Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp229 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (16897/30·(12−2)/1000 + 2)·30 = 229 m
Max Vert Disp137.4 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 229 × 0.6 = 137.4 m
Med Horiz Disp73.2 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 229 × 0.32 (σ=2) = 73.2 m
Med Vert Disp43.9 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 137.4 × 0.32 (σ=2) = 43.9 m
AP Pen Close775 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 × 2548 × 1157^0.69 × 0.419^-1.07 × 747^1.38 = 775 mm. Matches the in-game spec card.
AP Pen Far499.2 mm
Same formula at the ship's max firing range (21.1 km), where the shell has slowed to 543.1 m/s: 1e-7 × 2548 × 1157^0.69 × 0.419^-1.07 × 543.1^1.38 = 499.2 mm.
HE penetration70 mm
70 mm ≈ 419 mm caliber / 6 (standard HE penetration ratio).
AP overmatch29 mm
floor(419 mm caliber / 14.3) = 29 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius180
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 alpha6
All 6 barrels bear on the broadside.
Turret turn time45 s
180 degrees / 4 deg/s traverse speed = 45 s.
HE full-salvo alpha36,900
6,150 HE damage x 6 broadside guns = 36,900.
AP full-salvo alpha78,000
13,000 AP damage x 6 broadside guns = 78,000.
Base HE DPM85,154
36,900 HE full-salvo alpha x 60 / 26 s base reload = 85,154.
Base AP DPM180,000
78,000 AP full-salvo alpha x 60 / 26 s base reload = 180,000.
Base shells/min13.8
6 broadside guns x 60 / 26 s base reload = 13.8.
Base fires/min6.51
6 HE shells x 60 / 26 s reload x 47% fire chance = 6.51.
AA defense
Close-range AA DPS352
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (66×3.5×0.75) + (58×3.5×0.7) + (14×3.5×0.75) = 352. 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 range4.5 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index883
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.
Near aura range2 km
Secondary battery firepower
Secondary DPM (per side)125,700
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: 6×1 120 mm (3/side) × 60/5 × 1700 = 61,200 + 6×2 152 mm (6/side) × 60/12 × 2150 = 64,500. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2150
Maximum HE damage per shell across secondary HE families. Best on this ship: 2150 from the 152 mm family.
Max HE fire chance9%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 9% 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
Sonar
Secondary Battery Booster
Main Battery Reload Booster