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Summoner's War: Sky Arena Wiki

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Damage Multiplier Calculator

Zayler June 25, 2015 User blog:Zayler

This page illustrates how skill multipliers work and how to go about calculating them, as well as how they should be entered into monster pages. A handy calculator is provided for quick and convenient calculations.

Damage multipliers

The damage multiplier shows the damage done by a skill as a multiple of the monster's attack or a combination of other stats before reductions by the target's defense, damage reduction skills such as Knighthood (Passive), or elemental advantage/disadvantage effects. For example, without any reduction, a monster with 350 attack using a skill with a basic damage multiplier of 300% would be expected to deal 350x300% = 1050 damage.

Damage=DamageMultiplier \times Stat

Other factors that affect the Damage a monster does are runes, bonuses from Skill ups, leader skills, glory buildings, and in-battle buffs and debuffs.

Advanced multipliers

For some skills, the damage multiplier is based on two stats instead of a basic single stat (eg. Copper's third skill scales on both Attack and Defense). This is illustrated by the following formula:

{Total Multiplier=(Mult1 \times Stat1)+(Mult2 \times Stat2)}

To find the multipliers for both stats, you would need to run two trials. For the first, record the average damage done by the monster, leaving it's stats as is. For the second trial, alter at least one of the relevant stats (e.g. Defense) and record the average damage for this trial. Now all that's left is to plug the numbers into the formula at the bottom of the page or in the calculator below.

Skills that scale with Speed (eg. Hwa), use a slightly more complicated formula that can be found in the image here.

For ease of use, the pre-built calculator on this page can be used to calculate using both formulas.

Skill-Ups

Skill-Up damage bonuses (eg. +10% Damage) increase the total damage dealt and are not a flat additive increase to the Damage multiplier. Skill up bonuses is additive to other damage modifiers like crit damage, crushing blows or glancing hits. Below is the simplified version of how skill up affects damage before reduction:

Damage={TotalAttack\times Multiplier\times(100% + SkillUp +CritDamage)}

A skill with 3 skill up bonuses of +5%, +10% and +15% would increase the total damage to (100%+5%+10%+15%)=130% and NOT (100%*105%*110%*115%)=132.8%.

Other bonuses

Other Bonuses are applied to the base attack of the monster. Other bonuses include:

The applied bonuses can be checked in battle by clicking "settings > ally buff"

Multiple Other bonuses are additive like Skill-Up bonuses. For example, with a Leader skill of 30% attack and Glory building bonus of 10% attack, base attack would increase to (100+30+10)%=140% , NOT (100%x130%x110%)=143%

Guidelines for calculations

Attacker and Target

  1. Attacks should be tested on monsters with same element to avoid elemental advantages/disadvantages.

Suggested Testing Location

  1. Garen Forest NORMAL stages as listed below.
    • Fire: Stage 2 or 5
    • Water: Stage 5 or 6
    • Wind: Stage 2 or 6
    • Light/Dark :Stage 2, 5 or 6
    • Stages 1, 3, 4 and 7 are not used because the monsters have more defense.
  2. Trial of Ascension

Data size and Damage Adjustments

  1. An average of at least 10 attacks should be used to account for deviation.
  2. It is advised to use regular hits (not: glancing, crushing, critical).
  3. Average Damage should be adjusted to damage before reduction.
    • Garen Forest monsters, except chief monsters, in stages 2, 5 and 6 have an estimated damage reduction factor of 10% so players should adjust the average damage accordingly (Multiply damage by 1.111).

Damage Multiplier Calculator

Tip: You can use expressions such as "1000+1850", which will evaluate to 2850.
Notes: All inputs should be in integers and not percentages or decimals. (e.g. Total Skill-up Bonus of +20% will be 20). Notes: For multipliers that scale with two stats, two sets of test needs to be carried out where the tested stats should be changed for each test.

Calculator loading...
Please input the data above, and click Submit to see the results.
USAGE
  • Average Damage is the damage dealt to the enemy. Average Damage should be adjusted to damage before reduction, see this section for steps.
  • Base Stat is the tested Stat of the monster before any additions (base atk, def, hp, etc).
  • Shown Stat is the tested Stat of the monster shown when holding the monster during selection for battles (Includes bonuses from runes).
  • Total Skill-up Bonus is the total bonus from skill-ups of the monster. Can be checked by clicking Skills on the monster in your inventory.
  • Other Bonus is the total of other bonuses that affect the tested Stat from leader skills or glory buildings which can be found in battle by clicking "settings > ally buff".

Calculator loading...
Please input the data above, and click Submit to see the results.
Constant Data
  • Base Stat is the tested Stats of the monster before any additions. Let "x" be one stat (e.g. Attack) and "y" be the other (e.g. Defense). If the skill scales with speed, use "y" for speed.
  • Other Bonus is the total of other bonuses that affect the respective Stat (x or y) from leader skills or glory buildings which can be found in battle by clicking "settings > ally buff".
  • Total Skill-up Bonus is the total bonus from skill-ups of the monster. Can be checked by clicking Skills on the monster in your inventory.

First Test Data
Input the first set of data from the first test before changing the stats here.

Second Test Data
Input the second set of data from the second test with changed stats here.

  • Average Damage is the damage dealt to the enemy. Average Damage should be adjusted to damage before reduction, see this section for steps.
  • Shown Stat is the tested Stat of the monster shown when holding the monster during selection for battles (Includes bonuses from runes). If the skill scales with spd, use "y" for spd.


Damage reduction adjustment

Average Damage data input into the calculators should be adjusted to raw damage before reduction. Monsters in Garen Forest Stage 2, 5 and 6, excluding boss monsters, have an estimated damage reduction factor of 10% so players should multiply the average damage damage by 1.111 if tested there. If you wish to test the damage using other maps such as the Trial of Ascension since it costs 0 energy for repeats, you can use the following method to estimate damage reduction.

You will need one of the monster listed below for their skill that can ignore defense following a condition:

Below are steps for a method to estimate damage reduction and calculate damage before reduction:

  1. Select a target in the map that you wish to test the damage on. The target should have no elemental advantage or disadvantage with the attacker you are using. (i.e. same element or light/dark vs water/wind/fire)
    • It is suggested that you target a light/dark monster since they are only strong/weak against one other element
  2. Using one of the monsters above (eg. Randy), attack the target and record the damage into two categories:
    • Normal damage
    • Ignore Defense damage
    • Do not use glancing, crushing, and critical hits if possible as they introduce more variance and estimates in the calculations.
  3. Obtain at least 10 figures in each category and calculate the average damage for both categories. It doesn't matter if the categories have different number of data, as long as each columns has at least 10 inputs.
  4. Divide the Average Ignore Defense damage with the Average Normal damage to obtain the average damage multiple. Visual Example.

After obtaining the average damage multiple, you can use this to multiply your average damage of the tested skill in order to get the damage before reduction that you can use in the damage multiplier calculator.

Monster page format guidelines

Multiplier

  1. Multipliers should be written in multiples of 5% or rounded as you see fit. The damage multiplier is only an approximation and might not be an exact figure due to damage reduction, random deviation and other unknown mechanics.
  2. Multipliers that scale with two stats should be written as either 200%+200% or (130+ Spdx1.8)%. eg. Copper, Hwa
  3. Multi-Hit attacks should be written as Multiplier xhits. AOE skills should be counted by the number of hits and not the number of targets. eg. Seren, Mihyang, Lushen
  4. Skills that hit for a random number of hits should be written as Multiplier xN. eg. Lucasha, Zaiross
    • The range of numbers should be written in the multiplier tooltip using the "~" sign to indicate the min~max range eg. 2~5 hits.

Tooltip
If the skill scales only with attack, the tooltip for that skill can be left empty as the default tooltip will be used.

  1. The default tooltip for multipliers is:
    This skill deals approximately [Multiplier]% of the ATK stat before reduction.
  2. Skills that scale with one single stat that is not ATK should use the same tooltip as the default with "ATK" being replaced with the used stat (e.g. DEF for defense)
  3. Skills that scale with two stats should use the following tooltip:
    This skill deals approximately [Mult1]% of the [Stat1] stat and [Mult2]% of the [Stat2] stat before reduction.
  4. Skills that hit multiple times should use the following tooltip:
    This skill deals approximately [Mult per hit]% of the [Stat1] stat before reduction per hit for [number or range of hits] hits on ["random targets" or "per target"].


Formulas

The Damage in the multiplier formulas below should be adjusted for damage reduction.

Single Variable

{DamageMultiplier=\frac{Damage}{Total Attack\times(100%+TotalSkillUpBonus)}}

{Total Attack=Base Attack\times(100%+Rune%+Other%)+RuneFlat}

Two Variables

Advanced Multiplier calculations

Defense damage reduction

Although Damage reduction from Defense can be estimated, it is not advisable to use this method as the target's actual defense might not be reliably known. The following formula is for damage reduction from defense: {DamageReductionFactor=\frac{1000}{1000+(Defense\times3)}}

For Example, a monster with 600 defense would have a damage reduction factor of:
{\frac{1000}{1000+(600\times3)}=35.714%}
So an attack that deals 5,357 damage to that monster would actually be 15,000 damage before reduction.
{\frac{5,357}{35.714%}=15,000damage}

Damage reduction adjustment multiple

Average Damage Multiplier

Click to enlarge

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