Main battery formulas
Shell Grouping (σ)1.9
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp220 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (16000/30·(12−2)/1000 + 2)·30 = 220 m
Max Vert Disp132 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 220 × 0.6 = 132 m
Med Horiz Disp72.9 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 220 × 0.331 (σ=1.9) = 72.9 m
Med Vert Disp43.8 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 132 × 0.332 (σ=1.9) = 43.8 m
AP Pen Close659.6 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 × 2266 × 929^0.69 × 0.406^-1.07 × 788^1.38 = 659.6 mm. Matches the in-game spec card.
AP Pen Far321.8 mm
Same formula at the ship's max firing range (20 km), where the shell has slowed to 468.5 m/s: 1e-7 × 2266 × 929^0.69 × 0.406^-1.07 × 468.5^1.38 = 321.8 mm.
HE penetration102 mm
102 mm ≈ 406 mm caliber / 4 (improved HE penetration: German BBs, Yamato-class, and a handful of others).
Improved HE PenYes
This ship's HE shells use a 1/4 (~0.25) caliber-to-pen ratio instead of the standard 1/6 (~0.167) - 0.251 in this case. Lets HE pen ~101mm armor instead of ~67mm. Hits every German cruiser (150mm CL, 203mm CA) and BB (350mm+), British heavy cruisers / Lion / Nelson, a handful of other premiums.
AP overmatch28 mm
floor(406 mm caliber / 14.3) = 28 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius120
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 alpha62,100
6,900 HE damage x 9 broadside guns = 62,100.
AP full-salvo alpha108,000
12,000 AP damage x 9 broadside guns = 108,000.
Base HE DPM124,200
62,100 HE full-salvo alpha x 60 / 30 s base reload = 124,200.
Base AP DPM216,000
108,000 AP full-salvo alpha x 60 / 30 s base reload = 216,000.
Base shells/min18
9 broadside guns x 60 / 30 s base reload = 18.
Base fires/min8.28
9 HE shells x 60 / 30 s reload x 46% fire chance = 8.28.
AA defense
Close-range AA DPS428
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (64×3.5×0.75) + (91×3.5×0.7) + (14×3.5×0.75) = 428. 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 range4.5 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index1031
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)125,700
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: 6×1 120 mm (3/side) × 60/5 × 1700 = 61,200 + 6×2 152 mm (6/side) × 60/12 × 2150 = 64,500. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2150
Maximum HE damage per shell across secondary HE families. Best on this ship: 2150 from the 152 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 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
Secondary Battery Booster