Main battery formulas
Shell Grouping (σ)1.9
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp234.2 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (17420/30·(12−2)/1000 + 2)·30 = 234.2 m
Max Vert Disp140.5 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 234.2 × 0.6 = 140.5 m
Med Horiz Disp77.7 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 234.2 × 0.332 (σ=1.9) = 77.7 m
Med Vert Disp46.6 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 140.5 × 0.332 (σ=1.9) = 46.6 m
Dispersion familyUS/UK BB Disp.
2.5% overall improvement compared to EU BB Disp.
AP Pen Close847.6 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 × 2520 × 1225^0.69 × 0.406^-1.07 × 762^1.38 = 847.6 mm. Matches the in-game spec card.
AP Pen Far471.4 mm
Same formula at the ship's max firing range (21.8 km), where the shell has slowed to 498.1 m/s: 1e-7 × 2520 × 1225^0.69 × 0.406^-1.07 × 498.1^1.38 = 471.4 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 Radius250
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 alpha68,400
5,700 HE damage x 12 broadside guns = 68,400.
AP full-salvo alpha162,000
13,500 AP damage x 12 broadside guns = 162,000.
Base HE DPM136,800
68,400 HE full-salvo alpha x 60 / 30 s base reload = 136,800.
Base AP DPM324,000
162,000 AP full-salvo alpha x 60 / 30 s base reload = 324,000.
Installed HE DPM152,000
68,400 HE full-salvo alpha x 60 / 27 s installed reload (Main Battery Mod. 3 = -10%) = 152,000.
Installed AP DPM360,000
162,000 AP full-salvo alpha x 60 / 27 s installed reload (Main Battery Mod. 3 = -10%) = 360,000.
Base shells/min24
12 broadside guns x 60 / 30 s base reload = 24.
Installed shells/min26.7
12 broadside guns x 60 / 27 s installed Artillery reload = 26.7.
Base fires/min8.64
12 HE shells x 60 / 30 s reload x 36% fire chance = 8.64.
Installed fires/min9.6
12 HE shells x 60 / 27 s installed reload x 36% fire chance = 9.6.
AA defense
Close-range AA DPS777
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (146×3.5×0.75) + (107×3.5×0.7) + (50×3.5×0.75) = 777. 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 range5.2 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index2548
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)270,000
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: 10×2 127 mm (10/side) × 60/4 × 1800 = 270,000. 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 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