User:SaschB/sandbox

The basis for damage calculation is as simple as: $$ {Atk} - {Mit} $$ where

Atk is the Attack stat of the attacking unit (this includes the might of the equipped weapon, and any active buffs or debuffs).

Mit is the Mitigation stat of the defending unit. Physical attacks are mitigated by Def, while magical attacks are mitigated by Res.

Example: A red sword unit with Atk 15 attacks another red unit with Def 11.

$$ \text{Expected damage} = {15} - {11} $$

$$ \qquad \qquad \qquad \qquad = {4} $$

Since damage output cannot be negative, the value chosen is the highest one between the calculated damage and zero:

$$ \max({Atk} - {Mit},{0}) $$

Example: Switching around the values from the first example to Atk 11 and Def 15:

$$ \text{Expected damage} = \max({11} - {15},{0}) $$

$$ \qquad \qquad \qquad \qquad = \max({-4},{0}) $$

$$ \qquad \qquad \qquad \qquad = {0} $$

Adding in weapon-triangle advantage, but not yet considering special skills:

$$ \text{max} \bigl( {Atk} + \left \lfloor {Atk} \cdot {Adv} \right \rfloor - {Mit} \text{,} {0} \bigr) $$

where

Adv is the Advantage multiplier, this is 0 in a normal combat, but gets modified by weapon-type advantages. In a battle between a red unit and a green unit, the red unit's Adv is 0.2 while the green unit's Adv is -0.2 (normal disadvantage). This value can be further modified by passives such as Triangle Adept, or weapons such as Ruby Sword. Note, however, that Triangle Adept does not stack with the gemstone weapons. A red unit attacking an Emerald Axe wielding unit with Triangle Adept 3 equipped gets an Adv modifier of 0.4 - not 0.6.

Note: The $$ \left \lfloor \, \right \rfloor $$ notation is used to mean https://en.wikipedia.org/wiki/Truncation in this and subsequent formulae. This means that $$ \left \lfloor {-1.5} \right \rfloor = -1 $$, it is effectively a "round-towards-zero". This is not the same as the floor function https://en.wikipedia.org/wiki/Rounding#Rounding_to_integer, and is used only to improve legibility of the formulae.

Example: The same red sword unit with Atk 15 attacks a blue unit with Def 11. The red unit has a disadvantage, so Adv is -0.2.

$$ \text{Expected damage} = \text{max} \bigl( {15} + \bigl\lfloor {15} \cdot {-0.2} \bigr\rfloor - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {15} + \left \lfloor {15} \cdot {-0.2} \right \rfloor - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {15} + \left \lfloor {-3} \right \rfloor - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {15} + {-3} - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {12} - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {1} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = {1} $$

To expand on this formula, we can add in "Effective against" bonuses:

$$ \text{max} \bigl( \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor - {Mit} \text{,} {0} \bigr) $$

where

Eff is the Effectivity multiplier, this is 1 in a normal combat, 1.5 if the attack is effective (e.g. Archer vs. Flier, Armorslayer vs. Armored unit).

Example: Consider the red sword unit from before, wielding an Armorslayer and the blue unit from before being armored. Adv is still -0.2, but Eff is now 1.5.

$$ \text{Expected damage} = \text{max} \bigl( \left \lfloor {15} \cdot {1.5} \right \rfloor + \bigl\lfloor \left \lfloor {15} \cdot {1.5} \right \rfloor \cdot {-0.2} \bigr\rfloor - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( \left \lfloor {22.5} \right \rfloor + \bigl\lfloor \left \lfloor {22.5} \right \rfloor \cdot {-0.2} \bigr\rfloor - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {22} + \left \lfloor {22} \cdot {-0.2} \right \rfloor - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {22} + \left \lfloor {-4.4} \right \rfloor - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {22} + {-4} - {11} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {7} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = {7} $$

Staves have a special modifier ClassMod which makes them deal half the expected damage. This can be expressed by:

$$ \Bigl\lfloor \text{max} \bigl( \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor - {Mit} \text{,} {0} \bigr) \cdot {ClassMod} \Bigr\rfloor $$

where

ClassMod is the class modifier, being 1 for all current classes except staff users, having a ClassMod of 0.5.

Note: ClassMod will be omitted from the examples on this page, as it only currently affects attacking healers.

Considering special skills like Luna, which reduce the opponent's Def or Res for the attack, the formula becomes this:

$$ \Bigl\lfloor \text{max} \bigl( \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor   - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) \text{,} {0} \bigr) \cdot {ClassMod} \Bigr\rfloor $$

where

MitMod is the decimal value describing by how many percent the opponent's Def or Res is lowered, for Luna, this value would be -0.5 (-50%). For skills increasing a unit's Def or Res by a percentage, the values would be positive.

Example: Let's say our red sword unit, wielding an Armorslayer, activates New Moon and the blue unit from before being armored. Adv is still -0.2, Eff is still 1.5, but MitMod has been introduced at -0.3.

$$ \text{Expected damage} = \text{max} \bigl( \left \lfloor {15} \cdot {1.5} \right \rfloor + \bigl\lfloor \left \lfloor {15} \cdot {1.5} \right \rfloor \cdot {-0.2} \bigr\rfloor - \bigl( {11} + \left \lfloor {11} \cdot {-0.3} \right \rfloor \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( \left \lfloor {22.5} \right \rfloor + \bigl\lfloor \left \lfloor {22.5} \right \rfloor \cdot {-0.2} \bigr\rfloor - \bigl( {11} + \left \lfloor {-3.3} \right \rfloor \bigr) \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {22} + \left \lfloor {22} \cdot {-0.2} \right \rfloor - \bigl( {11} + {-3} \bigr) \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {22} + \left \lfloor {-4.4} \right \rfloor - {8} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {22} + {-4} - {8} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {10} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = {10} $$

If we also consider offensive skills which boost the damage of an attack by a percent of a certain stat (e.g. Bonfire or Iceberg), the formula looks like this:

$$ \Bigl\lfloor \text{max} \bigl(  \left \lfloor {Atk} \cdot {Eff} \right \rfloor    + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor    + \left \lfloor {SpcStat} \cdot {SpcPercent} \right \rfloor    - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) \text{,} {0} \bigr) \cdot {ClassMod} \Bigr\rfloor $$

where

SpcStat is the value of the stat which is being used by the Special move, such as Res for Glacies. The Dragon Fang family of specials also work like this, for the SpcStat Atk, despite their description.

SpcPercent is the decimal value by which said stat will affect the attack damage, such as 0.8 for Glacies.

Example: This time, let our red sword unit, wielding an Armorslayer, activate Dragon Fang on the blue armored unit. Adv is still -0.2, Eff is still 1.5, MitMod is again 0, but SpcStat is Atk (15) and SpcPercent is 0.5 from Dragon Fang.

$$ \text{Expected damage} = \text{max} \bigl( \left \lfloor {15} \cdot {1.5} \right \rfloor + \bigl\lfloor \left \lfloor {15} \cdot {1.5} \right \rfloor \cdot {-0.2} \bigr\rfloor + \left \lfloor {15} \cdot {0.5} \right \rfloor - \bigl( {11} + \left \lfloor {11} \cdot {0} \right \rfloor \bigr) \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {22} + \left \lfloor {22} \cdot {-0.2} \right \rfloor + \left \lfloor {7.5} \right \rfloor - \bigl( {11} + {0} \bigr) \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {22} + {-4} + {7} - \bigl( {11} + {0} \bigr) \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = \text{max} \bigl( {14} \text{,} {0} \bigr) $$

$$ \qquad \qquad \qquad \qquad = {14} $$

Finally, let's consider offensive special skills which grant a percentage increase to the damage dealt (e.g. Night Sky or Glimmer), and defensive special skills, which reduce the damage taken by a certain percent (e.g. Pavise or Aegis):

$$ \Biggl\lceil \biggl\lfloor \Bigl\lfloor \text{max} \bigl(  \left \lfloor {Atk} \cdot {Eff} \right \rfloor    + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor    + \left \lfloor {SpcStat} \cdot {SpcPercent} \right \rfloor    - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) \text{,} {0} \bigr) \cdot {ClassMod} \Bigr\rfloor \cdot ( 1 + {OffMult} ) \biggr\rfloor \cdot ( 1 - {DefMult} ) \biggr\rceil $$

where

OffMult is the decimal value by which the final damage dealt will be increased by the special, such as 0.5 for Night Sky and Glimmer, or 1.5 for Astra.

DefMult is the decimal value by which the final damage dealt will be decreased by the special, such as 0.3 for Buckler, or 0.5 for Pavise.

Note: Just as he $$ \left \lfloor \, \right \rfloor $$ notation is used to mean https://en.wikipedia.org/wiki/Truncation in this and preceding formulae, the $$ \left \lceil \, \right \rceil $$ notation is used to mean "round-towards-infinity". This means that $$ \left \lfloor {-1.5} \right \rfloor = -1 $$, and $$ \left \lceil {-1.5} \right \rceil = -2 $$. These are not the same as the floor and ceil functions https://en.wikipedia.org/wiki/Rounding#Rounding_to_integer. This notation is used only to improve legibility of the formulae.

Also note, that the outermost rounding is a "round-towards-infinity", as opposed to all the previous "round-towards-zero". This is a simplification of the formula $$ \left \lfloor {Total Damage} \right \rfloor + \left \lfloor {DefMult} \cdot {Total Damage} \right \rfloor $$ which may be preferable in some contexts, as it always truncates all fractions.

Example: For our last example, our red sword unit, wielding an Armorslayer, activate Night Sky on the blue armored unit, which activates Buckler. Adv is -0.2, Eff is 1.5, MitMod is 0, SpcPercent is 0, but OffMult is 0.5 from Night Sky and DefMult is 0.3 from Buckler.

$$ \text{Expected damage} = \biggl\lceil \Bigl\lfloor \text{max} \bigl(  \left \lfloor {15} \cdot {1.5} \right \rfloor    + \bigl\lfloor \left \lfloor {15} \cdot {1.5} \right \rfloor \cdot {-0.2} \bigr\rfloor    + \cancel{ \left \lfloor {N/A} \cdot {0} \right \rfloor }   - \bigl( {11} + \cancel{ \left \lfloor {11} \cdot {0} \right \rfloor } \bigr) \text{,} {0} \bigr) \cdot ( 1 + {0.5} ) \Bigr\rfloor \cdot ( 1 - {0.3} ) \biggr\rceil $$

$$ \qquad \qquad \qquad \qquad \, = \biggl\lceil \Bigl\lfloor \text{max} \bigl(  {22}    + {-4}   - {11} \text{,} {0} \bigr) \cdot ( {1.5} ) \Bigr\rfloor \cdot ( {0.7} ) \biggr\rceil $$

$$ \qquad \qquad \qquad \qquad \, \, = \Bigl\lceil \bigl\lfloor {7} \cdot ( {1.5} ) \bigr\rfloor \cdot ( {0.7} ) \Bigr\rceil $$

$$ \qquad \qquad \qquad \qquad \, \, = \bigl\lceil \left \lfloor {10.5} ) \right \rfloor \cdot ( {0.7} ) \bigr\rceil $$

$$ \qquad \qquad \qquad \qquad = \left \lceil {10} \cdot ( {0.7} ) \right \rceil \text{Note: Would have done 10 damage without Buckler} $$

$$ \qquad \qquad \qquad \qquad \, \, = {7} $$

New formulae:

1. Basic

$$ {Atk} - {Mit} $$

max. (No longer needed)

2. Adv

$$ {Atk} + \left \lfloor {Atk} \cdot {Adv} \right \rfloor - {Mit} $$

3. Eff

$$ \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor - {Mit} $$

4. ClassMod

$$ \Bigl\lfloor \bigl( \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor - {Mit} \bigr) \cdot {ClassMod} \Bigr\rfloor $$

5. MitMod

$$ \biggl\lfloor \Bigl( \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor   - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) \Bigr) \cdot {ClassMod} \biggr\rfloor $$

6. SpcStat

$$ \biggl\lfloor \Bigl(  \left \lfloor {Atk} \cdot {Eff} \right \rfloor    + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor    + \left \lfloor {SpcStat} \cdot {SpcMod} \right \rfloor    - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) \Bigr) \cdot {ClassMod} \biggr\rfloor $$

7. OffDefMult

$$ \Biggl\lceil \biggl\lfloor \Bigl\lfloor \Bigl(  \left \lfloor {Atk} \cdot {Eff} \right \rfloor    + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor    + \left \lfloor {SpcStat} \cdot {SpcMod} \right \rfloor    - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) \Bigr) \cdot {ClassMod} \Bigr\rfloor \cdot ( 1 + {OffMult} ) \biggr\rfloor \cdot ( 1 - {DefMult} ) \Biggr\rceil $$

New examples:

1. Basic

$$ \text{Atk} = {15}$$

$$ \text{Mit} = {11}$$

$$ \text{Atk} - \text{Mit} = $$

$$ \qquad \qquad \ \ = {15} - {11}$$

$$ \qquad \qquad \ \ = {4} \text{ damage}$$

max. No longer needed

$$ \text{Atk} = {11}$$

$$ \text{Mit} = {15}$$

$$ \text{max} \left( \text{Atk} - \text{Mit} \text{, } {0} \right) = $$

$$ \qquad \qquad \ \ = \text{max} \left( {11} - {15} \text{, } {0} \right)$$

$$ \qquad \qquad \ \ = \text{max} \left( {-4} \text{, } {0} \right)$$

$$ \qquad \qquad \ \ = {0} \text{ damage}$$

2. Adv

$$ \text{Atk} = {15}$$

$$ \text{Mit} = {11}$$

$$ \text{Adv} = {-0.2}$$

$$ {Atk} + \left \lfloor {Atk} \cdot {Adv} \right \rfloor - {Mit} = $$

$$ \qquad \qquad \ \ = {15} + \left \lfloor {15} \cdot {-0.2} \right \rfloor - {11}$$

$$ \qquad \qquad \ \ = {15} + \left \lfloor {-3} \right \rfloor - {11}$$

$$ \qquad \qquad \ \ = {15} + {-3} - {11}$$

$$ \qquad \qquad \ \ = {1} \text{ damage}$$

3. Eff

$$ \text{Atk} = {15}$$

$$ \text{Mit} = {11}$$

$$ \text{Adv} = {-0.2}$$

$$ \text{Eff} = {1.5}$$

$$ \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor - {Mit} = $$

$$ \qquad \qquad \ \ = \left \lfloor {15} \cdot {1.5} \right \rfloor + \bigl\lfloor \left \lfloor {15} \cdot {1.5} \right \rfloor \cdot {-0.2} \bigr\rfloor - {11}$$

$$ \qquad \qquad \ \ = \left \lfloor {22.5} \right \rfloor + \bigl\lfloor \left \lfloor {22.5} \right \rfloor \cdot {-0.2} \bigr\rfloor - {11}$$

$$ \qquad \qquad \ \ = \left \lfloor {22.5} \right \rfloor + \left \lfloor {22} \cdot {-0.2} \right \rfloor - {11}$$

$$ \qquad \qquad \ \ = \left \lfloor {22.5} \right \rfloor + \left \lfloor {-4.4} \right \rfloor - {11}$$

$$ \qquad \qquad \ \ = {22} + {-4} - {11}$$

$$ \qquad \qquad \ \ = {7} \text{ damage}$$

4. ClassMod

$$ \text{Atk} = {15}$$

$$ \text{Mit} = {11}$$

$$ \text{Adv} = {0}$$

$$ \text{Eff} = {1}$$

$$ \text{ClassMod} = {0.5}$$

$$ \Bigl\lfloor \bigl( \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor - {Mit} \bigr) \cdot {ClassMod} \Bigr\rfloor = $$

$$ \qquad \qquad \ \ = \Bigl\lfloor \bigl( \left \lfloor {15} \cdot {1} \right \rfloor + \bigl\lfloor \left \lfloor {15} \cdot {1} \right \rfloor \cdot {0} \bigr\rfloor - {11} \bigr) \cdot {0.5} \Bigr\rfloor$$

$$ \qquad \qquad \ \ = \Bigl\lfloor \bigl( \left \lfloor {15} \right \rfloor + \bigl\lfloor \left \lfloor {15} \right \rfloor \cdot {0} \bigr\rfloor - {11} \bigr) \cdot {0.5} \Bigr\rfloor$$

$$ \qquad \qquad \ \ = \Bigl\lfloor \bigl( \left \lfloor {15} \right \rfloor + \left \lfloor {0} \right \rfloor - {11} \bigr) \cdot {0.5} \Bigr\rfloor$$

$$ \qquad \qquad \ \ = \bigl\lfloor \left( {15} + {0} - {11} \right) \cdot {0.5} \bigr\rfloor$$

$$ \qquad \qquad \ \ = \left \lfloor {4} \cdot {0.5} \right \rfloor$$

$$ \qquad \qquad \ \ = \left \lfloor {2} \right \rfloor$$

$$ \qquad \qquad \ \ = {2} \text{ damage}$$

5. MitMod

$$ \text{Atk} = {15}$$

$$ \text{Mit} = {11}$$

$$ \text{Adv} = {-0.2}$$

$$ \text{Eff} = {1.5}$$

$$ \text{MitMod} = {-0.3}$$

$$ \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) = $$

$$ \qquad \qquad \ \ = \left \lfloor {15} \cdot {1.5} \right \rfloor + \bigl\lfloor \left \lfloor {15} \cdot {1.5} \right \rfloor \cdot {-0.2} \bigr\rfloor - \bigl( {11} + \left \lfloor {11} \cdot {-0.3} \right \rfloor \bigr)$$

$$ \qquad \qquad \ \ = \left \lfloor {22.5} \right \rfloor + \bigl\lfloor \left \lfloor {22.5} \right \rfloor \cdot {-0.2} \bigr\rfloor - \bigl( {11} + \left \lfloor {-3.3} \right \rfloor \bigr)$$

$$ \qquad \qquad \ \ = \left \lfloor {22.5} \right \rfloor + \left \lfloor {22} \cdot {-0.2} \right \rfloor - \left( {11} + {-3} \right)$$

$$ \qquad \qquad \ \ = \left \lfloor {22.5} \right \rfloor + \left \lfloor {-4.4} \right \rfloor - {8}$$

$$ \qquad \qquad \ \ = {22} + {-4} - {8}$$

$$ \qquad \qquad \ \ = {10} \text{ damage}$$

6. SpcStat

$$ \text{Atk} = {15}$$

$$ \text{Mit} = {11}$$

$$ \text{Adv} = {-0.2}$$

$$ \text{Eff} = {1.5}$$

$$ \text{MitMod} = {0}$$

$$ \text{SpcStat} = {15}$$

$$ \text{SpcMod} = {0.5}$$

$$ \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor + \left \lfloor {SpcStat} \cdot {SpcMod} \right \rfloor - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) = $$

$$ \qquad \qquad \ \ = \left \lfloor {15} \cdot {1.5} \right \rfloor + \bigl\lfloor \left \lfloor {15} \cdot {1.5} \right \rfloor \cdot {-0.2} \bigr\rfloor + \left \lfloor {15} \cdot {0.5} \right \rfloor - \bigl( {11} + \left \lfloor {11} \cdot {0} \right \rfloor \bigr)$$

$$ \qquad \qquad \ \ = \left \lfloor {22.5} \right \rfloor + \bigl\lfloor \left \lfloor {22.5} \right \rfloor \cdot {-0.2} \bigr\rfloor + \left \lfloor {7.5} \right \rfloor - \bigl( {11} + \left \lfloor {0} \right \rfloor \bigr)$$

$$ \qquad \qquad \ \ = \left \lfloor {22.5} \right \rfloor + \left \lfloor {22} \cdot {-0.2} \right \rfloor + \left \lfloor {7.5} \right \rfloor - \left( {11} + {0} \right)$$

$$ \qquad \qquad \ \ = \left \lfloor {22.5} \right \rfloor + \left \lfloor {-4.4} \right \rfloor + \left \lfloor {7.5} \right \rfloor - {11} $$

$$ \qquad \qquad \ \ = {22} + {-4} + {7} - {11}$$

$$ \qquad \qquad \ \ = {14} \text{ damage}$$

7. OffDefMult

$$ \text{Atk} = {15}$$

$$ \text{Mit} = {11}$$

$$ \text{Adv} = {-0.2}$$

$$ \text{Eff} = {1.5}$$

$$ \text{MitMod} = {0}$$

$$ \text{SpcStat} = {N/A}$$

$$ \text{SpcMod} = {0}$$

$$ \text{OffMult} = {0.5}$$

$$ \text{DefMult} = {0.3}$$

$$ \Biggl\lceil \biggl\lfloor \Bigl(   \left \lfloor {Atk} \cdot {Eff} \right \rfloor     + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor    + \left \lfloor {SpcStat} \cdot {SpcMod} \right \rfloor    - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) \Bigr) \cdot ( 1 + {OffMult} ) \biggr\rfloor \cdot ( 1 - {DefMult} ) \Biggr\rceil = $$

$$ \qquad \qquad \ \ = \Biggl\lceil \biggl\lfloor \Bigl(   \left \lfloor {15} \cdot {1.5} \right \rfloor     + \bigl\lfloor \left \lfloor {15} \cdot {1.5} \right \rfloor \cdot {-0.2} \bigr\rfloor     + \cancel{ \left \lfloor {N/A} \cdot {0} \right \rfloor }    - \bigl( {11} + \cancel{ \left \lfloor {11} \cdot {0} \right \rfloor } \bigr) \Bigr) \cdot ( 1 + {0.5} ) \biggr\rfloor \cdot ( 1 - {0.3} ) \Biggr\rceil $$

$$ \qquad \qquad \ \ = \Biggl\lceil \biggl\lfloor \Bigl(   \left \lfloor {15} \cdot {1.5} \right \rfloor     + \bigl\lfloor \left \lfloor {15} \cdot {1.5} \right \rfloor \cdot {-0.2} \bigr\rfloor     - {11} \Bigr) \cdot ( 1 + {0.5} ) \biggr\rfloor \cdot ( 1 - {0.3} ) \Biggr\rceil $$

$$ \qquad \qquad \ \ = \Biggl\lceil \biggl\lfloor \Bigl(   \left \lfloor {22.5} \right \rfloor     + \bigl\lfloor \left \lfloor {22.5} \right \rfloor \cdot {-0.2} \bigr\rfloor     - {11} \text{, } {0} \Bigr) \cdot ( 1 + {0.5} ) \biggr\rfloor \cdot ( 1 - {0.3} ) \Biggr\rceil $$

$$ \qquad \qquad \ \ = \biggl\lceil \Bigl\lfloor \left(   {22}     + \left \lfloor {-4.4} \right \rfloor     - {11} \right) \cdot ( 1 + {0.5} ) \Bigr\rfloor \cdot ( 1 - {0.3} ) \biggr\rceil $$

$$ \qquad \qquad \ \ = \Bigl\lceil \bigl\lfloor \left(   {22}     + {-4}     - {11} \right) \cdot ( 1 + {0.5} ) \bigr\rfloor \cdot ( 1 - {0.3} ) \Bigr\rceil $$

$$ \qquad \qquad \ \ = \bigl\lceil \left \lfloor {7}  \cdot ( 1 + {0.5} ) \right \rfloor \cdot ( 1 - {0.3} ) \bigr\rceil $$

$$ \qquad \qquad \ \ = \bigl\lceil \left \lfloor {7}  \cdot {1.5} \right \rfloor \cdot {0.7} \bigr\rceil $$

$$ \qquad \qquad \ \ = \bigl\lceil \left \lfloor {10.5} \right \rfloor \cdot {0.7} \bigr\rceil $$

$$ \qquad \qquad \ = \left \lceil {10} \cdot {0.7} \right \rceil \text{ Note: Would have done 10 damage without Buckler} $$

$$ \qquad \qquad \ \ = \left \lceil {7} \right \rceil $$

$$ \qquad \qquad \ \ = {7} \text{ damage} $$

8. Flat Damage Wo Dao, Dark Excalibur, Shield Pulse $$ \Biggl\lceil \Biggl( \biggl\lfloor  \Bigl( \left \lfloor {Atk} \cdot {Eff} \right \rfloor + \bigl\lfloor \left \lfloor {Atk} \cdot {Eff} \right \rfloor \cdot {Adv} \bigr\rfloor + \left \lfloor {SpcStat} \cdot {SpcMod} \right \rfloor - \bigl( {Mit} + \left \lfloor {Mit} \cdot {MitMod} \right \rfloor \bigr) \Bigr)  \cdot ( 1 + {OffMult} )  \biggr\rfloor + {OffFlat} \Biggr) \cdot ( 1 - {DefMult} ) - {DefFlat} \Biggr\rceil $$