Combat/Aerial Combat

= THIS PAGE IS NOW UNDER DEVELOMENT AND THERE CAN BE MANY ERROR AND CONTRADICTION EXIST IN THE PAGE. PLEASE USE OTHER PAGES ON THE WIKI FOR INFORATION AND DATA BEFORE MOST WORK OF THE PAGE IS DONE. = Aerial Combat refer to one of the stage conducted during combat in the game, conducted after detection and before Support Expedition and/or Opening Torpedo Salvo (if condition for them to happen are fulfilled).

Overview
Translate 艦載機の種類 in http://wikiwiki.jp/kancolle/?%B9%D2%B6%F5%C0%EF into this section.

Fighter Combat
$$\text {Fighter Power} = \sum^\text{All slots} \text{Floor(} \sqrt{\text{Number planes in slot}} \times \text {Plane anti-air stat} + \text{Aircraft Proficiency Bonus} \text{)}$$


 * Fighter planes, and specific Torpedo / Dive / Seaplane bombers with an +AA stat participate in the Fighter Combat.
 * Recon planes (carrier based or seaplane recon) will NOT participate in Fighter Combat.
 * Aircraft Proficiency is factored into Fighter Power on top of the above formula. The exact formula is under investigation.
 * The allied fleet and enemy fleet's Fighter Powers are compared to determine the result of Fighter Combat:
 * EFP: Enemy Fighter Power, FP: Fighter Power. Abbreviated to save space.
 * This calculation does not take into account any anti-air weaponry equipped on ships. Carrier anti-air stat is also not considered.
 * The percentage of planes shot down were originally believed to be applies for both sides' respective outcomes, however it is now under re-checking. If it is true, then for example, securing Air Superiority means allied planes shoot down up to 80% of enemy planes, and the enemy under Air Incapability will shoot down up to 40%.
 * Planes shot down are calculated per slot.
 * As this is applied per slot, 80% of one enemy bomber group can be shot down while a second has 0% shot down.
 * Planes loaded on moderately/heavily damaged carriers can still join this stage of fighter combat.
 * Even if allied planes secure air supremacy, planes can still be lost (up to 10%), and the subsequent anti-air defense stages can eliminate more bombers.
 * If the enemy fleet launches no fighters and any planes are launched from either side, the result defaults to Air Supremacy. If both sides launch no planes, then the rest of the battle is treated the same as if Air Parity was achieved.
 * Contact can't be triggered if it is Air Denial
 * Night Contact can be triggered in most case when it is not Air Denial, however it can't be triggered when it is under Air Parity, with the exception of during PvP or when it i9s a night battle node then it still Night Contact still can be triggered even if it is under Air Parity state.
 * Artillery Spotting can only be triggered with at least Air Superiority.

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". Different types of planes have different trigger rates. They are roughly estimated as (if only one is equipped):
 * Trigger conditions:
 * More air control than Air Denial
 * 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.
 * Note that after contact is triggered, it is another random process to decide which plane should be responsible for contact and probability listed here are not relevant to that part.
 * Too few plane in a slot would negatively influence contact trigger rate.
 * There's an hypothesis about contact rate related to LoS.

Contact Damage Modifier

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

Fleet Anti-air Defense
The Fleet Anti-air Defense system was updated on 14 November 2014, alongside the addition of the Anti-air Cut-in system. It was then patched on 26 June 2015 to fix several bugs.

System Mechanics The numbers of planes shot down are given by the equations below:
 * Each enemy bomber slot is assigned at random to a defending ship.
 * Those ships then, for each assigned enemy slot, have two approximately 50% sequential but independent chances to shoot down enemy planes.
 * The first chance (termed Proportional Air Defense) can shoot down a number proportional to the initial size of the enemy bomber squadron after anti-bomber combat.
 * The second chance (termed Fixed Air Defense) can shoot down a fixed number of enemy bombers determined by stats and equipment only.
 * Finally, one bomber from each enemy squadron will always be shot down regardless of success or failure of the previous two chances.

$$\text{Adjusted AA} = \text{Ship Base AA } + \sum^\text{Defender Slots}\text{Floor(Equipment Modifier} \times \text{(Equipment AA} + 0.7 \times \sqrt{ \text{Equipment Upgrade}}\text{))}$$

$$\text{Proportional } \texttt{\#} \text{ Shot Down} = \text{Floor(Floor(} 0.9 \times \text{Adjusted AA)} \text{/} 360 \times \text{Enemy Bomber Group Size)}$$

$$\text{Fixed } \texttt{\#} \text{ Shot Down} = \text{Floor(}\text{Adjusted AA} \text{/} 10 \text{)}$$

Formation Modifiers

 * As of the 26 June 2015 update, formations affect anti-air defense, but the exact effects are not yet clearly known. Prior to this update, a bug prevented formations from affecting anti-air calculations.

Equipment Modifiers

 * There may be other types of equipment with modifiers that affect the air defense equations which are not yet known.
 * A bug prior to the 26 June 2015 update gave several equipment such as (red) main cannons and Type 3 Shells modifiers of 0. The current values are not yet known.

Anti-Air Cut-In
Certain equipment combinations (see below) will provide a chance for an Anti-Air Cut-In (AACI) during the aerial combat. When activated, the cut-in animation (shown on the right) appears before engaging the enemy fighters. However, the effect of an Anti-Air Cut-In does not affect the resulting air control state (AS+, AS, Air Parity or Denial), and calculation wise, it only takes effect after fighters engage bombers in air combat. With an AA Cut-In and a good anti-air composition, it is sometimes possible to obliterate all incoming bombers before they inflict any damage, and even prevent enemy carriers from attacking during the shelling phase (since they have 0 bombers left).

Although several ships can be equipped with an AACI setup in one fleet, only one ship can perform an AACI during the aerial phase. The number of planes shot down is dependent on the ship performing the AACI and their equipment.(as given bellows.) Bringing more AACI capable ships will NOT increase the number of planes shot down via AACI.

Akizuki-class destroyers and Maya Kai-2 have a hidden bonus to certain AA Cut-in setups which increases the effectiveness tremendously.

In PVP Exercises, opposing fleets can do AA Cut-Ins, but the animation is not shown.

Also, note that AACI effects are added on to the regular anti-air fire of your fleet, thus it should be noted that anti air stat of other ships or/and equipment on those ships in your fleet would still matter even if AACI have been activated.

Equipment, API
The following table summarized information known so far about what type of equipment would trigger AACI, trigger rate, and effectiveness.
 * Note that if a setup fulfil multiple different API setup, the setup with higher number would take priority over those setup with lower number.
 * Built-in HA mount mean a single equipment that is in itself a HA Mount with AAFD built-in. That include 10cm Twin High-angle Gun Mount + Anti-Aircraft Fire Director and 12.7cm High-angle Gun + Anti-Aircraft Fire Director, also while 90mm Single High-angle Gun Mount don't have AAFD in its name, it do also count as an equipment with Built-in HA mount.

Opening Air Strike

 * Bombers attack ships in this stage
 * But if Detection failed, then this stage would not occur.
 * Each slot's plane would target one ship and attack for one time.
 * $$Damage=\lfloor (\lfloor cap_{150}\{(25 + P\sqrt{N})R\}C_v \rfloor T-A)L \rfloor$$
 * $$P$$ refer to firepower or torpedo value
 * $$N$$ refer to number of plane in the slot
 * $$R$$ is a fixed $$1.0$$ for Dive Bombers, but is a random $$0.8$$ or $$ 1.5 $$ for Torpedo Bombers/
 * The probability for Torpedo Bombers acquiring an $$1.5$$ multiplier in 1-1-A is around 50%
 * $$cap_{150}(x)$$ refer to the attack power cap, see Combat page for detail.
 * $$C_v$$ refer to Critical hit bonus from Aircraft Proficiency system. See Combat page and Aircraft Proficiency for details about its effect and etc.
 * If you bring more proficient planes, the rate to trigger it would increase.
 * With max proficiency Suisei Model 12A on 3 slot of a ship, critical hit rate is around 20%.
 * $$T$$ refer to contact multiplier, $$1.0$$ if contact failed
 * $$A$$ refer to enemy armor, see Combat page for detail.
 * $$L$$ refer to ammo modifier, see Combat page for detail.
 * No effect from engagement/formation/ship health when they launch planes/morale/fatigue on firepower or accuracy.
 * Get boost from Aircraft Proficiency system.
 * Carrier's level and plane's accuracy stat do not affect this stage.
 * Accuracy is around 80% when against those destroyers in 1-1-A.