Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp177.4 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (12967/30·(10−2.8)/1000 + 2.8)·30 = 177.4 m
Max Vert Disp141.9 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 177.4 × 0.8 = 141.9 m
Med Horiz Disp56.7 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 177.4 × 0.32 (σ=2) = 56.7 m
Med Vert Disp45.3 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 141.9 × 0.319 (σ=2) = 45.3 m
AP Pen Close540 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 × 2327 × 386^0.69 × 0.305^-1.07 × 831^1.38 = 540 mm. Matches the in-game spec card.
AP Pen Far143 mm
Same formula at the ship's max firing range (17.8 km), where the shell has slowed to 317.3 m/s: 1e-7 × 2327 × 386^0.69 × 0.305^-1.07 × 317.3^1.38 = 143 mm.
HE penetration51 mm
51 mm ≈ 305 mm caliber / 6 (standard HE penetration ratio).
AP overmatch21 mm
floor(305 mm caliber / 14.3) = 21 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius40
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 alpha10
All 10 barrels bear on the broadside.
Turret turn time41.9 s
180 degrees / 4.3 deg/s traverse speed = 41.9 s.
HE full-salvo alpha52,000
5,200 HE damage x 10 broadside guns = 52,000.
AP full-salvo alpha80,000
8,000 AP damage x 10 broadside guns = 80,000.
Base HE DPM124,800
52,000 HE full-salvo alpha x 60 / 25 s base reload = 124,800.
Base AP DPM192,000
80,000 AP full-salvo alpha x 60 / 25 s base reload = 192,000.
Base shells/min24
10 broadside guns x 60 / 25 s base reload = 24.
Base fires/min7.68
10 HE shells x 60 / 25 s reload x 32% fire chance = 7.68.
AA defense
Close-range AA DPS173
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (6×3.5×0.75) + (60×3.5×0.75) = 173. 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 range3 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index362
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)120,000
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: 16×1 152 mm (8/side) × 60/10 × 2500 = 120,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2500
Maximum HE damage per shell across secondary HE families. Best on this ship: 2500 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
Secondary Battery Booster