Damage, Defense and Criticals - The Damage Formula

Discussion in 'Guides & Game Mechanics' started by Rhaeven, May 23, 2014.

  1. Rhaeven

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    This thread will explain in depth how the damage formula works and how it was derived. The information here was taken straight from the guides I wrote two years ago, but the damage formula has not changed at all since then. The guide will be split up into three sections.

    Section 1: Damage - More specifically, raw damage; the damage you do when an object has 0 defenses.
    Section 2: Defense - How enemy defense mitigates the raw damage that you deal.
    Section 3: Criticals - Criticals are simply 1.5x damage, but this section covers how you can calculate your average damage once you consider criticals

    For people who want to just plug in values for damage calculations:
    https://docs.google.com/spreadsheets/d/1dsGWcrKtESPe5SPtv4zQunyiH7y8239takrUpZF5aFs/edit#gid=0

    I still have to double check my work on this, but it should be mostly fine.
     
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  2. Rhaeven

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    Section 1: Damage
    By: Rhaeven

    Intro

    So, you might be wondering what this guide is about. This guide aims to explain how to calculate damage and what factors affect your damage. Not only that, this guide also explains that difference between percentage damage (if you look at your skills, there should be numbers with %'s on them) and fixed damage (skills without %'s).

    This guide doesn't really contain anything new for people who are already familiar to the damage formula. It is a rewrite of previously known material that tries to explain in a simple manner how damage works.

    For now, this will only cover raw damage. I can try to cover damage when defenses are applied, but I want to make this as simple as possible.

    ---

    The Stats

    Strength: This stat comes from your character. It is used to calculate for all types of physical damage.
    [​IMG]

    Intelligence: This stat comes from your character. It is used to calculate for all types of magical damage.
    [​IMG]

    Physical Attack Base: This stat comes from your weapon. It is the physical attack that is there -without- upgrades.
    [​IMG]

    Physical Attack Enhanced: This stat comes from your weapon. It is the physical attack that comes from upgrades.
    [​IMG]

    Magical Attack Base: This stat comes from your weapon. It is the magical attack that is there -without- upgrades.
    [​IMG]

    Magical Attack Enhanced: This stat comes from your weapon. It is the magical attack that comes from upgrades.
    [​IMG]

    Skill Percentage: This stat comes from the attack / skill you're using. It is what determines whether an attack is percentage, fixed or mixed.
    [​IMG]

    Skill Fixed: This stat comes from the attack / skill you're using. It is what determines whether an attack is percentage, fixed or mixed.
    [​IMG]

    ---

    Variables
    In the coming sections, I will be replacing these values with variables. Here are the variables that will be associated with them. Because physical and magical damage never combine with each other, some of the values share the same variable.

    Physical damage variables
    Strength: I
    Physical Attack Base: A
    Physical Attack Enhanced: E

    Magical damage variables
    Intelligence: I
    Magical Attack Base: A
    Magical Attack Enhanced: E

    Skill based variables (used in both physical and magical damage calculations)
    Skill Percentage: P
    Skill Fixed: F
     
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  3. Rhaeven

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    Damage Types and Their Equations

    And now we get to the important part of this guide. This section includes the actual equations for your damage and the details that surround them.

    ---

    Percentage Damage

    Percentage damage is done by skills / attacks that only have a Skill Percent (P) value and not a Skill Fixed (F) value. A good example would be your basic attacks. All basic attacks (except for dusted witch attacks) are percent damage. Many skills were pure percent damage skills (elementalist, striker, etc) but most have been changed to include a small amount of fixed damage. Still, those skills are still mainly percentage damage.

    From this equation, we see the ways we can increase our percentage damage.
    • Raising Skill Percent (P) by levelling up your skills
    • Raising Attack Base (A) by getting higher level weapons (upgrades DO NOT modify Attack Base)
    • Raising Strength or Intelligence (I) by levelling up or getting better gear
    • Raising Attack Enhanced (E) by upgrading your weapons

    Something to note about Attack Base (A) and Attack Enhanced (E). Attack Base (A) is soooooo much better. It's more important that you have a weapon that's your level rather than a lower levelled weapon with upgrades (unless the upgrade was something ridiculous like +12). This is because both Attack Base (A) and Attack Enhanced (E) are modified by Skill Percent (P) but only Attack Base (A) is modified by Strength of Intelligence (I).

    ---

    Fixed Damage

    Fixed damage is kind of like the opposite of percentage damage. It only has a Skill Fixed (F) value and not a Skill Percent (P) value. Many skills are purely fixed damage (witch skills, launcher skills, etc). Out of all the equations, this is the simplest to use and also one of the most common cases.

    From this equation, we see the ways we can increase our percentage damage.
    • Raising Skill Fixed (F) by levelling up your skills
    • Raising Strength or Intelligence (I) by levelling up or getting better gear

    Fixed damage is so much more simpler to deal with than percent damage. The downside is, you have less ways to increase your damage. But worry not. To make up for it, a lot of fixed skills have good Skill Fixed (F) values and they usually scale very well. Each level really does make a difference.

    ---

    Mixed Damage

    Mixed damage is the combination of percent damage and fixed damage. It occurs when a skill has both a Skill Percent (P) and a Skill Fixed (F) value in the same hit. Many skills have been changed to mixed damage in the priest patch. Good examples are elementalist and striker skills. They used to be pure percent damage before, but now they have a little bit of fixed damage. This also means that skills like Broomspin which have percent and fixed damage in different hits are not considered mixed damage.

    From this equation, we see the ways we can increase our percentage damage.
    • Raising Skill Percent (P) by levelling up your skills
    • Raising Skill Fixed (F) by levelling up your skills
    • Raising Attack Base (A) by getting higher level weapons (upgrades DO NOT modify Attack Base)
    • Raising Strength or Intelligence (I) by levelling up or getting better gear
    • Raising Attack Enhanced (E) by upgrading your weapons

    As you can see, mixed damage is just the combination of percent and fixed damage. Instead of using (PA) or (F) as the first multiplier, you use (PA + F) instead. There are some things you should keep in mind though.
    • Mixed damage only occurs when a single hit has both Skill Percent (P) and Skill Fixed (F) values.
    • Attack Base (A) is still more important than Attack Enhanced (E). See percent damage for details.
    • Skill Fixed (F) still pretty much stands alone and is only modified by Strength or Intelligence (I).
    • Attack Enhanced (E) is also still stands alone and is only modified by Skill Percent (P).
     
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  4. Rhaeven

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    Section 2: Defense

    This is a simplified guide that shows how exactly Defense, Magic Defense, Vitality and Spirit interact with raw damage. Before I get started, I would like to credit Spore for doing the original work. It still astounds me that he was able to pin down the equation so accurately.

    _______________________________________________________​

    Variables

    First, let's get to know our variables

    Variable Name (Abbreviation) - Description
    • Reduction (R) - This is what this topic is all about. Every variable in this topic builds up to this. Reduction is a ratio that is multiplied to you non-piercing raw damage. It lowers the damage by this ratio. Reduction can be either physical or magical.
    • Defense (D) - This variable makes up a majority of the physical damage reduction this game has. The most common source of defense is armor. Vitality also gives you a flat amount of defense.
    • Magic Defense (D) - This is basically defense, but with magical damage reduction. The most common source of magic defense are your accessories. You also get a flat amount of magic defense from your spirit.
    • Vitality (S) - A previously useless stat, Vitality was revamped with the rebirth update. Now it adds a flat amount of defense and modifies your max hp and hp regen just like how strength and int modifies your damage.
    • Spirit (S) - Think of this as a magic version of Vitality. It adds a flat amount of magic defense and modifies your max mp and mp regen.
    • Level (L) - The attacker's level. Whether it's you or your opponent/monster, this affects damage reduction.

    Both Defense and Magic Defense use the same variable (D) because physical damage and magical damage never mix.

    _______________________________________________________​

    Vitality and Spirit

    We'll start with these two first because they're the simplest of the variables (except maybe level which requires no explanation) and they're one of the building blocks of the other variables.

    Vitality has to do with your physical stats (max hp, hp regen, physical defense) while Spirit has to do with your magical stats (max mp, mp regen, magical defense).

    First, we'll take a look at how they affect your physical and magical defense (since that's what we're here for).

    For every 1 Vitality (S) you have, you get 5 additional Physical Defense (D).
    For every 1 Spirit (S) you have, you get 5 additional Magical Defense (D).

    Simple, right? Using these rules, we get the equation.

    Example: Let's say you take off all your armor and accessories but you still have 300 Vitality and Spirit left. That means you'll still have some Physical Defense and Magical Defense despite not having anything equipped. The amount you would have would be.

    D = 0 + 5(300) = 1500

    You would have 1500 Physical Defense and Magic Defense

    _______________________________________________________​

    Vitality and Spirit also modifies your max hp/mp and hp/mp regen as well. It multiplies it by a ratio just like how str and int multiplies your damage by a ratio. In fact, it's the same ratio.

    Example: Let's say you have 500 Vitality. You're thinking about enchanting your shoes with a GT-9600 card which adds 280 base hp. However, because Vitality modifies hp, you actually get more than 280 max hp.

    Base hp gain * (1 + Vitality/250)
    280 * (1 + 500/250)
    280 * (1 + 2)
    280 * (3)
    840

    You'd actually get 840 max hp from doing that enchant.
     
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  5. Rhaeven

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    Physical Defense, Magical Defense and Reduction

    Now we get to the heart of the topic. First of all, let's get a better sense of how Reduction works before we look at how to find it. Reduction multiplies the non-piercing part of raw damage and reduces it (derp).

    Recall that Raw Damage is
    The PE is piercing and the rest is non-piercing. Reduction works on that part of the equation (which accounts for most of your damage). If you have an unupgraded weapon, then PE is equal to 0 meaning all of your damage is non-piercing. This will be the scenario we use because it simplifies things.

    Let's say your Reduction is .5 or 50%. That means the amount of non-piercing damage you do will be half as effective.
    (PA + F)(1 + I/250)(.5)

    Now, let's say your Reduction is .25 or 25%. That means the amount of non-piercing damage you do will be reduced by a quarter. It is not reduced TO a quarter. It is reduced BY a quarter.
    (PA + F)(1 + I/250)(.75)

    With these examples, we can deduce that Reductions behaves as such
    _______________________________________________________​

    We now know where R belongs in the damage equation. However, we still do not know how to find R. R is based on a few things. It is based on the defender's Physical Defense or Magical Defense and the attacker's Level. Once again, I'd like to credit Spore with the original research.

    It's as simple as that. You do have to remember that it's the attacker's level that is used for L. This also means that the higher level you are, the less your opponent's reduction will be just because you're that level. If you had the same stats at level 1 and at level 70 (which is a ridiculous premise, but bear with me here), you would still be doing more damage.

    Example: Let's say you have 20000 Physical Defense and you're attack by a level 65 mob. How much damage would you reduce its attack by?

    R = 20000 / (20000 + 200*65)
    R = 20000 / (20000 + 13000)
    R = 20000 / 33000
    R = .61

    You would reduce the attack by about 61%. That means you'll only receive 39% of the damage that would have been dealt if you had 0 Defense.

    _______________________________________________________​

    There are a few more things that can affect Reduction though. It is not solely dependent on Physical and Magical Defense. Reduction can be increased with armor / accessory upgrades and avatar skins. These things add a flat amount to your Reduction, not to your defense.

    Example: Let's take a look at the previous example. But let's say you had a skin that reduces Physical Damage by 3% or .03.

    R = 20000 / (20000 + 200*65) + .03
    R = 20000 / (20000 + 13000) + .03
    R = 20000 / 33000
    R = .61 + .03
    R = .64

    It's as simple as that.

    Example: Now, let's say you had full +7 armors. That means you'd have 5 pieces with 1.2% or .012 Physical Damage Reduction each. How much reduction would you have now?

    R = (20000 / (20000 + 200*65)) + .03 + 5(.012)
    R = (20000 / (20000 + 13000)) + .03 + .06
    R = (20000 / 33000) + .03 + .06
    R = .61 + .03 + .06
    R = .70

    Simple, right?

    Something to note; this is how strikers used to get 100% physical damage reduction before rebirth. Their high defenses would give them a high base reduction and then super upgraded armor allowed them to add on to that high base and make it go over the top.
     
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    Last edited: May 26, 2014
  6. Rhaeven

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    Section 3: Criticals
    Intro:
    Everyone already knows that a critical hit will do 1.5x damage than a regular attack. In most cases however, one usually doesn't have 100% crit rate. In this section, I will talk about how criticals affect your overall DPS on average.

    This guide covers 2 things
    1. Critical basics
    2. Calculating average damage taking into account criticals

    _______________________________________________________
    Critical Basics
    There's really not much to criticals on a basic level. In almost all cases when a critical occurs, your damage is multiplied by 1.5x. It doesn't matter how much defense a mob might have or how much piercing you have, your critical damage will be 1.5x your normal damage. As such, the formula for critical damage is

    Critical Damage = Normal Damage * 1.5
    -or-
    Critical Damage = ((PA + F)(1 + I/250)(1 - R) + PE) * 1.5

    Criticals are a 1.5x overall multiplier to all components of the damage formula.

    _______________________________________________________
    Average Damage with Criticals

    Now that we know how critical damage affects individual hits, we can look at how critical damage affects your average damage. Some people think of their regular damage as their average damage and critical hits as bonus damage. In this section, I will explain how to calculate how much bonus damage you are getting because of critical hits on average.

    Variables:
    C = Critical hit rate (will be in decimal form). The chance you perform a critical hit instead of a normal attack
    N = Normal Damage. Damage you would normally be doing without crits
    F = Final / Adjusted damage. How much damage you're doing on average once you take crits into account

    The way I view critical damage is if you perform a critical hit, you are not performing a normal (non-crit) hit.

    So let's say you have a 0% crit rate, meaning you have a 100% chance to do a normal hit. Your Final Adjusted damage would just be equal to your Normal Damage

    F = N

    Now let's say that you have a 20% crit rate from your armor mastery. We would have to subtract 20% from your normal hit chance because you're performing a critical hit instead .

    F = N * (1 - .2) + Critical Damage * .2
    F = N * (.8) + Critical Damage * .2

    Now we take into account that Critical Damage is simply 1.5x normal damage.
    Note: If your are playing ranger, DBR makes Critical Damage to 2x.

    F = N * .8 + N * 1.5 * .2

    From this example, we can conclude that the equation for Final / Adjusted damage is...

    F = N * (1 - C) + 1.5 * N * C
    F = N((1 - C) + 1.5 * C)
    F = N(1 + .5C)

    If you want to know how much of a percent increase that means for my normal damage.

    % increase due to criticals = F / N
    % increase due to criticals = N * (1 + .5C) / N
    % increase due to criticals = 1 + .5C

    In the example we provided above, 20% critical hit rate, the damage improvement from normal damage would be.

    % increase due to criticals = 1 + .5C
    % increase due to criticals = 1 + .5 * .2
    % increase due to criticals = 1 + .1
    % increase due to criticals = 1.1

    The result is 1.1, meaning that due 20% critical hit rate, we have a 10% increase in average damage from normal damage.
     
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  7. Rhaeven

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    ---reserved---
     
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    ---reserved---
     
  9. Rhaeven

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    ---reserved---
     
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  10. Rhaeven

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    To do:
    Rewrite the entire criticals section. The old criticals thread I worked on is EXTREMELY outdated
    Clean up the guide so it doesn't look like 3 guides copy pasted together
    Re-test the mechanics when and if DFO goes live
     
    Last edited: May 24, 2014
  11. Clarrisia AFK

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    Yay Rhaeven is back!
     
  12. puccisweet Reasonable White Man

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    this might be hella dumb but 4 shit like acid rain w/ the debuff that stacks how is the formula applied then w/ tick damage. witch prob the worst class to damage analyze b/c of tick dmg.
     
  13. Rhaeven

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    The damage formula is no different for Acid Rain. Acid Rain is considered as a fixed damage skill so it's covered by what the damage formula shows.

    What I don't cover in the damage formula (off the top of my head) is status damage, buffs (Dice Dragon is working on this) and how elemental damage affects elemental attacks (I will work on the write up for this in the future).
     
  14. KShrike

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    Rogue also stacks crit because IIRC they get a passive increase in crit damage from armor mastery.
     
  15. puccisweet Reasonable White Man

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    would it b possible to make a google excel sheet for formula imputting to calculate chit we we can all help idk o_o
     
  16. Rhaeven

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    Yes, but it wouldn't be practical. Because we don't have a table of mob defenses. It's definitely possible to make one to calculate raw damage (when enemy defense is 0), but it wouldn't be applicable.
    edit: I will make one in the future though. Might as well, for fun.
     
  17. Rhaeven

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  18. Necrofancy Blame Blobâ„¢

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    There was also like a 15-20% resistance to piercing as far as I know. People called it "pierce dampening".

    No idea if it was just a general damage reduction that also affected physical/magical reduction or a specific resistance to piercing element only. Really hard to tell if there was even a net difference.
     
  19. Dubin carried by fmage

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    I actually tested it with a bunch of videos and number crunching before the shutdown. Whether Skasa's Lair, Arden, or Leshpon Kings, it came out to the exact same value everywhere I went, scaled only to difficulty selection. Not even to target--0def Chuseol resisted exactly as much pierce on Kings as NINETY PERCENT DAMAGE REDUCTION True Delezie on Kings.

    15%? I think it was 15%. 20% feels steeper than I number crunched.
     
  20. Necrofancy Blame Blobâ„¢

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    But the thing is; is that a 15% general damage reduction, or a 15% reduction to piercing only?

    If it's a general reduction, then a mob with 90% net physical/magical reduction (~126000 def assuming L70 mob/player) only has 88% (~105000 def) and the 15% general reduction. There'd be a slight difference if you reduced those defenses by 15k like with Bremen debuff and whatnot; the difference would be ~12% improvement in non-piercing damage vs 15% improvement in non-piercing.
     

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