Main battery formulas
Shell Grouping (σ)1.9
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp231.7 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (17172/30·(12−2)/1000 + 2)·30 = 231.7 m
Max Vert Disp139 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 231.7 × 0.6 = 139 m
Med Horiz Disp76.8 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 231.7 × 0.331 (σ=1.9) = 76.8 m
Med Vert Disp46.1 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 139 × 0.332 (σ=1.9) = 46.1 m
AP Pen Close778.8 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 × 2598 × 1225^0.69 × 0.406^-1.07 × 701^1.38 = 778.8 mm. Matches the in-game spec card.
AP Pen Far445.1 mm
Same formula at the ship's max firing range (21.5 km), where the shell has slowed to 467.4 m/s: 1e-7 × 2598 × 1225^0.69 × 0.406^-1.07 × 467.4^1.38 = 445.1 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 Radius150
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 time40 s
180 degrees / 4.5 deg/s traverse speed = 40 s.
HE full-salvo alpha51,300
5,700 HE damage x 9 broadside guns = 51,300.
AP full-salvo alpha117,900
13,100 AP damage x 9 broadside guns = 117,900.
Base HE DPM102,600
51,300 HE full-salvo alpha x 60 / 30 s base reload = 102,600.
Base AP DPM235,800
117,900 AP full-salvo alpha x 60 / 30 s base reload = 235,800.
Installed HE DPM114,000
51,300 HE full-salvo alpha x 60 / 27 s installed reload (Main Battery Mod. 3 = -10%) = 114,000.
Installed AP DPM262,000
117,900 AP full-salvo alpha x 60 / 27 s installed reload (Main Battery Mod. 3 = -10%) = 262,000.
Base shells/min18
9 broadside guns x 60 / 30 s base reload = 18.
Installed shells/min20
9 broadside guns x 60 / 27 s installed Artillery reload = 20.
Base fires/min6.48
9 HE shells x 60 / 30 s reload x 36% fire chance = 6.48.
Installed fires/min7.2
9 HE shells x 60 / 27 s installed reload x 36% fire chance = 7.2.
AA defense
Close-range AA DPS627
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (90×3.5×0.75) + (106×3.5×0.7) + (50×3.5×0.75) = 627. 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 index2003
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)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: 10×2 127 mm (10/side) × 60/6 × 1800 = 180,000. 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