In Blood Brothers, there is a formula used to determine the damage dealt when one familiar attacks another familiar or a boss. It has been derived via data gathering and linear regression, then the results corroborated by information gathered from the game files by Chinhodado.
Damage Formula - Generalized Form
This format of the damage formula allows it to be applied to any attack in the game. It can be used to describe the damage output by any type of skill from any familiar or warlord, from any position, against any type of opponent. It is as follows:
Dmg/hit = 0.5 * Atk_Pos * Def_Pos * Skill_Mod * Rand * (Atk_Stat - 0.4 * Def_Stat)
Dmg/hit = The damage dealt by one strike of a skill or autoattack against one target.
Atk_Pos = Position modifier for the attacking familiar or warlord. It equals 1.2 for attackers in the front row, 1.0 for attackers in the middle row, 0.8 for attackers in the rear row, and 1.0 for attackers using position independent attacks.
Def_Pos = Position modifier for the targeted familiar or boss. It equals 1.2 for targets in the front row, 1.0 for targets in the middle row, 0.8 for targets in the rear row, and 1.0 for targets in any row when the attacker is using a position independent attack.
Most auto attacks use a Skill_Mod of 1.0, unless specified implicitly on the familiar's page (e.g.: 1.4 for Alberich, the Ceratophrys II).
Rand = A random number between 0.9 and 1.1. This serves to add some variance to the damage dealt in an attack (as much as +/- 10%). If the desired result of a calculation is average damage, this variable may be ignored.
Atk_Stat = The value of the stat (inclusive of title bonus and all out bonus) used by the attacking familiar or warlord to deal damage. Usually, this is the ATK stat for autoattacks (with the exception of fams with WIS-based autoattacks: e.g. Typhon II, or Lahamu, Royal Viper II). For skills, this could be ATK, WIS, or AGI, depending on the skill being used.
Def_Stat = The value of the stat used by the target familiar to mitigate damage dealt by the attacker. For damage dealt by an attacker’s ATK or AGI stat, the target’s DEF stat (not including title bonus or all out bonus) is used to defend. For damage dealt by an attacker’s WIS stat, the average of the target’s WIS and DEF stats (inclusive of title bonus and all out bonus) is used to defend.
Note: if 0.5 * Atk_Pos * Def_Pos * (Atk_Stat - 0.4 * Def_Stat) < Atk_Stat * 0.03, then Dmg/hit = 0.03 * Atk_Stat * Rand * Skill_Mod.
Position Dependent Attacks
For position dependent attacks, the position modifiers can make a significant impact on the total damage dealt. Following is a table summarizing the overall position modifier applied to an attack for any combination of attacker and target positions.
|Attacker - Front (1.2)||Attacker - Middle (1.0)||Attacker - Rear (0.8)|
|Target - Front (1.2)||1.44||1.20||0.96|
|Target - Middle (1.0)||1.20||1.00||0.80|
|Target - Rear (0.8)||0.96||0.80||0.64|
Note that position dependent attacks will be either ATK or AGI-based, and the target’s stat used for resisting the attack will always be DEF. Furthermore, note that an attacker’s ATK or AGI stat may have a title bonus or all out bonus that needs to be included, whereas the target’s DEF stat will never have a title bonus applied. All ATK-based autoattacks are position dependent. View this page to see a list of position dependent skills: Category:Skills/Position_Dependent.
Position Independent Attacks
For position independent attacks, both Atk_Pos and Def_Pos are equal to 1.0, so they may effectively be dropped from the equation so that it looks like this:
Dmg/hit = 0.5 * Skill_Mod * (Atk_Stat - 0.4 * Def_Stat)
Most position independent skills are WIS-based, but there are a few ATK and AGI-based skills which are also position independent. Don’t forget that for WIS-based attacks, the target’s title bonus and all out bonus does need to be factored in their WIS stat used to resist the attack. Any WIS-based autoattacks are also position independent. View this page to see a list of position independent skills: Category:Skills/Position_Independent.
Effect of Buffs/Debuffs
If an attacker or target received buffs or debuffs at the opening of a battle, the damage dealt in an attack may change due to pertinent attacking/defending stats having been increased or decreased.
The source of both buffs and debuffs is the caster’s WIS stat (inclusive of title bonus and all out bonus). To determine the value of a buff, simply multiply the caster’s WIS by the title bonus and the modifier of the skill (e.g.: 0.2 for Strength of Blades 2, 0.3 for Grace of Winds 3, 0.5 for Guile of Runes, etc.).
Debuffs work similarly, but in most cases are significantly mitigated by the target’s own WIS stat. For nearly all debuff skills, the target’s WIS (inclusive of title bonus and all out bonus) is subtracted from the caster’s WIS (inclusive of title bonus and all out bonus) before applying the skill multiplier. There are debuff skills that are excluded from this typical mode of calculation and ignore the target's WIS, namely the ones that use the terminology "greatly reduce" in their description. Examples are Broken Vow and Wail of Sorrow. These debuffs are calculated just like buffs: the caster's WIS multiplied by the title bonus and the skill modifier.
To incorporate buffs and debuffs in the damage equation, modify the Atk_Stat and/or Def_Stat in the formula. Thus, for a familiar with a buffed attacking or defending stat:
Buffed_Stat = (Base_Stat + Buff_WIS * Buff_Mod) * Title_Bonus
Buffed_Stat = New value of attacking or defending stat after the value of the buff is incorporated.
Base_Stat = The original value of a familiar or warlord's attacking or defending stat prior to receiving a buff/debuff.
Buff_WIS = The WIS stat of the familiar or WL casting the buff skill.
Buff_Mod = The skill modifier of the buff skill.
Title_Bonus = The title bonus of the brigade containing the buffer and the recipients of the buff.
Similarly, if a target’s defending stat has been debuffed (with a typical debuff skill such as Shield Rend 4), Def_Stat becomes:
Debuffed_Stat = Base_Stat – (Atk_WIS * Atk_Title_Bonus – Def_WIS * Def_Title_Bonus) * Debuff_Mod
Or in the case of a debuff skill that ignores the target's WIS:
Debuffed_Stat = Base_Stat - Atk_WIS * Atk_Title_Bonus * Debuff_Mod
Debuffed_Stat = New value of attacking or defending stat after the value of the debuff is incorporated.
Atk_WIS = The WIS stat of the familiar or warlord casting the debuff skill.
Atk_Title_Bonus = The title bonus of the familiar or warlord casting the debuff skill.
Def_WIS = The WIS stat of the familiar or warlord targeted by the debuff skill.
Def_Title_Bonus = The title bonus of the familiar or warlord targeted by the debuff skill.
Debuff_Mod = The skill modifier of the debuff skill.
Note: if Atk_WIS * Atk_Title_Bonus – Def_WIS * Def_Title_Bonus < Atk_WIS * Atk_Title_Bonus * 0.1, then Atk_WIS * Atk_Title_Bonus * 0.1 will be used as a minimum value in the calculation.
These formulas assume a single buff or debuff is being applied, but buffs and debuffs do stack, i.e. multiple buffs can be applied to a single familiar or warlord, each one adding to the value of the stats. If a scenario with multiple buffs needs to be analyzed, simpy add a term to the above equations for each additional buff or debuff applied.
Reflection skills are some of the most complicated skills in this game. They use multiple modifiers and multiple sources for their damage. In addition, they not only deal damage but also reduce damage taken, like a ward. The general formula for damage per hit is:
Refl_Dmg/hit = Atk_Pos * Def_Pos * Skill_Mod * Rand * (Calculated_Incoming_Pos_Indep_Dmg + (Caster_Def_Stat - Target_Def_Stat) * 0.7)
Refl_Dmg/hit = Damage per hit dealt to opponents as a result of the reflect skill.
Calculated_Incoming_Pos_Indep_Dmg = The damage which should be dealt to the familiar possessing the reflect skill, ignoring position modifiers, but factoring all other typical damage variables (including stats, skill modifiers, and wards). Use the other damage formulas on this page to derive this value.
Caster_Def_Stat = The defending stat of the familiar casting the reflect skill. Currently, all reflect skills utilize DEF for this.
Target_Def_Stat = The defending stat of the familiar receiving the damage from the reflect skill. DEF is used when reflecting ATK or AGI damage. The average of WIS and DEF is used when reflecting WIS damage.
These skills are reactive skills, triggered by damage dealt by a particular source (e.g. ATK only, or AGI and WIS). Once damage is received by the familiar possessing the reflect skill, if the reflect skill triggers two things happen. First, the skill reduces incoming damage just like a ward. For this stage of the skill's operation, the damage taken is the reciprocal of the total damage reflection skill modifier assuming all targets are struck. Thus, if a reflect skill has a modifier of 45% per target and is designed to hit two targets, the total reflection modifier is 45% * 2 = 90%, and incoming damage will be reduced to only 10% of its normal value (100% - 90% = 10%). The second thing that happens is that damage is reflected according to the formula above. It is important to note that the incoming damage referenced in the reflect skill damage/hit formula is not the damage value after having been reduced by the skill mod, but rather the full damage, ignoring position. As with regular attacking skills, if WIS damage is being reflected both Atk_Pos and Def_Pos will equal 1.
Effect of Wards
If a target has received a damage ward at the opening of the battle, then a fixed reduction will be applied to the damage in accordance with the multiplier of the ward. This works much differently than buffs or debuffs, which impact the Atk_Stat or Def_Stat. The ward is simply a multiplier added at the end of the damage formula. Thus, damage becomes:
Ward_Dmg/hit = Base_Dmg/hit * (1 – Ward_Mod)
Ward_Dmg/hit = The normal damage per hit, modified (reduced) by the effect of the ward.
Base_Dmg/hit = The normal damage per hit, using the formulas above (equal to Dmg/hit in the Generalized Form of the damage formula).
Ward_Mod = The skill modifier of the ward skill.
Raid Boss Damage
All of the above formulas apply not only to PvP damage calculations, but to raid boss damage calculations as well. Before attempting to apply these calculations to an attack on a raid boss, the following rules must be followed:
- Raid bosses have a DEF stat of zero, and while WIS-based bosses have a WIS stat used in their own attacks, it is not used to defend, thus for all attacks against a raid boss, Def_Stat = 0 in the damage formula.
- Raid bosses are always placed in the front row position, so for position dependent attacks against a raid boss, Def_Pos = 1.2 in the damage formula.
Online Damage Calculator
An online Google Sheets spreadsheet has been created for use as a damage calculator. Any Warlord, or Epic, Legendary, or Mythic familiar may be selected and analyzed for damage output against a target. Wards and buffs are also included. Please be aware at this time that the Rally Cry buff is not yet usable in the calculator, but when it is working, this article will be updated accordingly.
Please click here to visit the Online Damage Calculator.