Combat/Damage Calculation

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Main Formula

${\text{Damage Value}}={\bigg \lfloor }\left(\left\lfloor \left\lfloor \operatorname {cap} \left({\hat {F}}\cdot M_{pre}\right)\right\rfloor \cdot C\right\rfloor \cdot M_{post}-{\hat {A}}\right)\cdot R{\bigg \rfloor }$

Where:

• $\hat{F}$ is Basic Attack Power.
• $M_{pre}$ is the combination of Pre-Cap Modifiers.
• $M_{post}$ is the combination of Post-Cap Modifiers.
• $C$ is the Critical Hit modifier. Assumes a value of 1.5 if the attack is a Critical Hit, and is 1 otherwise.
• $\operatorname{cap}$ is the soft cap to attack power.
• $\hat{A}$ is Defense Power.
• $R = \min \left ( 2A_{s} , 1 \right )$
  • $R$ is the remaining ammo penalty
  • $A_{s}$ is the ship's current ammo percentage (1 bar = 10% = 0.1)
  • $\min$ is the minima function, which takes the lowest value between two quantities.
• $\left\lfloor x \right\rfloor$ is the floor function; that is, the rounding down of input $x$

Defense Power is calculated as follows:

$\hat{A} = 0.7 A_{t} + 0.6 \big ( \text{rand} \in \left [ 0 , A_{t} - 1 \right ] \big )$

Where:

• $A_{t}$ is the defending ship's armor stat
• The random number function outputs a value between 0 and $A_{t} - 1$ (inclusive).

If Damage Value is less than 1, it becomes scratch damage, and the following formula is applied instead:

$\text{Damage Value} = \Big \lfloor H_{t} \cdot \text{rand} \in \left [ 0.06 , 0.14 \right ] \Big \rfloor$

Where:

• $H_{t}$ is the target's current HP.
• The random number function outputs a value between 0.06 and 0.14 (inclusive).

Basic Attack Power

For Shelling:

$\hat{F} = F_{s} + F_{\bigstar} + C_{f} + 5$

• $F_s$ is the ship's firepower stat
• $F_{\bigstar}$ is the sum of all improvements to shelling damage
• $C_{f}$ is the Combined Fleet factor

For Torpedo:

$\hat{F} = T_{s} + T_{\bigstar} + 5$

• $T_s$ is the ship's torpedo stat
• $T_{\bigstar}$ is the sum of all improvements to torpedo damage

For Carrier Shelling:

$\hat{F} = 55 + \big \lfloor 1.5 \left ( F_{s} + T_{s} + \left \lfloor 1.3 D_{s} \right \rfloor + F_{\bigstar} + T_{\bigstar} + C_{f} \right ) \big \rfloor$

• $D_{s}$ is the ship's dive bombing stat

For the Opening Airstrike:

$\hat{F} = M_{a} \left ( P_{a} \sqrt{N} + 25 \right )$

• $N$ is the current plane count (slot size) of a given slot
• $P_{a}$ is the plane's dive bombing or torpedo stat
• $M_a$ is the Plane Scaling modifier:
  • For Dive Bombers and Seaplane Bombers: 1
  • For Torpedo Bombers: 0.8 or 1.5; one value is picked at random (~50% chance of each).

For Anti-Submarine Warfare:

$\hat{F} = \left ( 2 \sqrt{A_{s}} + A_{\bigstar} + 1.5 E_{asw} + C_{t} \right ) \cdot S_{asw} \cdot \left ( 1 + S_{a} + S_{b} \right )$

• $A_{s}$ is the ship's base ASW stat (no equipment ASW is considered)
• $A_{\bigstar}$ is the sum of all improvements to ASW damage
• $E_{asw}$ is the sum of the displayed ASW stat of the ship's equipment. Recon Seaplanes are not considered.
• $C_{t}$ is the ASW type constant:
  • If Sonar or Depth Charge (DD, CL): 13
  • If aircraft-based (AV, CVL, CAV, BBV): 8
• $S_{asw}$ is the basic synergy modifier for ASW. Becomes 1.15 if the ship is equipped with a Sonar and Depth Charge Projector pair; assume 1 otherwise.
• $S_a$ is a secondary synergy modifier. Becomes 0.15 if the ship is equipped with a Sonar and New Depth Charge pair; assume 0 otherwise.
• $S_b$ is a secondary synergy modifier. Becomes 0.1 if the ship is equipped with a Depth Charge Projector and New Depth Charge pair; assume 0 otherwise.

For Night Battle:

$\hat{F} = F_{s} + T_{s} + N_{\bigstar} + C_{r}$

• $N_{\bigstar}$ is the sum of all improvements to night battle damage
• $C_r$ is the Night Contact bonus; 5 if Night Scout has activated, 0 otherwise

Notes:

• Multiple SONAR/Depth charges do not boost the ASW Bonus (i.e. 2 of each still makes the bonus 1.15)
• Please read Akashi's Improvement Arsenal page for effects given by upgraded equipment.
• Please read Combined Fleet page for combined fleet factor in combined fleets.
• All carriers that participate in night battle, including friendly side and abyssal's, use the standard night battle formula.
• During Night Battle, the basic attack power of anti-submarine warfare can be treat as zero, with the exception of in Combined Fleet maps and Night Battle nodes.

Pre-Cap Modifiers

These are the factors directly applied to your ship's attack power.

• Anti-Installation Attack Modifier
• Formation Modifier (see "Damage modifier")
• Engagement Modifier
• Health Modifier
• Night Special Attack Modifier
• Light Cruiser Fit Bonus

Effects from the modifiers are multiplied/added cumulatively.

Anti-Installation Attack Modifier

Main article: Installation Type

• The Type 3 Shell multiplies Attack Power by 2.5.
• The WG42 (Wurfgerät 42) adds at least 75 Attack Power, exact number depend on amount of WG42 equipped, see WG42's page. In the event both are present, this is added after the Type 3 Shell's effects, but before the sum is multiplied by the other modifiers.
• Landing Crafts give varying bonuses against installations.

Note also that against installations, only firepower is taken into account; in night battle, even though attack power is normally the sum of firepower and Torpedo, for installations specifically the Torpedo stat is disregarded.

Ship's Health Modifier

Damage	Modifier
Minor damage (小破 Shouha) or less	100%
Moderate damage (中破 Chuuha)	70%
Heavy damage (大破 Taiha)	40%

These modifiers do not affect Aerial Combat.

Night Special Attack Modifier

An example of a cut-in

Certain Equipment setups have a chance to trigger special attacks at night, giving boost to both attack power and accuracy. This stage is usually the most rewarding / dangerous because both sides have drastically increased attack power.

The ship must be able to participate in the night battle in order to trigger the special attacks.

Light Cruiser Fit Bonus

Main article: Overweight Penalty and Fit Gun Bonus

a few points would be added for CL's attack power after all pre-cap firepower but before the cap if they used fit guns.

• Applicable Twin Gun Mounts: 15.2cm Twin Gun Mount, 15.2cm Twin Gun Mount Kai, 14cm Twin Gun Mount
• Applicable Single Gun Mounts: 15.2cm Single Gun Mount, 14cm Single Gun Mount
• Not Applicable Guns: All the 15.5cm and 20.3cm guns, OTO 152mm Triple Rapid Fire Gun Mount, 15cm Twin Secondary Gun Mount, etc.

Attack Power Cap

Applies after the pre-cap modifiers. This is a soft limit on your effective attack power. It is given by:

$\operatorname{cap} \left ( x \right ) = \begin{cases} S + \sqrt{x - S}, & \text{if } x > S \\ x, & \text{otherwise} \end{cases}$

Where:

• $x$ is the input of the function; or in other words, the value of Basic Attack Power multiplied by all Pre-Cap Modifiers.
• $S$ is the attack power cap, represented by different thresholds according to the type of attack:
  • 180 for Day Battle Shelling
  • 300 for Night Battle
  • 100 for ASW (Anti-Submarine) attacks
  • 150 for Others (support shelling, aerial attack, torpedo attack, etc.)

Daytime Shelling Attack Cap (180) often makes it important to utilize Artillery Spotting since they boost your attack power after the cap, Night Combat can be very dangerous and/or rewarding due to having a very high cap (300) and the inclusion of torpedo to firepower for the basic attack power calculation.

Post-Cap Modifiers

In damage calculation, Post-cap modifiers apply after the cap, but before enemy armor reduction. Thus they are very effective approach to boost your damage output (esp. against heavy armor enemies).

Currently, the post-cap modifiers are from:

• Artillery Spotting (aka. Day time special attacks)
• Critical Damage and Aircraft Proficiency
• Contact (Opening air strike)
• AP Shell (against certain targets)
• PT Imp Pack (unconfirmed)

Artillery Spotting

Certain equipment setups provide a chance to trigger special attacks during day battle, giving boost to both attack power and accuracy. The damage modifiers are applied after the cap (180), thus very effective against heavy armor targets. Note that the ship requires at least 1 seaplane on board to perform Artillery Spotting.

Critical Modifier

Most forms of attack (Torpedo, Shelling, Anti-Submarine, Preemptive Bombing) have a chance to crit the target. The damage modifier applies after the cap.

Attack Type	Modifier
Normal Attack	100%
Critical Hit	150%

It should be noted that the critical message always appears when damage dealt is greater than or equal to 40, regardless of whether the 150% modifier was applied or not. On the other hand, the critical message will never appear when damage dealt is less than or equal to 14, even if the 150% modifier was applied.

Critical damage rate seems to depend on accuracy.

Aircraft Proficiency boost Critical Hit Modifier.

Contact

Contact takes place during the Aerial Combat phase. It increases bombing damage for all allied bombers. When successful, an image of the squadron performing contact is shown in the opposing fleet's formation indicator, with the text "触接中".

• Trigger conditions:
  • More air control than Air Incapability
  • At least one carrier scout plane, seaplane scout, or torpedo bomber equipped.
    • Seaplane bombers, Type 3 Spotter, and Ka-type Autogyros cannot perform contact.
  • It's thought that each carrier scout plane, seaplane scout, and/or torpedo bomber slot equipped is given a chance to trigger contact. Once successful, the bonus applied is chosen at random with weighting preferential towards higher modifiers from all eligible equipped planes.

Different types of planes have different trigger rates. They are roughly estimated as (if only one is equipped):

Type	Contact Rate
Torpedo Bomber	~2%
Night Scout	~5%
Seaplane Scout	~20%
Carrier Scout	~60%
Flying Boat	~70%

Contact Damage Modifier

• The damage increase depends on the +accuracy bonus of the squadron performing contact.

Accuracy Bonus	Damage Modifier
+0	112%
+1	112%
+2	117%
+3	120%

Notes

• Type 2 Recon Aircraft is useful in the case that the bombing damage bonus is desired while not removing the chance for T-disadvantage, due to its high trigger rate.
• With contact, the maximum attack power of bombing (before defense, critical and ammo) is around 180. With some luck, it's possible to sink even Ru-class Flagships (Armor = 99) in one strike without a critical.
• See Contact section in Aerial Combat about triggering rate of this mechanism.

AP Shell

Damage against certain targets increases when both large-caliber main guns and AP shells are equipped.

This modifier works against the following enemy classes:

• Battleships (including Fast Battleships and Aviation Battleships)
• Heavy Cruisers
• Standard Carriers
• Demons and Princesses (including land installations)
• Floating Fortresses (Escort Fortress and Floating Fortress)

Type	Modifier
Main + Main + AP Shell + Seaplane	108%
Main + Main + AP Shell + AA gun	108%
Main + Main + AP Shell + Radar	110%
Main + Main + Secondary + AP Shell	115%
Main + Secondary + AP Shell + Radar	114~115%?
Main + Secondary + AP Shell + Seaplane	115~116%?

Notes

• The AP shell and seaplane used in the tests were Type 91 AP Shell and Type 0 Observation Seaplane.
• Numbers for the setups involving secondary guns are not confirmed yet, but believed to be near.
• Has not been tested against Light Cruiser Demon and Destroyer Princess at the moment.
• Has not been tested against Armored Carriers and Aviation Cruisers as of 02/06/2015.
• Detailed tests are still ongoing. Values differ slightly from test to test (source). Current values are taken off wikiwiki.
• Exercise caution as this modifier works for enemy ships as well (practice matches and special enemies with Deteriorate AP Shell equipped).

Remaining Ammo Modifier

Remaining Ammunition	Modifier
5 to 10 bars	100%
4 bars	80%
3 bars	60%
2 bars	40%
1 bar	20%
0 bars	Scratch Damage

• In general, two bars of will be used in Day Battle for all ships, regardless of whether they attack or not.
• The Remaining Ammo Modifier affects all phases, including the opening Aerial Combat Phase.
• When entering night battle, the Remaining Ammo Modifier on a vessel remains same as the previous day battle. One bar of is used for all ships in Night Battle, regardless of whether they attack or not.
• Because most battles will consume 2 bars of ammunition each, try to engage the boss before the 5th battle, or else achieving victory becomes unlikely (but not impossible).
• When attempting to defeat boss nodes, avoid night battles and whirlpools on the way.
  • Whirlpools will decrease either or bars of your sorted fleet, which can be disadvantageous in long sorties.  Equipping one or more ships with RADAR can help reduce losses taken from these.
    • Only one RADAR is required per ship.  Equipping multiple RADAR to the same ship will not reduce the penalty further.
    • The max reduction typically occurs at 3 ships with RADAR. In events special caveats such as only RADAR in the main fleet of a Combined Fleet being considered can exist.
• Submarine-only nodes on limited-time event maps do not consume ammo in Day or Night Battle.
• Hayasui with Underway Replenishment can temporarily resupply ammo/fuel when players choose to use the item.
• Ammo/Fuel reduced in Air Raid nodes are reduced. Read Events/Mechanics for details.

Player Ship Protection Mechanisms

$\text{Damage Value} = \left \lfloor \frac{H_{t}}{2} \right \rfloor + \Big \lfloor 0.3 \big ( \text{rand} \in \left [ 0 , H_{t} - 1 \right ] \big ) \Big \rfloor$

While the above formulas and statements are generally true for damage taken by a player's ships, there are additional limits that apply to friendly units only. These protection mechanisms are important for game balance and to protect your fleet from sinking.

• For ships entering battle at chuuha (orange) or higher HP:
  • Damage taken cannot reduce HP below 1.
    • Any further hits will become misses.
  • For flagships, as well as ships with 20 morale or more (i.e. not red face):
    • If damage taken exceeds a ship's current HP, then instead of taking full damage, the damage of the current attack is limited to 50%-79% (rounded down) of current HP.
      • For multi-hit attacks, such as night battle torpedo cut-in attacks, each hit is calculated separately.
      • This can occasionally help ships avoid taiha (red HP), because it narrows the range of damage where it is possible to be hit into taiha.
      • For ships with at full HP and an odd HP total, it is occasionally possible to stop damage at lightly damaged.

See Also

• WikiWiki section on damage calculation
• ja.kancolle.wikia pages:
  • Common parts
  • Night Battle formula
  • ASW formula
  • Carrier Shelling formula
  • Air Strike formula
• Online calculator (explanations)