View source for Accuracy, Evasion and Criticals

This page is to provide an in-depth look into the hit rate mechanics in-game for '''single/combined fleets and land-based air squadrons'''. The formulas presented in this page are still subject to change as more testing is done. 
*'''Please note that all formulas between <math>\lfloor \ \rfloor</math> are rounded down.'''

=Hit Rate=
The hit rate is used by all attacks. 

<math>\text{Hit %} = \bigl\lfloor \text{Hit}_\text{cap} \bigr\rfloor + \text{Acc}_\text{proficiency} +1</math>

Where, the Capped Hit Rate <math>\left( \text{Hit}_\text{cap} \right)</math> is:

<math>\text{Hit}_\text{cap} = \text{cap}_\text{max}\left( \text{cap}_\text{min} \left(\text{Accuracy}_\text{atk} - \text{Evasion}_\text{def}\right) \times \text{Morale}_\text{defender} \right)</math>

* <math>\text{Accuracy}_\text{atk}</math> is the calculated accuracy of the attack. Please see [[#Accuracy_Formulas|below]] for the various accuracy formulas.
* <math>\text{Evasion}_\text{def}</math> is the calculated evasion of the defending ship. Please see [[#Evasion_Formulas|below]] for the various evasion formulas.
* <math>\text{Morale}_\text{defender}</math> is the morale state modifier of the defending ship. Morale is referring to the value of attacking timing, not the value before entering battle. Please see [[Morale_and_Fatigue#Morale Effects|Morale and Fatigue]] for more details.
** Sparkled is '''0.7''',
** Normal is '''1.0''',
** Orange is '''1.2''',
** Red is '''1.4'''.
* <math>\text{Acc}_\text{proficiency}</math> is the '''average''' plane proficiency accuracy bonus. Please see [[Plane Proficiency]] for more details.
** The average is calculated only from dive bombers, torpedo bombers, seaplane bombers and large flying boats.
** The value is '''12''' for {{Double Chevron}} planes.

'''Hit Rate Caps'''

There is a minimum and maximum hit rate in the game. 
* The minimum of <math>\text{cap}_\text{min}\left(x\right)</math> '''is 10'''.
* The maximum of <math>\text{cap}_\text{max}\left(x\right)</math> '''is 96'''.

'''Notes:'''
* Hit rate has an effective '''minimum of 11%''' and a '''maximum of 97%'''.
* Plane proficiency is the only factor that allows a ship to go beyond 100% hit rate.

==Critical Hit Rate==
The following are the various formulas for determining critical hits for attacks.

* Shelling/ASW (including carriers): <math>\lfloor 1.3 \times \sqrt{\text{Hit}_\text{cap}} \rfloor + \text{Crit}_\text{proficiency} + 1</math>
* Torpedo: <math>\lfloor 1.5 \times \sqrt{\text{Hit}_\text{cap}} \rfloor + 1</math>
* Airstrike: <math>\lfloor 0.2 \times \sqrt{\text{Hit}_\text{cap}} \rfloor + \text{Crit}_\text{proficiency} + 1</math>
* Night Battle (including carriers): <math>\lfloor \left(1.5 + \text{Const}_\text{contact} \right) \sqrt{\text{Hit}_\text{cap}} \rfloor + 1</math>
* Shelling Support: <math>\lfloor 1.0 \times \sqrt{\text{Hit}_\text{cap}} \rfloor + 1</math>
* Airstrike Support: <math>\lfloor 0.2 \times \sqrt{\text{Hit}_\text{cap}} \rfloor + 1</math>

* <math>\text{Crit}_\text{proficiency}</math> is the plane proficiency critical bonus. Please see [[Plane Proficiency]] for more details.
* <math>\text{Const}_\text{contact}</math> is the night contact constant from {{Night Recon}} {{Equipment/Link|Type 98 Reconnaissance Seaplane (Night Recon)|Type 0 Reconnaissance Seaplane Model 11B Kai (Night Recon)|Loire 130M|text=Night Recons|link_category=Night Recon}}. It is '''0.07''' if night contact is triggered, '''0''' otherwise.

=Accuracy Formulas=
Below are the common variables used in all accuracy formulas:
* <math>\text{Level}</math> is the level of the attacking ship.
* <math>\text{Luck}</math> is the luck {{Luck}} of the attacking ship.
* <math>\text{Acc}_\text{equip} = \text{Acc}_\text{equip base} + \text{Acc}_\text{equip bonus} + \text{Acc}_\bigstar</math> is the total accuracy {{Hit}} provided by an equipment, with:
** <math>\text{Acc}_\text{equip base}</math> is the base accuracy {{Hit}} of the equipment,
** <math>\text{Acc}_\text{equip bonus}</math> is the [[Equipment Bonuses|visible]] accuracy {{Hit}} bonuses,
** <math>\text{Acc}_\bigstar</math> is the equipment's accuracy {{Hit}} gained from [[Improvement]],
* <math>\text{Mod}_\text{fit}</math> is the [[Gun Fit Bonuses|Hidden Fit]] bonuses or penalties when applicable.
* <math>\text{Mod}_\text{formation}</math> is the formation modifier for the applicable attack. ''See [[Combat#Formation Selection|Combat]] for more details.''

{|class="wikitable mw-collapsible mw-collapsed"
!colspan=5|<math>\text{Mod}_\text{formation}</math>
|-
!Formation
!Day Shelling &<br>Carrier Attacks
!Torpedo Attacks
!ASW
!Night Battles
|-
|Line Ahead||1.0||1.0||1.0||1.0
|-
|Double Line||1.2||0.8||1.2||0.9
|-
|Diamond||1.0||0.4||1.0||0.7
|-
|Echelon||1.2||0.75||1.2||0.9
|-
|Line Abreast||1.2||0.3||1.2||0.8
|-
|Vanguard (Top)||0.8||0.7||?||?
|-
|Vanguard (Bottom)||1.2||0.9||?||?
|-
|Vanguard (Both) vs DD||1.1||1.2||?||?
|-
|Double Line vs Line Abreast||rowspan=3|1.0||rowspan=3|N/A||rowspan=3|1.0||rowspan=3|N/A
|-
|Echelon vs Line Ahead
|-
|Line Abreast vs Echelon
|-
|Combined Fleet Cruising Formation 1||?||?||?||?
|-
|Combined Fleet Cruising Formation 2||1.0||?||?||?
|-
|Combined Fleet Cruising Formation 3||?||?||?||?
|-
|Combined Fleet Cruising Formation 4||1.1||?||?||?
|}

* <math>\text{Mod}_\text{morale}</math> is the morale modifier of the attacking ship. Morale is referring to the value of attacking timing, not the value before entering battle. ''See [[Morale_and_Fatigue#Morale Effects|Morale and Fatigue]] for more details''.
{|class="wikitable mw-collapsible mw-collapsed" style="text-align:center"
!colspan=2|<math>\text{Mod}_\text{morale}</math>
|-
|Sparkled||1.2
|-
|Normal||1.0
|-
|Orange||0.8
|-
|Red||0.5
|}

'''Notes:'''
* Because of the number of modifiers to accuracy in-game, it is trivial to increase accuracy. Therefore it is '''more important''' to prioritize firepower.

==Daytime Shelling==
This formula applies to both surface shelling and carrier attacks during daytime combat. It does not apply to carrier airstrikes.

<math>\text{Accuracy}_\text{shelling} = \bigg\lfloor \bigg( \Big( \text{Acc}_\text{base} + 2 \times \sqrt{\text{Level}} + 1.5 \times \sqrt{\text{Luck}} + \sum_{\text{All Equips}} \text{Acc}_\text{equip} \Big) \times \text{Mod}_\text{formation} \times \text{Mod}_\text{morale} + \text{Mod}_\text{fit} \bigg) \times \text{Mod}_\text{spotting} \times \text{Mod}_\text{AP} \bigg\rfloor </math>

* <math>\text{Acc}_\text{base}</math> is the base accuracy value of the attack.
** These values apply for Player as attacker and Enemy as targets. Values for Enemy attacker vs Player target are unclear/unknown, except single vs single = 90.

{|class="wikitable mw-collapsible mw-collapsed" style="text-align:center; margin:auto"
!colspan=4| Fleet type base accuracy values for Player side<ref>https://twitter.com/Xe_UCH/status/1172380690207215616</ref><ref>https://twitter.com/Divinity__123/status/1447941755182227458</ref>
|-
!rowspan=2 colspan=2|'''<big>vs.</big>'''!!colspan=2|Enemy
|-
| '''Single Fleet'''|| '''Combined Fleet'''
|-
!rowspan=7|Player
| '''Single Fleet'''|| 90|| 80
|-
| '''CTF Main'''|| 78|| 77
|-
| '''CTF Escort'''|| 45|| 67
|-
| '''STF Main'''|| 45|| 77
|-
| '''STF Escort'''|| 67|| 67
|-
| '''TCF Main'''|| 54|| 54
|-
| '''TCF Escort'''|| 45|| 67
|}

* <math>\text{Mod}_\text{spotting}</math> is the artillery spotting bonus if applicable. Please see [[Artillery_Spotting#Setups and Attack Types|Artillery Spotting]] for more details.

{|class="wikitable mw-collapsible mw-collapsed" style="text-align:center"
!colspan=6|<math>\text{Mod}_\text{spotting}</math>
|-
!Attack Type
!Prerequisites
![[Damage_Calculations#Damage_Formula|Post-cap]]<br>Damage<br>Modifier
!Accuracy<br>Modifier
!Hits
!Notes
|-
!style="background-color:#ff7f50" |{{color|black|Main Suisei Cut-in<br>(Suisei CI)}}
|{{RedGunHeavy}}{{RedPlane}}{{RedPlane}}
|1.3||?||1
|rowspan=2|{{Ship/Link|Ise/Kai Ni|Hyuuga/Kai Ni|text=''Ise''-class Kai Ni|link_class=Ise}} only
|-
!style="background-color:#ff7f50" |{{color|black|Main Zuiun Cut-in<br>(Zuiun CI)}}
|{{RedGunHeavy}}{{ZuiunPlane}}{{ZuiunPlane}}
|1.35||?||1
|-
!style="background-color:#81c784" |{{color|black|Main AP Shell Cut-in<br>(APCI)}}
|{{RedGunHeavy}}{{RedGunHeavy}}{{Seaplane}}{{RedAmmo}}
|1.5||1.2||1
|
|-
!style="background-color:gold"|{{color|black|Secondary AP Shell Cut-in<br>(Sec APCI)}}
|{{RedGunHeavy}}{{YellowGun}}{{Seaplane}}{{RedAmmo}}
|1.3||1.3||1
|
|-
!style="background-color:gold"|{{color|black|Secondary Radar Cut-in<br>(Radar CI)}}
|{{RedGunHeavy}}{{YellowGun}}{{Seaplane}}{{Radar}}
|1.2||1.5||1
|
|-
!style="background-color:gold"|{{color|black|Secondary Cut-in<br>(Sec CI)}}
|{{RedGunHeavy}}{{YellowGun}}{{Seaplane}}
|1.1||1.3||1
|
|-
!style="background-color:#59f"|{{color|black|Double Attack<br>(DA)}}
|{{RedGunHeavy}}{{RedGunHeavy}}{{Seaplane}}
|1.2||1.1||2
|
|}

* <math>\text{Mod}_\text{AP}</math> is the {{RedAmmo}} {{Equipment/Link|Type 91 Armor Piercing Shell|Type 1 Armor Piercing Shell|Type 1 Armor Piercing Shell Kai|text=AP Shells|link_category=Armour-Piercing Shells}} accuracy modifier:
{|class="wikitable mw-collapsible mw-collapsed" style="text-align:center"
!colspan=2|<math>\text{Mod}_\text{AP}</math>
|-
!Type!!Modifier
|-
|{{RedAmmo}}{{RedGunHeavy}}||1.1
|-
|{{RedAmmo}}{{RedGunHeavy}}{{YellowGun}}||1.2
|-
|{{RedAmmo}}{{RedGunHeavy}}{{Radar}}||1.25
|-
|{{RedAmmo}}{{RedGunHeavy}}{{YellowGun}}{{Radar}}||1.3
|}

'''Notes:'''
* It is '''inadvisable''' to run any of the other setups beyond the most basic Gun+AP. This is because the other setups will interfere with artillery spotting and cost you better attack bonuses.
* Unlike when calculating damage, the bonus applies to all targets.
<references/>

==Shelling Support==
This formula applies to surface shelling and carrier attacks during shelling support.

<math>\text{Accuracy}_\text{shelling support} = \bigg\lfloor \Big( 64 + 2 \times \sqrt{\text{Level}} + 1.5 \times \sqrt{\text{Luck}} + \sum_{\text{All Equips}} \text{Acc}_\text{equip base} \Big) \times \text{Mod}_\text{formation}? \times \text{Mod}_\text{morale} \bigg\rfloor </math>

* <math>\text{Acc}_\text{equip base}</math> does not include any [[Equipment Bonuses|visible bonus]] nor [[Improvement]].
* <math>\text{Mod}_\text{formation}</math> exists in KanColle Kai, but it is unclear if it applies to browser KanColle using the Daytime Shelling formation modifier of the main fleet.

==Torpedo Attacks==
This formula only applies to opening and closing torpedo attacks in day.

<math>\text{Accuracy}_\text{torpedo} = \left( 85 + 2 \times \sqrt{\text{Level}} + 1.5 \times \sqrt{\text{Luck}} + \sum_{\text{All Equips}} \text{Acc}_\text{equip} + \left \lfloor{\frac{\text{Attack}_\text{torp}}{5}} \right \rfloor + \text{Mod}_\text{ship} \right) \times \text{Mod}_\text{formation} \times \text{Mod}_\text{morale}</math>

* <math>\text{Attack}_\text{torp}</math> is the final basic torpedo attack power of the ship. Please see [[Damage_Calculations#Torpedo_Attacks|Damage Calculations]] for details.
** The figure incorporates any pre-cap and post-cap modifiers and takes into account the attack cap.
** This means that engagement and damage state play a role in torpedo accuracy.
* <math>\text{Mod}_\text{ship}</math> is the innate torpedo accuracy of the ship. Currently, only Abyssal ships have values above '''0'''.

==Aerial Combat==

This formula applies to the airstrikes performed during the aerial combat phase and support. Although ASW support functions like an airstrike for damage, it '''does not''' use this formula.

<math>\text{Accuracy}_\text{airstrike} = 95</math>

'''Important Notes'''
* Airstrike accuracy is a constant and '''not affected''' by any outside factors.

==Anti-Submarine Warfare==
This formula applies to all ASW attacks in the combat phase and support.

<math>\text{Accuracy}_\text{ASW} = \left( 80 + 2 \times \sqrt{\text{Level}} + 1.5 \times \sqrt{\text{Luck}} + \sum_{\text{All Equips}} \text{Acc}_\bigstar + 2 \times \sum \text{ASW}_\text{sonar} \right) \times \text{Mod}_\text{formation} \times \text{Mod}_\text{morale} \times \text{Mod}_\text{synergy}</math>

* <math>\text{Acc}_\bigstar</math> does '''not''' include {{Hit}} accuracy stat of the equipment, only the amount from [[Improvement]] related to ASW accuracy
* <math>\text{ASW}_\text{sonar}</math> is the '''base''' ASW stat of any sonars equipped.
* <math>\text{Mod}_\text{synergy}</math> is the synergy bonus from equipping certain combinations of ASW equipment.
** Synergy bonus is either currently bugged or so small it cannot be tested.

'''Notes:'''
* Equipping more sonars is the best way to boost ASW accuracy.
** {{Equipment/Link|Type 0 Passive Sonar|text=Large Sonars|link_category=Large Sonar}} are not counted for this bonus.

==Night Battles==
This formula applies to '''all''' night battle attacks. 

<math>\text{Accuracy}_\text{NB} = \bigg( \text{Mod}_\text{contact} \times \Big( 69 + \text{Mod}_\text{star shell} \Big) + 2 \times \sqrt{\text{Level}} + 1.5 \times \sqrt{\text{Luck}} + \sum_{\text{All Equips}} \text{Acc}_\text{equip} \bigg) \times \text{Mod}_\text{formation} \times \text{Mod}_\text{morale} \times \text{Mod}_\text{special} + \text{Mod}_\text{searchlight} + \text{Mod}_\text{fit}</math>

* <math>\text{Mod}_\text{contact}</math> is '''1.1''' if a {{Night Recon}} {{Equipment/Link|Type 98 Reconnaissance Seaplane (Night Recon)|Type 0 Reconnaissance Seaplane Model 11B Kai (Night Recon)|Loire 130M|text=Night Recon|link_category=Night Recon}} triggered, '''1.0''' otherwise.
* <math>\text{Mod}_\text{star shell}</math> is '''5.0''' if a {{StarShell}} {{EquipmentLink|Star Shell}} is triggered, '''0''' otherwise.
* <math>\text{Mod}_\text{searchlight}</math> is '''7.0''' if a {{Searchlight}} {{EquipmentLink|Searchlight|Type 96 150cm Searchlight|text=Searchlight|link_category=Searchlight}} is triggered, '''0''' otherwise,
* <math>\text{Mod}_\text{special}</math> is the night battle special attack modifier. ''See [[Night Battle]] for more details.''
** Torpedo Cut-in: '''1.65''',
** Gun Cut-in: '''2.0''',
** Mixed Cut-in: '''1.5''',
** Secondary Cut-in: '''1.5''',
** Double Attack: '''1.1''',
** Other multipliers are unknown.

==Land-Based Air Squadron==
This formula applies to attacks made by [[Land-Based Air Squadron]]s. The accuracy is calculated '''independently''' per squadron.

<math>\text{Accuracy}_\text{LBAS} = \left( ( {\text{Acc}_\text{equip}} + \text{Acc}_\text{Sp} ) \times 7 + 95 \right) \times \text{Mod}_\text{morale} + \text{Acc}_\text{proficiency}</math> <ref>https://twitter.com/yukicacoon/status/1432364331694374914</ref>

* <math>\text{Acc}_\text{equip}</math> is the accuracy stat of the plane.
* <math>\text{Acc}_\text{Sp}</math> is accuracy bonus for [[Land-Based Air Squadron#LBAS Special Bombers|LBAS Special Bombers]] on some targets.
* <math>\text{Mod}_\text{morale}</math> is the morale modifier of the plane.
** Normal/Orange morale: '''1.0'''
** Red morale: '''0.8'''
* <math>\text{Acc}_\text{proficiency}</math> is the plane proficiency accuracy bonus. ''See [[Plane Proficiency]] for more details.''
** Unclear if applied here or after <math>\text{Hit}_\text{cap}</math>. If applying here, skip <math>\text{Acc}_\text{proficiency}</math> for [[#Hit Rate|hit rate]].
** The value is '''12''' for {{Double Chevron}} planes.
<references/>

=Evasion Formulas=
Evasion has several caps depending on the calculated base evasion of the ship. Base evasion is calculated as follows:

<math>\text{Evasion}_\text{base} = \bigl\lfloor \left( \text{Evasion}_\text{ship} + \sqrt{2\text{Luck}} \right) \times \text{Mod}_\text{formation} \bigr\rfloor</math>

* <math>\text{Evasion}_\text{ship}</math> is the evasion of the ship '''including''' any visible equipment bonuses.
* <math>\text{Mod}_\text{formation}</math> is the formation modifier. It varies based on the attack being received. Please see [[Combat#Formation Selection|Combat]] for more details.
** Currently modifiers for Vanguard are unknown.


The various capped evasion formulas to calculate the final evasion rate is as follows:

* <math>\text{Evasion}_\text{base} < 40: \text{Evasion}_\text{cap} = \text{Evasion}_\text{base}</math>
* <math>40 < \text{Evasion}_\text{base} < 65: \text{Evasion}_\text{cap} = \lfloor 40 + 3\sqrt{\text{Evasion}_\text{base} - 40} \rfloor</math>
* <math>\text{Evasion}_\text{base} > 65: \text{Evasion}_\text{cap} = \lfloor55 + 2\sqrt{\text{Evasion}_\text{base} - 65}\rfloor</math>

Capped evasion is then modified by post-cap modifiers:

<math>\text{Evasion %} = \biggl\lfloor \text{Mod}_\text{searchlight} \times \left( \text{Evasion}_\text{cap} + \text{Mod}_\text{sonar} + \text{Mod}_\text{CA} + \text{Mod}_\text{vanguard} - \text{Mod}_\text{fuel} \right) \biggr\rfloor</math>

* <math>\text{Mod}_\text{searchlight}</math> is the searchlight evasion penalty. It is '''0.2''' for any ship equipped with a searchlight (even if not triggered) and '''1.0''' otherwise.
* <math>\text{Mod}_\text{sonar}</math> is the sonar improvement modifier that '''only applies to''' opening and closing torpedo attacks. It is '''0''' otherwise.
** <math>\text{Mod}_\text{sonar} = \sum_{\text{All Sonars}} 1.5\sqrt{\bigstar}</math> 
* <math>\text{Mod}_\text{CA}</math> is the heavy/aviation cruiser night battle evasion bonus. It is '''5''' for heavy/aviation cruisers and '''0''' otherwise.
* <math>\text{Mod}_\text{vanguard}</math> is the Vanguard evasion bonus. This is different from the formation modifier that gets taken into account for base evasion. Bonuses are:
** For ships at the top (slots 1-2 or 1-3): Non-destroyers get a 5% bonus. Destroyers get a 20% bonus.
** For the rest of the ships at the bottom (slots 3-5 or 4-7): Non-destroyers get a 20% bonus. Destroyers get a 40% bonus.
* <math>\text{Mod}_\text{fuel}</math> is the remaining fuel penalty.
** <math>\text{Mod}_\text{fuel} = 75 - \text{Fuel}</math>
** If fuel is above 75%, the penalty is 0. 
** The penalty is an integer and not a percentage.

{|class="wikitable" style="text-align:center"
|+ Remaining Fuel Penalty
|-
!Battle #<ref>This only takes into account normal day battles. Special nodes have different resource consumption.</ref>
!Remaining Fuel!!Penalty
|-
|2nd Battle||80%||0
|-
|3rd Battle||60%||15
|-
|4th Battle||40%||35
|-
|5th Battle||20%||55
|-
|6th+ Battle||0%||75
|}
<references/>
{{clear}}

'''Notes:'''
* The speed of the fleet is supposed to play a role in evasion. Currently, said increase is either nonexistent or too small to test.
* Using [[AO]] equipped with {{Supplies}} {{EquipmentLink|Underway Replenishment}} is a way to medigate fuel penalties.

=Special Cases=
==PT Imps==
{{Anti-PT Imp Setups|uncollapsed=true}}

=See Also=
{{Mechanics}}