Main battery formulas
Shell Grouping (σ)1.7
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp221.1 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15810/30·(13−1.1)/1000 + 1.1)·30 = 221.1 m
Max Vert Disp165.9 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 221.1 × 0.75 = 165.9 m
Med Horiz Disp78.8 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 221.1 × 0.356 (σ=1.7) = 78.8 m
Med Vert Disp59.1 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 165.9 × 0.356 (σ=1.7) = 59.1 m
AP Pen Close812.2 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 × 2300 × 1108^0.69 × 0.406^-1.07 × 830^1.38 = 812.2 mm. Matches the in-game spec card.
AP Pen Far504.2 mm
Same formula at the ship's max firing range (21.7 km), where the shell has slowed to 587.5 m/s: 1e-7 × 2300 × 1108^0.69 × 0.406^-1.07 × 587.5^1.38 = 504.2 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 alpha9
All 9 barrels bear on the broadside.
Turret turn time30 s
180 degrees / 6 deg/s traverse speed = 30 s.
HE full-salvo alpha52,200
5,800 HE damage x 9 broadside guns = 52,200.
AP full-salvo alpha119,250
13,250 AP damage x 9 broadside guns = 119,250.
Base HE DPM94,909
52,200 HE full-salvo alpha x 60 / 33 s base reload = 94,909.
Base AP DPM216,818
119,250 AP full-salvo alpha x 60 / 33 s base reload = 216,818.
Installed HE DPM105,455
52,200 HE full-salvo alpha x 60 / 29.7 s installed reload (Main Battery Mod. 3 = -10%) = 105,455.
Installed AP DPM240,909
119,250 AP full-salvo alpha x 60 / 29.7 s installed reload (Main Battery Mod. 3 = -10%) = 240,909.
Base shells/min16.4
9 broadside guns x 60 / 33 s base reload = 16.4.
Installed shells/min18.2
9 broadside guns x 60 / 29.7 s installed Artillery reload = 18.2.
Base fires/min6.55
9 HE shells x 60 / 33 s reload x 40% fire chance = 6.55.
Installed fires/min7.27
9 HE shells x 60 / 29.7 s installed reload x 40% fire chance = 7.27.
AA defense
Close-range AA DPS367
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (61×3.5×0.75) + (37×3.5×0.75) + (20×3.5×0.7) + (23×3.5×0.75) = 367. 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 index1306
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 range3.1 km
Secondary battery firepower
Secondary DPM (per side)188,600
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: 4×2 100 mm (4/side) × 60/3.75 × 1400 = 89,600 + 6×2 152 mm (6/side) × 60/8 × 2200 = 99,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2200
Maximum HE damage per shell across secondary HE families. Best on this ship: 2200 from the 152 mm family.
Max HE fire chance12%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 12% 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
Catapult Fighter
Observation Seaplane
Secondary Battery Booster