Main battery formulas
Shell Grouping (σ)1.8
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp214.2 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15423/30·(12−2)/1000 + 2)·30 = 214.2 m
Max Vert Disp128.5 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 214.2 × 0.6 = 128.5 m
Med Horiz Disp73.7 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 214.2 × 0.344 (σ=1.8) = 73.7 m
Med Vert Disp44.2 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 128.5 × 0.344 (σ=1.8) = 44.2 m
AP Pen Close787.7 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 × 2636 × 1016^0.69 × 0.406^-1.07 × 768^1.38 = 787.7 mm. Matches the in-game spec card.
AP Pen Far424.3 mm
Same formula at the ship's max firing range (19.3 km), where the shell has slowed to 490.5 m/s: 1e-7 × 2636 × 1016^0.69 × 0.406^-1.07 × 490.5^1.38 = 424.3 mm.
HE penetration68 mm
68 mm ≈ 406 mm caliber / 6 (standard HE penetration ratio).
AP overmatch28 mm
floor(406 mm caliber / 14.3) = 28 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius120
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 time45 s
180 degrees / 4 deg/s traverse speed = 45 s.
HE full-salvo alpha45,600
5,700 HE damage x 8 broadside guns = 45,600.
AP full-salvo alpha99,200
12,400 AP damage x 8 broadside guns = 99,200.
Base HE DPM91,200
45,600 HE full-salvo alpha x 60 / 30 s base reload = 91,200.
Base AP DPM198,400
99,200 AP full-salvo alpha x 60 / 30 s base reload = 198,400.
Base shells/min16
8 broadside guns x 60 / 30 s base reload = 16.
Base fires/min5.76
8 HE shells x 60 / 30 s reload x 36% fire chance = 5.76.
AA defense
Close-range AA DPS156
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (8×3.5×0.75) + (25×3.5×0.7) + (28×3.5×0.75) = 156. 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 range4.2 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index456
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 range1.2 km
Secondary battery firepower
Secondary DPM (per side)173,143
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: 8×1 127 mm (4/side) × 60/4.5 × 1800 = 96,000 + 10×1 127 mm (5/side) × 60/7 × 1800 = 77,143. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1800
Maximum HE damage per shell across secondary HE families. Best on this ship: 1800 from the 127 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 127 mm family.
Max HE pen21 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: 21 mm from the 127 mm family.
Damage Control Party
Repair Party
Catapult Fighter
Observation Seaplane
Secondary Battery Booster