Combat

Effects of Ship Damage
Amount of damage on a ship will affect its performance.

Aerial Combat
Aerial Combat Stages

Fighter Combat
$$\text {Fighter Power} = \sum^\text{All slots} \text{Floor(} \sqrt{\text{Number fighters in slot}} \times \text {Plane anti-air bonus} \text{)}$$

Fighter planes, fighter-bombers, and Zuiun participate in Fighter Combat.

The allied fleet and enemy fleet's Fighter Powers are compared to determine the result of Fighter Combat:
 * This calculation does not take into account any anti-air weaponry equipped on ships. Carrier anti-air stat is also not considered.
 * Even if allied planes secure air supremacy, planes can still be lost due to the subsequent anti-air defense stages.

Fleet Anti-air Defense
Each enemy bomber slot is assigned at random to a defending ship. Those ships then, for each assigned enemy slot, have an approximately 50% chance to shoot down enemy planes. The number of planes shot down is given by the equations below:

$$\text{Planes Shot Down} = \text{Floor((Ship AA } + \text{Floor(Fleet Anti-air Bonus} \times \text{Formation Modifier))} \times 0.2125\text{)}$$ $$\text{Fleet Anti-air Bonus} = \text{Floor(} \sum^\text{All slots}\text{Equipment AA Bonus} \times \text{Equipment Modifier)}$$

Equipment Modifiers

 * Any equipment that gives an anti-air bonus will contribute to shooting down enemy planes.
 * The forward sliding and machine gun animations seem to have no correlation with the calculations.
 * These calculations only apply for the allied fleet's anti-air defense.

Damage Calculation
Main Formula

Basic Attack Power

Engagement Form Modifer (Pre-Cap Modifier)
Engagement Forms
 * Night battle and air combat are not affected by engagement form.
 * The engagement form attack modifier affects both your fleet and the enemy fleet.
 * This also applied for the Crossing the T (both Advantage or Disadvantage) modifier. It may be a bug or a design flaw.
 * Crossing the T (Disadvantage) can be avoided by equipping a 彩雲 Saiun (Carrier-based recon plane).

Parallel Engagement

The course of the player's fleet and the enemy fleet are the same. Head-on Engagement

The course of the player's fleet and the enemy fleet are opposite each other. Crossing the T

The course of the player's fleet and the enemy fleet are perpendicular to each other (that's 90 degrees, which results in a T figure). A fleet is in disadvantage if it is coming from「｜」direction, and is in advantage it is is coming from「―」direction.

(Historically, the point of this was for the「―」fleet to bring as many guns to bear on the enemy while limiting the firepower of the enemy that can only use guns mounted forward.)

Night Combat
Night Battle Attack Types
 * Night battle damage depends on both the Firepower and Torpedo stats for attack power. Consequently, DDs, CLs, CLTs and CAs have drastically increased strength at night.
 * Any vessel at night must not have taken more than moderate (orange) damage before attacking in order to participate in night battle.
 * Main Gun = Red guns or 10cm High-angle Gun
 * Secondary (Sub) Gun = Yellow guns / 12.7cm High-angle Gun / 8cm High-angle Gun
 * Auxiliary equipment (e.g radar, turbine, special ammunition, pure AA equipment(green), and mini-sub) will not affect the combination.

Cut-in Equipment Setups
NOTE: These are only a few examples. See the above table.

NOTE: Midget subs don't count as torpedoes for this.

Double Attack Equipment Setups
NOTE: These are only a few examples. See the above table.

Cut-in Attack
Cut-in chance: (Ship Luck + 15 + Health Modifier + Flagship Modifier + Searchlight Modifier) [%]

Double Attack
Two consecutive attacks at 120%. Almost always procs, compared to cut-ins which proc only by chance and is affected by the luck stat.

Ship's Health Modifier (Pre-Cap Modifier)
This modifier does not affect Aerial Combat.

Attack Power Cap (Applies After All Pre-Cap Modifiers)
Conditions for the attack power cap to activate: [Basic attack power x Pre-cap modifiers] exceeds 150 for day battle, 300 for night battle, and 100 for anti-sub attacks. This is the attack power cap, and it's represented below by $$x$$:

$$\text {Attack Power After Caps} = x + \sqrt {\text {Pre Caps Attack Power} - x}$$

What we can draw from this is that during the day, firepower or torpedo stats above 145 have a high probability breaking the cap immediately and thus becoming nerfed. However, depending on the exact engagement form and fleet formation, this will not always occur.

Critical Modifier
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.

Remaining Ammo Modifier

 * 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 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.
 * While early maps' whirpools decrease your resources directly, later maps will decrease either  or  bars of your sorted fleet, which can be disadvantageous in long sorties.
 * There exist cases in which ships will consume no ammuntion in battle, but these are rare and their causes are not well documented.  Most battles will consume ammuntion even if none of your ships are able to attack at all.  Please report in the comments below with the exact fleet, equipment setups, map, node, and enemy pattern if you encounter battles where no ammunition is consumed.

Victory Conditions

 * Perfect S
 * No damage taken, all enemy ships sunk.
 * S (Victory)
 * All enemy ships sunk.
 * A (Victory)
 * No friendly ships sunk and required number of enemy ships sunk. (see below)
 * B (Tactical Victory)
 * Enemy flagship sunk.
 * If your flagship not sunk and enemy doesn't met the minimum sunk requirement (see below), you'll got B regardless how bad are you damaged if enemy's flagship sunk.
 * No damage taken, and enemy took over a certain amount of damage.
 * Damage gauge at least twice enemy damage gauge.
 * Friendly ship sunk, specified number of enemy ships sunk (see below), and damage gauge twice enemy gauge.
 * Friendly ship sunk, enemy flagship sunk, and damage gauge twice enemy gauge.
 * C (Tactical Defeat)
 * Didn't clear any of the conditions for A or B, but enemy took over a certain amount of damage.
 * Damage gauge higher than enemy gauge, but not reaching twice as much.
 * Friendly ship sunk, damage gauge higher than enemy, but not twice as much.
 * Friendly flagship got heavy damage while doesn't met the conditions for A or B.
 * Even if your damage gauge is bigger then enemy, if you unable to sink their flagship or met the minimum sunk requirement (see below) while your flagship is heavily damaged, you'll be counted as C.
 * D (Defeat)
 * Enemy took less than a certain amount of damage.
 * Both sides taking 0 damage is also D.
 * Damage gauge lower than enemy gauge.
 * Friendly ship sunk, not all enemy ships sunk, and gauge lower than enemy gauge.
 * E (Defeat)
 * Over a certain number of friendly ships sunk. (see below)
 * Friendly ship sunk while not meeting any victory conditions.
 * No damage done to enemy, while taking over a certain amount.

Notes
 * The Minimum Sunk Requirement is around 60% of the enemy fleet, thus:
 * 4 ships out of a fleet of 6
 * 3 ships out of a fleet of 5
 * 2 ships out of a fleet of 4
 * 2 ships out of a fleet of 3
 * 1 ship out of a fleet of 2
 * Heavy damage on the 1st ship for a fleet of 1
 * Victory status affects the chance of getting drops and rare drops on the specified node.
 * B victories tend to have no drops, while Perfect S has the highest chance for rare drops.

Additional Explanation/Details
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