Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp238.7 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (17625/30·(12−2.2)/1000 + 2.2)·30 = 238.7 m
Max Vert Disp143.2 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 238.7 × 0.6 = 143.2 m
Med Horiz Disp76.3 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 238.7 × 0.32 (σ=2) = 76.3 m
Med Vert Disp45.8 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 143.2 × 0.32 (σ=2) = 45.8 m
AP Pen Close969.6 mm
Canonical community AP formula (jcw780/wows_shell), evaluated at muzzle velocity: 1e-7 × Krupp × mass^0.69 × caliber_m^-1.07 × v0^1.38 = 1e-7 × 2550 × 1321^0.69 × 0.431^-1.07 × 840^1.38 = 969.6 mm. Matches the in-game spec card.
AP Pen Far514.1 mm
Same formula at the ship's max firing range (22 km), where the shell has slowed to 530.4 m/s: 1e-7 × 2550 × 1321^0.69 × 0.431^-1.07 × 530.4^1.38 = 514.1 mm.
HE penetration72 mm
72 mm ≈ 431 mm caliber / 6 (standard HE penetration ratio).
AP overmatch30 mm
floor(431 mm caliber / 14.3) = 30 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius350
AP shell over-penetration splash radius; scales with shell mass. Wickes 102mm = 3, standard 152mm CL ~ 20, Iowa 406mm ~ 270, Yamato 460mm = 400, Incomparable 650mm = 550 (max). Larger value = bigger splash damage area when AP over-pens.
Broadside guns used for alpha8
All 8 barrels bear on the broadside.
Turret turn time36 s
180 degrees / 5 deg/s traverse speed = 36 s.
HE full-salvo alpha48,000
6,000 HE damage x 8 broadside guns = 48,000.
AP full-salvo alpha112,000
14,000 AP damage x 8 broadside guns = 112,000.
Base HE DPM115,200
48,000 HE full-salvo alpha x 60 / 25 s base reload = 115,200.
Base AP DPM268,800
112,000 AP full-salvo alpha x 60 / 25 s base reload = 268,800.
Installed HE DPM128,000
48,000 HE full-salvo alpha x 60 / 22.5 s installed reload (Main Battery Mod. 3 = -10%) = 128,000.
Installed AP DPM298,667
112,000 AP full-salvo alpha x 60 / 22.5 s installed reload (Main Battery Mod. 3 = -10%) = 298,667.
Base shells/min19.2
8 broadside guns x 60 / 25 s base reload = 19.2.
Installed shells/min21.3
8 broadside guns x 60 / 22.5 s installed Artillery reload = 21.3.
Base fires/min9.22
8 HE shells x 60 / 25 s reload x 48% fire chance = 9.22.
Installed fires/min10.24
8 HE shells x 60 / 22.5 s installed reload x 48% fire chance = 10.24.
AA defense
Close-range AA DPS501
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (140×3.5×0.75) + (11×3.5×0.75) + (40×3.5×0.75) = 501. Covers AA-only mounts plus dual-purpose secondaries (Bismarck 105mm, USN 5"/38 cruiser secondaries) and dual-purpose main batteries (Sumner-class 5"/38, Akizuki-line 100mm). Formula validated against in-game captures on California, Sumner, Manfred von Richthofen, Dante Alighieri (exact) and within +/-17% on the remaining verified ships.
Maximum AA range5.2 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index2344
SUM over AA auras of (aura DPS x aura range km). A plane crossing the AA bubble is exposed to each aura for a time proportional to that aura's range, so long-reach DPS is worth more than the same DPS in a short bubble. Units: DPS*km; used to rank overall AA threat across the cohort.
Secondary battery firepower
Secondary DPM (per side)290,250
Sum across all secondary families of (per-side barrels × 60 / reload_s × alpha), where per-side barrels = mounts × barrels-per-mount / 2 (the guns that bear on one broadside target). Per-family: 8×2 127 mm (8/side) × 60/4 × 1800 = 216,000 + 3×3 152 mm (4.5/side) × 60/8 × 2200 = 74,250. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2200
Maximum HE damage per shell across secondary HE families. Best on this ship: 2200 from the 152 mm family.
Max HE fire chance12%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 12% from the 152 mm family.
Max HE pen25 mm
Maximum HE armor penetration across secondary HE families (caliber × 1/6 for most nations; 1/4 for German/UK BBs). Shells whose pen falls under a plate's armor thickness shatter for 0 hull damage though fire chance still applies. Best on this ship: 25 mm from the 152 mm family.
Damage Control Party
Repair Party
Secondary Battery Booster
Engine Boost
