Main battery formulas
Shell Grouping (σ)1.6
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp209.2 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (14611/30·(12−2.2)/1000 + 2.2)·30 = 209.2 m
Max Vert Disp125.5 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 209.2 × 0.6 = 125.5 m
Med Horiz Disp77.2 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 209.2 × 0.369 (σ=1.6) = 77.2 m
Med Vert Disp46.3 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 125.5 × 0.369 (σ=1.6) = 46.3 m
Dispersion familyEU BB Disp.
Standard BB dispersion. Used as the baseline for cross-family comparisons.
AP Pen Close607.3 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 × 2408 × 585^0.69 × 0.34^-1.07 × 780^1.38 = 607.3 mm. Matches the in-game spec card.
AP Pen Far294.4 mm
Same formula at the ship's max firing range (20.1 km), where the shell has slowed to 461.5 m/s: 1e-7 × 2408 × 585^0.69 × 0.34^-1.07 × 461.5^1.38 = 294.4 mm.
HE penetration57 mm
57 mm ≈ 340 mm caliber / 6 (standard HE penetration ratio).
AP overmatch23 mm
floor(340 mm caliber / 14.3) = 23 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius55
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 alpha56,400
4,700 HE damage x 12 broadside guns = 56,400.
AP full-salvo alpha114,000
9,500 AP damage x 12 broadside guns = 114,000.
Base HE DPM112,800
56,400 HE full-salvo alpha x 60 / 30 s base reload = 112,800.
Base AP DPM228,000
114,000 AP full-salvo alpha x 60 / 30 s base reload = 228,000.
Base shells/min24
12 broadside guns x 60 / 30 s base reload = 24.
Base fires/min6.24
12 HE shells x 60 / 30 s reload x 26% fire chance = 6.24.
AA defense
Close-range AA DPS87
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (11×3.5×0.75) + (14×3.5×0.7) + (9×3.5×0.75) = 87. 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 range4 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index222
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)166,500
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: 18×1 139 mm (9/side) × 60/10 × 2000 = 108,000 + 6×1 90 mm (3/side) × 60/4 × 1300 = 58,500. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2000
Maximum HE damage per shell across secondary HE families. Best on this ship: 2000 from the 139 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 139 mm family.
Max HE pen23 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: 23 mm from the 139 mm family.
Damage Control Party
Repair Party
Secondary Battery Booster
