Damage caused by both standard attacks and active skills in this game can be determined by a simple linear formula. It has been derived via collection of many points of damage data against fixed NPC targets in the game's story mode. There are a number of factors that impact the amount of damage dealt during an attack. At a high level, these are:
Commander StatsEdit
It is best to start the description of the damage formula by first looking at what drives a commander's stats during battle. Each commander has a unique set of HP, ATK, DEF, and WIS stats determined by the commander’s minimum and maximum stat values and current level. Commanders are obtained at level one, at which point they exhibit their minimum stats. They may be leveled up to a maximum level equal to Rarity * 10 + 10. (Although, 6* commanders break this rule and have a maximum level of 80.) At the maximum level, a commander’s maximum base stats are reached. Every commander’s stats grow linearly as levels increase.
The base stats determined by commander and level are then increased by any applicable additions due to soul fusion, equipment, masteries, leader skills, or race synergy bonuses. Soul fusion boosts are calculated first, by multiplying the commander's current base stat by 1 + Fusion Boost. After the soul fusion boost, equipment is factored (souls and gear). These elements produce the stats that appear when viewing a commander in the Roster menu.
When a commander enters battle, stats are further modified by mastery boosts, leader skills, and any applicable race synergy bonuses. There are a number of masteries that can be used to increase all commanders' stats. The total percentage increase is dependent upon the number of masteries completed. The individual mastery stat boosts stack in an additive manner, thus the stats are increased by the sum of the mastery boost percentages, rather than the product. The maximum attainable stat boosts when all masteries are complete may be found in the following table.
Total Stat Boost | 19% | 19% | 18% | 18% |
Leader skill and race synergy bonuses are added to the mastery boosts before factoring the pre-battle stats. Leader skills are passive and apply to all five commanders in a brigade. Most leader skills buff particular stats, but there are a few that do things such as regen or boost capture rates. Race synergy bonuses apply to some levels in the game and can be found in the level preview and detail screens before entering a level.
The overall formula for determining a commander's in-battle stats is as follows:
Battle_Stat = (Base_Stat * (1 + Fusion Boost) + Soul_Stat + Gear_Stat) * (1 + Masteries_Boost + LeaderSkill_Mod + Race_Synergy_Mod)
Some active skills may also further increase stats during battle, but this will be addressed in more detail below, in the section about skills.
AffinitiesEdit
There are three affinities in this game:
Each commander is assigned an affinity, which can be determined by the icons used in the below table. The circle of affinities (seen on every loading screen in the game) dictates how strong each affinity is against the others. Each affinity does normal damage to other members of their own affinity, but deal greater damage to the affinity against which they are strong, and reduced damage to the affinity against which they are weak. This table demonstrates the damage multipliers used for each combination of affinities.
Target | Target | Target | |
---|---|---|---|
Attacker | 1.00 | 1.35 | 0.65 |
Attacker | 0.65 | 1.00 | 1.35 |
Attacker | 1.35 | 0.65 | 1.00 |
Proper use of these damage modifiers will be explained in the section about the damage formula.
SkillsEdit
There are two primary ways for a commander to attack an opponent. The first is with a standard attack (initiated by simply tapping the desired commander on the screen when in battle). The second is with active skills (initiated by swiping a commander up onto the battlefield when it is glowing). Damage is calculated in the same way for either type of attack, but skills present the opportunity to deal damage based on a stat other than ATK, or to hit multiple times, or to hit much harder than standard.
Active skills that deal damage have the following key attributes:
- Skill Modifier
- Targeting Pattern
- Number of Targets Struck
- Number of Triggers
Each particular combination of the above factors determines what kind of total damage a commander is capable of dealing with an active skill. The other major factor is which of the commander's stats is used as the main source of damage for the skill. The game started with both ATK-based and WIS-based commanders, and has since added DEF-based and HP-based commanders.
Note that not all active skills deal damage. Some only poison, regen, heal, buff, or debuff. These skills also have use, and may indirectly affect the damage dealt, but do not directly deal damage to the target (see heal skills and indirect skills for reference).
Buff and debuff skills modify a stat or stats of the active commanders in the brigade. Active buff and debuff skills have parameters that control how many commanders are affected as well as the magnitude of the buff or debuff. The commander's source stat (inclusive of fusion, equipment, masteries, and leader skills) is multiplied by the modifier of the skill to determine the value of the buff or debuff.
Damage FormulaEdit
With a good understanding of the preceding information, it is time to tackle the actual damage formula. It can generally be written as follows:
- DMG = Affinity_Mod * ((Atk_Stat + Atk_Buff) * Skill_Mod - 0.2 * (Def_Stat + Def_Buff))
Where:
- DMG =
- The calculated damage, per hit, dealt by an attack.
- Affinity_Mod =
- The damage modifier derived from combining the affinity of the attacker and the affinity of the target, as per the affinity table above.
- Atk_Stat =
- The stat of the attacker used to deal damage in the attack. This is ATK for all standard attacks, as well as for ATK-Based active skills. This is WIS for all WIS-Based active skills. It is HP for HP-Based active skills and DEF for DEF-Based active skills. The value used for this variable should be inclusive of all masteries, souls, gear, and leader skills.
- Atk_Buff =
- The sum of all buffs and debuffs applied to the attacking commander's attacking stat (value will be negative if the net stat modificaiton is a debuff).
- Skill_Mod =
- The modifier of the active skill used for the attack. This can be found on the wiki at each skill's page. For standard attacks, a value of 1.0 should be used.
- Def_Stat =
- The stat used by the targeted commander to defend against the incoming damage. For all ATK-Based, DEF-Based or HP-Based damage, this will be the commander's DEF stat. For all WIS-Based damage, it will be the targeted commander's WIS stat.
- Def_Buff =
- The sum of all buffs and debuffs applied to the targeted commander's defending stat (value will be negative if the net stat modificaiton is a debuff).
The damage formula is a fairly simple linear equation. The most prominent variable in determining the final damage value for each attack is the attacking commander's own attacking stat (either ATK or WIS). This is the basis for all damage. Use the information from the commander stats section above to determine the attacking commander's attack stat.
Once the attacking stat is known, it is then modified by any pertinent buffs applied to the attacking commander during battle. This is done by adding the net value of all buffs and debuffs applied to the commander.
The modified attacking stat is then multiplied by the modifier of the active skill being used. If the commander is performing a standard attack, this value will simply be 1.0.
Once all modifiers have been applied to the attack stat, the damage is then mitigated by the target commander's defending stat. For ATK-Based skills, this is DEF, for WIS-Based skills, it is the target's WIS stat. Similar to what was done for the attacker's attacking stat, the target's defending stat is modified by any pertinent buffs or debuffs. Finally, a constant of 0.2 is applied to the defending stat, which means that only 20% of a commander's defensive stat is used to mitigate damage.
Once all the above calculations are complete, the final step is to multiply the entire result by the affinity modifier, as outlined above. The affinity modifier is not an attack stat modifier, but a damage modifier, effectively being applied to both the attacking stat and the defending stat.
Note: In the case of an attacker with a very low attacking stat attacking a target with a very large defending stat, zero or negative values may at times be produced by the above formula. In such a case, there is a floor for the damage formula. For ATK-based damage, if (Atk_Stat + Atk_Buff) * Skill_Mod - 0.2 * (Def_Stat + Def_Buff) is less than Atk_Stat * 0.05, then ATK * 0.05 will be used as the minimum damage dealt. For WIS-based damage, if (Atk_Stat + Atk_Buff) * Skill_Mod - 0.2 * (Def_Stat + Def_Buff) is less than Def_Stat * 0.2, then WIS * 0.2 will be used as the minimum damage dealt. For DEF-based damage, if (Atk_Stat + Atk_Buff) * Skill_Mod - 0.2 * (Def_Stat + Def_Buff) is less than Atk_Stat * 0.05, then DEF * 0.05 will be used as the minimum damage dealt. For HP-based damage, if (Atk_Stat + Atk_Buff) * Skill_Mod - 0.2 * (Def_Stat + Def_Buff) is less than Atk_Stat * 0.05, then HP* 0.00 will be used as the minimum damage dealt.
Sample Calculation
Xanti, Cruelwing | Nunu, Hill Strider | |||
0/4 Asc HP | 1,513 | 0/4 Asc HP | 1,962 | |
0/4 Asc ATK | 631 | 0/4 Asc ATK | 867 | |
0/4 Asc DEF | 593 | 0/4 Asc DEF | 1,218 | |
0/4 Asc WIS | 1,071 | 0/4 Asc WIS | 753 | |
Active Skill | Firestorm | Active Skill | Massive Assault | |
Skill Source | WIS | Skill Source | ATK | |
Affinity | Ranged | Affinity | Melee |
Following are four sample damage calculations given the above two commanders. These calculations will assume:
- All masteries have been researched, giving the full stat boosts possible from masteries.
- No soul fusions have been performed on either commander.
- Xanti has been equipped with her own 3* soul and Studded Armor, and is in a brig using the ATK Up 2 leader skill.
- Nunu has been equipped with his own 3* soul and Studded Armor, and is in a brig using the HP Up 2 leader skill.
The four calculations will be:
- Xanti attacking Nunu with a standard attack.
- Xanti attacking Nunu with an active skill attack.
- Nunu attacking Xanti with a standard attack.
- Nunu attacking Xanti with an active skill attack.
The first step for all calculations is finding the in-battle stats by factoring base stats, soul fusion, equipment, masteries, leader skills, and race synergy bonuses. When playing the game, these stats can be seen by viewing your brig details while in a battle, but they they can also be forecast, as below (refer to the commander stats section).
- Battle_Stat = (Base_Stat * (1 + Fusion Boost) + Soul_Stat + Gear_Stat) * (1 + Masteries_Boost + LeaderSkill_Mod + Race_Synergy_Mod)
Given the commanders and assumptions above, this results in new stats for Xanti and Nunu:
Xanti, Cruelwing | Nunu, Hill Strider | ||
---|---|---|---|
HP | 1,982 | HP | 2,810 |
ATK | 837 | ATK | 1,162 |
DEF | 804 | DEF | 1,825 |
WIS | 1,511 | WIS | 985 |
- Xanti attacking Nunu with a standard attack
- Affinity_Mod = 1.35
- Atk_Stat = ATK = 837
- Skill_Mod = 1.0
- Atk_Buff_Mods = 0.0
- Def_Stat = 1,825
- Def_Buff_Mods = 0.0
- DMG = 1.35 * (837 * 1.0 * 1.0 - 0.2 * 1,825 * 1.0) = 637
- Xanti attacking Nunu with an active skill attack
- Affinity_Mod = 1.35
- Atk_Stat = WIS = 1,511
- Skill_Mod = 0.95
- Atk_Buff_Mods = 0.0
- Def_Stat = 985
- Def_Buff_Mods = 0.0
- DMG = 1.35 * (1,511 * 0.95 * 1.0 - 0.2 * 985 * 1.0) = 1,671
- Nunu attacking Xanti with a standard attack
- Affinity_Mod = 0.65
- Atk_Stat = ATK = 1,162
- Skill_Mod = 1.0
- Atk_Buff_Mods = 0.0
- Def_Stat = 805
- Def_Buff_Mods = 0.0
- DMG = 0.65 * (1,162 * 1.0 * 1.0 - 0.2 * 805 * 1.0) = 650
- Nunu attacking Xanti with an active skill attack
- Affinity_Mod = 0.65
- Atk_Stat = ATK = 1,162
- Skill_Mod = 1.75
- Atk_Buff_Mods = 0.0
- Def_Stat = 805
- Def_Buff_Mods = 0.0
- DMG = 0.65 * (1,162 * 1.75 * 1.0 - 0.2 * 805 * 1.0) = 1,217
An online spreadsheet-based calculator has been developed to assist with these calculations. Please follow this link to get to it: Online BB2 Damage Calculator.