Shelling: ((90 + sqrt(LUK*1.5) + sqrt(LVL)*2 + equipACC + improveBonus)*formationMod*moraleMod + fitBonus)*artillerySpotMod*APShellMod

Torpedo: (85 + sqrt(LUK*1.5) + sqrt(LVL)*2 + equipACC + improveBonus + floor(torpedoPower/5) + shipTorpAcc)*formationMod*moraleMod

ASW: (80 + sqrt(LUK*1.5) + sqrt(LVL)*2 + sonarASW*2 + improveBonus)*formationMod*moraleMod

Airstrike: 95

Night Battle: ((69 + starShellBonus)*scoutMod + sqrt(LUK*1.5) + sqrt(LVL)*2 + equipACC + improveBonus)*formationMod*specialAttackMod*moraleMod + CABonus + searchlightBonus + fitBonus

Source: http://s.webry.info/sp/bs-arekore.at.webry.info/201502/article_4.html

formationMod

Day Shelling	Torpedo	ASW	Night Battle
1	1	1	1
1.2	0.9	1.2	0.9
1	0.4	1	0.7
1.2	0.6	1.2	0.8
1.2	0.3	1.2	0.8

moraleMod:

Morale	Shelling/ASW/NB	Torpedo
53 - 100	1.2	1.3
33 - 52	1	1
23 - 32	0.8	0.7
0 - 22	0.5	0.35

artillerySpotMod:

Attack Type	Modifier
Double Attack	1.1
Sec. Gun Cut-In	1.3
Sec. + Radar Cut-In	1.5
Sec. + AP Cut-In	1.3
AP Shell Cut-In	1.2

APShellMod:

Equips	Modifier
	1.3
	1.2
	1.25
	1.1

specialAttackMod:

NB Attack	Modifier
Double Attack	1.1
Mixed Cut-In	1.5
Torpedo Cut-In	1.65
Sec. Gun Cut-In	1.5
Main Gun Cut-In	2

starShellBonus = 5 if star shell activated

scoutMod = 1.1 if night scout activated

searchlightBonus = 7 if searchlight activated

CABonus = 10 if 20.3cm Twin Cannon equipped, 15 if 20.3(no.3) Twin Cannon equipped, 10 if both are equipped

improveBonus = sqrt(★)*improveMod

improveMod:

Equip Type	Day Shelling	Night Battle	Torpedo	ASW
	1	1.3
	1	1.3
	1	1.3
	1	1.3
			2
w/ ACC ≤ 2	1.7	1.3
w/ ACC ≥ 3	1.7	1.6
	1	1.3
			2
				1.3
	1			1.3
	1	1.3
	1	1.3
	1	1.3
	1	1.3

Source: http://akashi-list.me/

Fit Bonus

Fit Value:

	All 35.6cm, 38cm	All 381mm	All 41cm	Proto 46cm	46cm	All 16inch	All 38.1cm
Kongou	6	-2	-5	-7	-10	-2	3
Bismarck	4	1	-5	-7	-10	-2	1
Vittorio-Veneto	4	-2	-5	-7	-10	-2	3
Iowa	4	1	-5	-7	-10	0	1
Warspite	6	2	2	-3	-7	0	6
Ise/Fusou	4	2	0	-3	-7	-2	4
Fusou Kai Ni	4	2	4	-3	-7	0	4
Nagato	2	2	0	-3	-3	0	2
Yamato	0	0	0	0	0	0	0

BB Fit Acc = sum Fit Value * sqrt(# of gun class equipped)

CL Fit FP = 1*(# 14cm/15.2cm single equipped) + 2*(# 14cm/15.2cm double equipped)
CL Fit Acc = 4*(# 14cm/15.2cm single equipped) + 3*(# 14cm/15.2cm double equipped)

Source: http://i.imgur.com/ng7hl1P.png
Source: http://ch.nicovideo.jp/pixy_for_ever/blomaga/ar994724

Evasion Term

precapEV = (EV + sqrt(LUK*2))*formationMod

postcapEV =

55 + 2*sqrt(precapEV - 65)		if precapEV ≥ 65
40 + 3*sqrt(precapEV - 40)		if 40 ≤ precapEV < 65
precapEV		if precapEV < 40

Evasion Term = (postcapEV - fuelPenalty + sonarImproveBonus + CABonus)*searchlightPenalty

Source: http://s.webry.info/sp/bs-arekore.at.webry.info/201502/article_4.html

formationMod:

Day Shelling	Torpedo	ASW	Night Battle	Airstrike
1	1	1	1	1
1	1	1	1	1.2
1.1	1.1	1	1	1.6
1.2	1.3	1.3	1.1	1
1.3	1.4	1.1	1.2	1

fuelPenalty = 75 - % Fuel Leftif % Fuel Left < 75

sonarImproveBonus = sum( 1.5*sqrt(★) ) for each sonar if Torpedo Phase

CABonus = 5 if Night Battle and ship is a CA/CAV

searchlightPenalty = 0.2 if Night Battle and ship has a Searchlight equipped

Determining Result

Hit Rate = (Accuracy Term - Evasion Term)*targetMoraleMod + proficiencyAccBonus
*(Accuracy Term - Evasion Term) is max 96, min 10

targetMoraleMod:

Morale	Modifier
53 - 100	0.7
33 - 52	1
23 - 32	1.2
0 - 22	1.4

Critical Chance

Crit Rate = critMod*sqrt(Hit Rate) + nightScoutBonus + proficiencyCritBonus

critMod

Phase	Modifier
Day Shelling	1.3
Torpedo	1.5
ASW	1.3
Airstrike	0.2
Night Battle	1.5
Support Shelling	1
Support Torpedo	1.2

nightScoutBonus = 7 if Night Battle and activated

Aircraft Proficiency

Planes may have EXP values ranging from 0 to 120. The EXP range determines the rank.

Rank	EXP Range	EXP used by simulator	accValue	critRateValue	critDamageValue
None	0 - 9	0	0	0	0
\|	10 - 24	10	0	0	0
\|\|	25 - 39	25	1	0	0
\|\|\|	40 - 54	40	2	0	0
\	55 - 69	55	3	0	0
\\	70 - 79	70	4	0	0
\\\	80 - 99	80	6	4.2	5.6
>>	100 - 120	120	9	6	8

proficiencyAccBonus = sqrt(EXP) + accValue for the AVERAGE rank/EXP of all equipped planes
proficiencyCritBonus = SUM( critRateValue ) of all equipped planes
proficiencyCritMultiplier = SUM( sqrt(EXP*1.2) + critDamageValue ) of all equipped planes, doubled for plane in first slot

Source: http://kankoregouchin.blog.fc2.com/blog-entry-54.html

To determine hit result:
Roll a random integer r from 0 to 99 (inclusive).
If r ≤ Crit Rate, attack is a critical.
Else if r ≤ Hit Rate, attack is a normal hit.
Else, attack misses.

Air Battle

Fighter Combat

In Air Phase Stage 1, fighter power is compared and planes on each side are shot down depending on result.
This is applied to all fighters, torpedo bombers, dive bombers, seaplane bombers, and seaplane fighters.

Player Plane Loss:

Air State	% Planes Lost (distributed linearly)
AS+	2.5% - 5.83%
AS	7.5% - 17.5%
AP	12.5% - 29.17%
AI	17.5% - 40.83%
AD	25% - 58.33%

Source: http://kancolle-calc.net/stage1losttable.html

Enemy Plane Loss:

Air State	% Planes Lost	Calculation (randInt inclusive)
AS+	0% - 10%	10(.35randInt(0,1) + .65*randInt(0,1))
AS	0% - 40%	10(.35randInt(0,4) + .65*randInt(0,4))
AP	0% - 60%	10(.35randInt(0,6) + .65*randInt(0,6))
AI	0% - 80%	10(.35randInt(0,8) + .65*randInt(0,8))
AD	0% - 100%	10(.35randInt(0,10) + .65*randInt(0,10))

Source: http://ja.kancolle.wikia.com/wiki/%E3%82%B9%E3%83%AC%E3%83%83%E3%83%89:1542
Source: https://cdn.discordapp.com/attachments/230559622711345152/234134364198273024/-4ada3Q2f-5czcK2sT3cS1gr-ib.jpg

Anti-Air Cut-In

Enemies cannot AACI.

ID	# shot down	Activation Rate	AACImod
1	7	65%	1.75
2	6	58%	1.7
3	4	50%	1.6
4	6	52%	1.5
5	4	55%	1.55
6	4	40%	1.5
7	3	45%	1.35
8	4	50%	1.45
9	2	40%	1.3
10	8	60%	1.65
11	6	55%	1.5
12	3	45%	1.25
14	4	35%	1.35
15	3	35%	1.35
16	4	35%	1.35
17	2	35%	1.35
18	2	35%	1.35

Source: http://i.imgur.com/SDVf61K.png
Source: AACImod http://ja.kancolle.wikia.com/wiki/%E5%AF%BE%E7%A9%BA%E3%82%AB%E3%83%83%E3%83%88%E3%82%A4%E3%83%B3#.E8.BF.BD.E5.8A.A0.E3.83.9C.E3.83.BC.E3.83.8A.E3.82.B9.E3.83.87.E3.83.BC.E3.82.BF

Ship Anti-Air

50% chance to shoot down Proportional AA.
50% chance to shoot down Flat AA.
100% chance to shoot down 1 if player side.

Proportional AA = floor(weightedAA*#inSlot*0.0025)
Flat AA (Player) = floor((weightedAA + fleetAA)*.1)*AACImod
Flat AA (Enemy) = floor((weightedAA + fleetAA)*0.09375)

weightedAA = baseAA + sum( AA*equipMod + improveBonus) of the ship's equips

Equip Type	equipMod	improveMod
High-Angle Gun	4	2
High-Angle Gun + FD	4	3
Fire Director	4	2
Air Radar	3	0
Machine Gun	6	2
Other	0	0

improveBonus = improveMod * sqrt(★)

fleetAA (Player) = 1.54*formationMod*sum( equipMod*AA ) for all equipment in the fleet
fleetAA (Enemy) = 2*formationMod*sum( equipMod*AA ) for all equipment in the fleet

Formation	formationMod
	1
	1.2
	1.6
	1
	1

Equip Type	equipMod
High-Angle Gun	0.35
Fire Director	0.35
Air Radar	0.4
Type 3 Shell	0.6
46cm Gun	0.25
Other	0.2

Artillery Spotting Chance

Night Battle Cut-In Chance

AS Type	typeMod
Double Attack	1.3
Sec. Gun Cut-In	1.2
Sec. + Radar Cut-In	1.3
Sec. + AP Cut-In	1.4
AP Shell Cut-In	1.5

if double attack: 99%
if LUCK < 50: NB chance = (15 + LUK + 0.75*sqrt(LVL) + flagshipBonus + chuuhaBonus + lookoutBonus + searchlightBonus + starshellBonus)/typeMod
if LUCK ≥ 50: NB chance = (65 + sqrt(LUK-50) + 0.8*sqrt(LVL) + flagshipBonus + chuuhaBonus + lookoutBonus + searchlightBonus + starshellBonus)/typeMod

flagshipBonus = 15 if flagship
chuuhaBonus = 18 if medium damaged
lookoutBonus = 5 if lookout equipped
searchlightBonus: +7 if self, -5 if enemy
starshellBonus: +4 if self, -10 if enemy

NB Attack	typeMod
Mixed Cut-In	1.15
Torpedo Cut-In	1.22
Sec. Gun Cut-In	1.3
Main Gun Cut-In	1.4

Installation Damage

Miscellaneous

Formation	Protection Rate
	0.45
	0.6
	0.75
	0.6
	0.6

Searchlight Targeting

Roll randomly for a target.
If small searchlight was activated and target is not holding a searchlight, reroll once for a new target. (With 6 ships, searchlight ship targeted chance = (1/6) + (5/6)*(1/6) = 30.56%.)
If large searchlight was activated and target is not holding a searchlight, reroll up to twice for a new target. (With 6 ships, searchlight ship targeted chance = (1/6) + (5/6)*(1/6) + (5/6)²*(1/6) = 42.13%.)

Source: http://i.imgur.com/ElrJxcM.jpg

Combined Fleet

Shelling power bonuses are applied to both player and enemy side.
Shelling uses same formula, but with different base value (instead of 90).
Carrier Task Force:
Player Main: 90
Player Escort: 55
Enemy vs Main: 90
Enemy vs Escort: 65

Surface Task Force:
Player Main: 50
Player Escort: 75
Enemy vs Main: 65
Enemy vs Escort: 75

Transport Task Force:
Player Main: 50
Player Escort: 75
Enemy vs Main: 65
Enemy vs Escort: 75

Source: https://docs.google.com/spreadsheets/d/1Nw8ykFYlAPv2znhYy_hRBX3HRtEAB7oclEh3XaAYv5A/edit#gid=0

Kancolle Sortie Simulator - Calculations

Accuracy and Evasion

Accuracy Term