Main battery formulas
Shell Grouping (σ)1.6
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp204.1 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (14376/30·(13−1.1)/1000 + 1.1)·30 = 204.1 m
Max Vert Disp153.1 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 204.1 × 0.75 = 153.1 m
Med Horiz Disp75.3 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 204.1 × 0.369 (σ=1.6) = 75.3 m
Med Vert Disp56.5 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 153.1 × 0.369 (σ=1.6) = 56.5 m
AP Pen Close719.7 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 × 2350 × 747.8^0.69 × 0.356^-1.07 × 823^1.38 = 719.7 mm. Matches the in-game spec card.
AP Pen Far345.9 mm
Same formula at the ship's max firing range (19.8 km), where the shell has slowed to 483.9 m/s: 1e-7 × 2350 × 747.8^0.69 × 0.356^-1.07 × 483.9^1.38 = 345.9 mm.
HE penetration59 mm
59 mm ≈ 356 mm caliber / 6 (standard HE penetration ratio).
AP overmatch24 mm
floor(356 mm caliber / 14.3) = 24 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius90
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 alpha12
All 12 barrels bear on the broadside.
Turret turn time60 s
180 degrees / 3 deg/s traverse speed = 60 s.
HE full-salvo alpha62,400
5,200 HE damage x 12 broadside guns = 62,400.
AP full-salvo alpha126,000
10,500 AP damage x 12 broadside guns = 126,000.
Base HE DPM113,455
62,400 HE full-salvo alpha x 60 / 33 s base reload = 113,455.
Base AP DPM229,091
126,000 AP full-salvo alpha x 60 / 33 s base reload = 229,091.
Base shells/min21.8
12 broadside guns x 60 / 33 s base reload = 21.8.
Base fires/min8.29
12 HE shells x 60 / 33 s reload x 38% fire chance = 8.29.
AA defense
Close-range AA DPS321
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (24×3.5×0.75) + (63×3.5×0.75) + (23×3.5×0.7) + (14×3.5×0.75) = 321. 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 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index995
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)148,300
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: 6×2 100 mm (6/side) × 60/5 × 1400 = 100,800 + 10×1 130 mm (5/side) × 60/12 × 1900 = 47,500. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1900
Maximum HE damage per shell across secondary HE families. Best on this ship: 1900 from the 130 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 130 mm family.
Max HE pen22 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: 22 mm from the 130 mm family.
Damage Control Party
Repair Party
Secondary Battery Booster