so on.

Elemental Resistance
If a monster has any (usually this is only through Resist Elements), it will be added here when you cast an attack with the respective element. For example, if you have 100 Lightning Resist, only Lightning-based skills (Electrocute and Zaibas) will add said Lightning Resist to your defense when they are used on you. Simple non-elemental attacks but where the attacker has "Lightning Attack" stats are not added here, but along with the Lightning Attack value itself further into the formula. See "Extra Elemental Attack" below.

Critical Hit
When you land a critical hit, you simply add 50% to the formula above and then add your Critical Damage. As magic can't crit, this will just always be +0% + 0 for those skills. Sorry mages!

Extra Elemental Attack
This is where all your Elemental Attack stats are added, after crits, before everything else. These all add on to each other if you have multiple types of elements and are always applied, no matter what the attack is (even on DoT effects like Bleeding!).
This Elemental Attack is already multiplied by Elemental Bonuses on its own, so yes, having Fire Elemental Attack and then casting a Fire skill on a Ice enemy will make it multiply by 150% once for itself, then again for the whole skill.
Elemental Resistances and Resistance buffs/debuffs are accounted for again here too, just like the bonus being applied twice. The full formula for Elements is :

((Elemental Attack - (Elemental Resistance + Debuff/Buff)) * Elemental Modifier) (+ ...)

Where (+ ...) is a repeat of the first part for every element you have Elemental Attack for.

Enemy Specific Damage
You know the ones. Additional damage to Beast-Type enemies and the like. Very simply added straight on here, after crits, before everything else, just like Elemental Attack.

T1 : Skill Damage Modifiers
These are the modifiers that are directly listed on the skill tooltips right in front of the skill's raw attack value.
Modifiers of this tier include Meteor, Stone Shot, and Claymore.

T2 : Common Modifiers
The main bulk of the modifiers. A lot of things in here will end up being added together in the game as they are rather common.
Modifiers of this tier include Elemental Properties, the Missile penalty, hidden modifiers like Ice Bolt and Cartar Stroke, certain attributes like Quick Cast : Magic, and so on.

T3 : Target Modifiers
The modifiers here are all dependant on what you hit, what type of attack you hit it with, and so on. This includes all of the Armor-type modifiers, but also some Size-related modifiers and certain attributes There's no real distinction between these modifiers and T2 modifiers, but these all have something to do with what state the enemy is in or what it's properties are.

Enhance
The main damage attribute every damage skill has.
Add +1% to +100% to the formula above depending on attribute level.

Bonus Damage
Additional bonus damage. They are just extra damage values that even appear as a separate yellow number to tell you they're there, complete with skill name of what caused it. They never get multiplied and are added way at the end of everything
These include buffs like Blessing and Concentration.

Additional Attacks
"But these aren't even in the formula!" Well, no, they aren't, because these pesky little guys have their own very slightly different formula.

(Additional Attack + Extra Elemental Attack) * (100% + T1) *(100% + T2) * (100% + T3) * (100% + Enhance) + T4

Very similar isn't it? You just drop defense, magic amplification, critical hits and all that out of the equation, replacing Skill/Base Attack with the "Additional Attack" from the tooltip.
These hits are caused by buffs such as Enchant Fire and Sacrament.


If you find anything that does not adhere to the formula I created and others perfected, then be sure to say so! I'll see what's up as soon as I can.
Many thanks to people who made rough formulas for a lot of separate things, as well as those who helped simplify it! Sometimes it was just piecing things together.


Attack Modifiers

Scout

  • Cloaking "Physical Damage" Attribute :
    +50%

Cryomancer

  • Subzero Shield "Counter Attack" Attribute :
    +50% to +200% of Shield's Defense value

Swordsman

  • Pommel Beat :
    +200 on Stunned status

  • Double Slash :
    +200 on Bleeding status

Barbarian

  • Stomping Kick :
    +Boot's Evasion

Rodelero

  • Shield Charge :
    -50%

Defense Modifiers

Archer

  • Basic [Missile] Attack :
    -10% Phys. Defense per shot (Up to -50%)

  • Full Draw "Decreased Defense" Attribute :
    -10% to -50% Phys. Defense (Depending on Attribute Level)

Peltasta

  • Umbo Thrust :
    -100% All Defense (Armor Break Status)

Highlander

  • Skull Swing :
    -100% All Defense (Armor Break Status)

Rodelero

  • Shield Push :
    -15 to -225 Phys. Defense (Depending on Skill Level)

Cleric

  • Deprotected Zone :
    -(2 + SPR) to -(12 + SPR) All Defense for 6 to 39 seconds (Depending on Skill/Attribute Level)

  • Deprotected Zone "Sword Attack" Attribute :
    -1 to -8 All Defense per [Weakened Defense] stack (Up to 10 times). Stacks are applied when hitting an enemy within Deprotected Zone with a Sword.

  • Deprotected Zone "Enhance" Attribute :
    -1 to -50 All Defense (Depending on Attribute Level). Applies after [Weakened Defense] stacks.

Priest

  • Monstrance :
    -(6 + SPR x 0.4) to -(39 + SPR x 0.4) Phys. Defense for 20 to 25 seconds. (Depending on Skill/Attribute Level)

Bokor

  • Hexing :
    -(12 + SPR x 0.3) to -(57 + SPR x 0.3) Magic Defense for 15 to 29 seconds.(Depending on Skill Level)

Paladin

  • Resist Elements :
    -30 to -100 Magic Defense for 65 to 135 seconds. (Depending on Skill Level)

Tier 0 : Base Damage Modifiers

Scout

  • Split Arrow :
    +100% on bounced arrow

Highlander

  • Sky Liner :
    +100% on Bleeding status

Hoplite

  • Synchro Thrusting "Pierce" Attribute :
    +10% to +50% on Spear attack
    -10% to -50% on Shield attack

Tier 1 : Skill Damage Modifiers

Quarrel Shooter

  • Stone Shot :
    +50%

Sapper

  • Claymore :
    +200%

Elementalist

  • Meteor :
    +300%

Sadhu

  • Astral Body Explosion :
    +150%

Tier 2 : Common Modifiers

Archer

  • Full Draw :
    +50% on Leather armor

  • Heavy Shot :
    +50% on Plate armor

  • Twin Arrows :
    +50% on Cloth armor

  • [Missile] Attacks (applies to subclasses too) :
    -10% to ?% on Medium
    -15% to ?% on Large and Extra Large
    Note: Penalty goes down by ?% per Bow Upgrade Level (+) for the Large penalty, and ?% for the Medium Penalty.

Ranger

  • Time Bomb Arrow (explosion) :
    +50% on Plate armor

  • Steady Aim :
    +6% to +20% for [Missile] attacks for 20 seconds. (Depending on Skill Level)

Quarrel Shooter

  • Stone Shot :
    +50% on Plate armor

Wizard

  • Energy Bolt :
    +50%

  • Energy Bolt "Additional Sleep Damage" Attribute :
    +40% to +120% on Sleep status (Depending on Attribute Level)

  • Earthquake :
    +100% on Lethargic status

  • Quick Cast "Magic" Attribute :
    +10% to +50% (Depending on Attribute Level)

Cryomancer

  • Cryomancer "Freeze Speciality" Attribute :
    +10% to +50% from Lightning Attacks on Frozen Status (Depending on Attribute Level)

  • Ice Bolt :
    +50%

Linker

  • Joint Penalty "Poison", "Earth" and "Electric" Attributes :
    +10% to +50% from Poison/Earth/Lightning Attacks on Linked enemies. (Depending on Attribute Level)

Elementalist

  • Freezing Sphere :
    +50%

  • Rain :
    +35% from Lightning Attacks

Highlander

  • Wagon Wheel :
    +10%

  • Cartar Stroke :
    +50%

Peltasta

  • Umbo Blow (When enemy is staggered by a block) :
    +100% on Plate armor
    +150% on Cloth armor
    +200% on Leather armor

  • High Guard "Umbo Blow Speciality" and "Rim Blow Speciality" Attribute :
    +250% to +330% (Depending on Attribute Level)

Barbarian

  • Stomping Kick :
    -10% to +Infinite% (Depending on height from ground).
    Note: Normal jumping height is +0%. Nearly landing is -10%.

  • Seism :
    +50%

Sadhu

  • Attack Soul (Out of Body) :
    +50%
    Note: Uses Magic Attack and goes through the normal main formula as any skill, but does not include T4 bonuses.

Paladin

  • Smite :
    +200% on Demon and Mutant type

Elemental Properties

  • Fire :
    +50% on Ice
    -50% on Fire

  • Ice :
    +50% on Fire
    -50% on Ice

  • Lightning :
    +100% on Ice
    -50% on Lightning and Earth

  • Poison :
    +50% on Earth
    -50% on Poison

  • Earth :
    +50% on Lightning
    -50% on Poison

  • Holy :
    +100% on Dark

  • Dark :
    +100% on Holy

Tier 3 : Target Modifiers

Scout

  • Flare Shot :
    -10%

Wizard

  • Lethargy "Additional Damage" Attribute :
    +20% to +100% from Strike attacks for 30 seconds. (Depending on Attribute Level)

Cryomancer/Elementalist

  • Frozen Status :
    +100% from Strike attacks.

Highlander

  • Cross Guard :
    +100% from Pierce attacks for 5 seconds.

Barbarian

  • Cleave :
    +150% on Stunned status

Hoplite

  • Pierce :
    +100% on Medium
    +200% on Large and Extra Large

  • Pierce "Continuous Attack" Attribute :
    +300% on Extra Large (Replaces +200% above)

Rodelero

  • Targe Smash "Frozen Stone" Attribute :
    +20% to +100% on Frozen or Petrified Status

  • Slithering "Additional Damage" Attribute :
    +20% to +100% from Strike attacks for 10 seconds. (Depending on Attribute Level)

  • High Kick :
    +100% from Strike attacks for 10 seconds.

Bokor

  • Hexing "Darkness" Attribute :
    +10% to +30% from Dark Element attacks

Armor Modifiers

  • Slash :
    +50% on Cloth armor
    -25% on Plate and Ghost armor

  • Strike :
    +50% on Plate armor
    -25% on Leather and Ghost armor

  • Pierce :
    +50% on Leather armor
    -25% on Cloth and Ghost armor

  • Magic :
    +50% on Ghost armor

Bonus Damage

Swordsman

  • Concentrate :
    +5 to +126 Damage for 5 to 26 Attacks (Depending on Skill/Attribute Level)

Priest

  • Blessing :
    +15 to +170 Damage for 10 to 180 Attacks (Depending on Skill/Attribute Level)
Edited by vegax87
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