Main battery formulas
Shell Grouping (σ)1.8
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp182.9 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (16060/30·(10−1.6)/1000 + 1.6)·30 = 182.9 m
Max Vert Disp109.7 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 182.9 × 0.6 = 109.7 m
Med Horiz Disp64 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 182.9 × 0.35 (σ=1.8) = 64 m
Med Vert Disp38.4 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 109.7 × 0.35 (σ=1.8) = 38.4 m
AP Pen Close756.9 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 × 2945 × 580^0.69 × 0.356^-1.07 × 823^1.38 = 756.9 mm. Matches the in-game spec card.
AP Pen Far375.4 mm
Same formula at the ship's max firing range (20.1 km), where the shell has slowed to 495.1 m/s: 1e-7 × 2945 × 580^0.69 × 0.356^-1.07 × 495.1^1.38 = 375.4 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 time45 s
180 degrees / 4 deg/s traverse speed = 45 s.
HE full-salvo alpha57,000
4,750 HE damage x 12 broadside guns = 57,000.
AP full-salvo alpha114,000
9,500 AP damage x 12 broadside guns = 114,000.
Base HE DPM110,323
57,000 HE full-salvo alpha x 60 / 31 s base reload = 110,323.
Base AP DPM220,645
114,000 AP full-salvo alpha x 60 / 31 s base reload = 220,645.
Base shells/min23.2
12 broadside guns x 60 / 31 s base reload = 23.2.
Base fires/min5.11
12 HE shells x 60 / 31 s reload x 22% fire chance = 5.11.
AA defense
Close-range AA DPS548
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (78×3.5×0.75) + (92×3.5×0.7) + (45×3.5×0.75) = 548. 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 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index1758
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 dispersion
Secondary dispersion typeImproved (50%) + Standard
This ship's secondary families don't share one dispersion bracket. Each family is listed below with its own slope; max dispersion = secondary range (km) × that family's slope + 30 m.
127 mm × 4 dispersion typeImproved (50%, Massachusetts type)
Max dispersion = range (km) × 27 + 30 for this family. Slope is set per gun model in the binary.
127 mm × 4 max disp @ 5 km165 m
5 km × 27 + 30 = 165 m.
127 mm × 6 dispersion typeStandard
Max dispersion = range (km) × 57 + 30 for this family. Slope is set per gun model in the binary.
127 mm × 6 max disp @ 5 km315 m
5 km × 57 + 30 = 315 m.
Secondary battery firepower
Secondary DPM (per side)180,000
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: 4×1 127 mm (2/side) × 60/3 × 1800 = 72,000 + 6×2 127 mm (6/side) × 60/6 × 1800 = 108,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1800
Maximum HE damage per shell across secondary HE families. Best on this ship: 1800 from the 127 mm family.
Max HE fire chance5%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 5% 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