Main battery formulas
Shell Grouping (σ)1.9
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp218.5 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15850/30·(12−2)/1000 + 2)·30 = 218.5 m
Max Vert Disp131.1 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 218.5 × 0.6 = 131.1 m
Med Horiz Disp72.4 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 218.5 × 0.331 (σ=1.9) = 72.4 m
Med Vert Disp43.5 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 131.1 × 0.332 (σ=1.9) = 43.5 m
AP Pen Close826.9 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 × 2400 × 750^0.69 × 0.356^-1.07 × 895^1.38 = 826.9 mm. Matches the in-game spec card.
AP Pen Far410.6 mm
Same formula at the ship's max firing range (19.8 km), where the shell has slowed to 538.9 m/s: 1e-7 × 2400 × 750^0.69 × 0.356^-1.07 × 538.9^1.38 = 410.6 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 alpha9
All 9 barrels bear on the broadside.
Turret turn time45 s
180 degrees / 4 deg/s traverse speed = 45 s.
HE full-salvo alpha47,700
5,300 HE damage x 9 broadside guns = 47,700.
AP full-salvo alpha101,250
11,250 AP damage x 9 broadside guns = 101,250.
Base HE DPM102,214
47,700 HE full-salvo alpha x 60 / 28 s base reload = 102,214.
Base AP DPM216,964
101,250 AP full-salvo alpha x 60 / 28 s base reload = 216,964.
Base shells/min19.3
9 broadside guns x 60 / 28 s base reload = 19.3.
Base fires/min7.91
9 HE shells x 60 / 28 s reload x 41% fire chance = 7.91.
AA defense
Close-range AA DPS265
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (52×3.5×0.75) + (14×3.5×0.7) + (36×3.5×0.75) = 265. 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 index1010
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)182,400
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: 8×2 130 mm (8/side) × 60/5 × 1900 = 182,400. 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 chance8%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 8% 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
Catapult Fighter
Observation Seaplane
Secondary Battery Booster