Night Battle Hit Rate Formula Test (July 2023)

	A	B	C	E
1	Data from TsunDB. Samples with historical ships/gears are removed unless specified otherwise.
2	This is joint work with fourinone.
3
4	In this test, we look at the night hit rate formula. Our findings are listed below.
5
6
7	1. General formula
8	We find that the general shape of the formula in the vita version of the game still works in the browser version of the game.
9	The formula is as follows:
10
11	Accuracy term = Floor(([Mod contact] * (69 + [Mod star shell]) + 2 * sqrt([Level]) + 1.5 * sqrt([Luck]) + [Equip acc]) * [Mod formation] * [Mod morale] * [Mod cutin] + [Mod searchlight] + [Fit bonus])
12
13	Pre-cap evasion term = [Evasion] + sqrt(2[Luck]) [Mod formation]
14	Capped evasion term = [Pre-cap evasion term] Floor(40 + 3sqrt([Pre-cap evasion term]-40)) Floor(55 + 2sqrt([Pre-cap evasion term]-65))			if [Pre-cap evasion term] < 40, if [Pre-cap evasion term] >= 40 and [Pre-cap evasion term] < 65, if [Pre-cap evasion term] >= 65.
15	Post-cap evasion term = Floor([Mod searchlight] * ([Capped evasion term] + [Mod CA] + [Mod DD] - [Mod fuel]))
16
17	The formula for the final hit rate is the same as that of the day battle so it is omitted here. See the English wikipedia for more details.
18	https://en.kancollewiki.net/Accuracy,_Evasion_and_Criticals#Hit_Rate
19	The modifiers in the formula above are listed below.
20
21
22	2. Standard modifiers
23	The conditions and values for the standard modifiers (those that are well-established) are listed below.
24
25	Modifier	Value	Trigger condition
26	Mod contact	1.1 (1 acc) 1.15 (2 acc)	Night recon is triggered in night battle. The assumed value depends on the accuracy of the night recon.
27	Mod star shell	5	Star shell is triggered or night zuiun CI is triggered. For Night Zuiun CI, only the attacks after the night Zuiun CI enjoy [Mod star shell]. The bonus from star shell and night zuiun CI do NOT stack.
28	Mod formation (accuracy)	0.9 (double line) 0.7 (diamond) 0.9 (echelon) 0.8 (line abreast)	Note: for vanguard formation, [Mod formation] assumes 0.8 for the ships in the top half, 1.2 for the ships in the bottom half; an additional 1.1x is applied if the target is DD.
29	Mod searchlight (accuracy)	7	Search light is triggered.
30	Mod formation (evasion)	1.3 (echelon) 1.2 (line abreast)
31	Mod searchlight (evasion)	0.2	If the ship is equipped with search light.
32	Mod CA	5	If the ship is a CA or a CAV.
33	Mod DD	10	If the ship is a DD and has surface radar and (torpedo squadron) skilled lookout.
34
35
36	3. Accuracy from improvements
37	The accuracy bonus formula in vita works as follows:
38	- Radar with accuracy >= 3 gets 1.6*sqrt(star).
39	- AAMG, small/large sonar, medium/large bulges, boilers and depth charges get no bonus.
40	- All other gears get 1.3*sqrt(star).
41
42	https://github.com/johndpope/kancolle-kai-decompile-source/blob/ad0e37c14f140cb343367ee818951df84dc65d5c/Server_Controllers.BattleLogic/Exec_Midnight.cs#L691
43
44	We find that improvements from seaplane recon, seaplane bomber and seaplane fighter do not get accuracy bonus from improvement.
45	The list of gears that we cannot confirm whether they give improvement accuracy bonus are: fighter, DB, TB, carrier-based recon, rotorcraft, liaison plane, large flying boat, and combat ration.
46
47
48	4. Combined fleet formation modifiers
49	We have identified the following accuracy and evasion formation modifiers for combined fleet.
50
51		Accuracy	Evasion
52	CF2	0.9	?
53	CF3	0.7	1.1
54	CF4	1	1
55
56
57	5. Morale Behaviour
58	Ships with strictly greater than 49 effective morale have sparkled status in night battle, i.e. enjoy a 1.2x accuracy bonus.
59	The effective morale is calculated from the starting morale (BEFORE entering the combat node) as follows.
60
61	Case 1: 6v6
62	If node is a day battle node and the starting morale >= 30, [effective morale] = [starting morale] - 5 (-3 from day, -2 from night)
63	If node is a day battle node and the starting morale < 30, [effective morale] = [starting morale] - 11 (-9 from day, -2 from night)
64	If node is a night-only node, [effective morale] = [starting morale] - 2
65
66	Case 2: 6v12, 12v6, 12v12
67	If node is a day battle node and the starting morale >= 30, [effective morale] = [starting morale] - 3 (-3 from day, no -2 from night)
68	If node is a day battle node and the starting morale < 30, [effective morale] = [starting morale] - 9 (-9 from day, no -2 from night)
69	If node is a night-only node, [effective morale] = [starting morale]
70
71
72	6. Mod cutin
73	We have identified [Mod cutin] for different cutin types as follows.
74
75	Attack type	Mod cutin
76	Double attack	1.1
77	Mixed torpedo cutin	1.42~1.76
78	Torpedo cutin	1.5
79	Mixed gun cutin	1.31~>2
80	Main gun cutin	1.32~>2
81	GTR	1.1
82	TLR	1.20~>2
83	TLT	1.37~>2
84	Nelson touch	1.05
85	Night Zuiun cutin	1.02~1.11
86
87	These estimations are different from the values seen in the vita version:
88	https://github.com/johndpope/kancolle-kai-decompile-source/blob/ad0e37c14f140cb343367ee818951df84dc65d5c/Server_Controllers.BattleLogic/Exec_Midnight.cs#L137
89
90
91	7. CA(V) fit bonus
92	We find that for CA(V), the accuracy bonus from 20.3cm No.2 is +15 (same as 20.3cm No.3).
93
94
95	8. Known inconsistencies
96	Our current formula overestimates the hit rate in the 6-5 night-only node (node J) by ~1%.
97	The reason for the overestimation is not clear. It is possible that night-only nodes behave differently from day battle nodes.
98	Data from 6-5-J are only used in Night Zuiun related tests (as the node is the primary source of samples). The node is filtered out for other tests.
99
100