Main battery formulas
Shell Grouping (σ)1.8
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp202.6 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (13936/30·(12−2.2)/1000 + 2.2)·30 = 202.6 m
Max Vert Disp121.5 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 202.6 × 0.6 = 121.5 m
Med Horiz Disp69.7 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 202.6 × 0.344 (σ=1.8) = 69.7 m
Med Vert Disp41.8 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 121.5 × 0.344 (σ=1.8) = 41.8 m
AP Pen Close576.1 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 × 2289 × 415^0.69 × 0.305^-1.07 × 850^1.38 = 576.1 mm. Matches the in-game spec card.
AP Pen Far202.2 mm
Same formula at the ship's max firing range (19.2 km), where the shell has slowed to 398 m/s: 1e-7 × 2289 × 415^0.69 × 0.305^-1.07 × 398^1.38 = 202.2 mm.
HE penetration76 mm
76 mm ≈ 305 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) - 0.249 in this case. Lets HE pen ~76mm armor instead of ~50mm. Hits every German cruiser (150mm CL, 203mm CA) and BB (350mm+), British heavy cruisers / Lion / Nelson, a handful of other premiums.
AP overmatch21 mm
floor(305 mm caliber / 14.3) = 21 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius50
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 alpha10
All 10 barrels bear on the broadside.
Turret turn time60 s
180 degrees / 3 deg/s traverse speed = 60 s.
HE full-salvo alpha35,000
3,500 HE damage x 10 broadside guns = 35,000.
AP full-salvo alpha81,000
8,100 AP damage x 10 broadside guns = 81,000.
Base HE DPM80,769
35,000 HE full-salvo alpha x 60 / 26 s base reload = 80,769.
Base AP DPM186,923
81,000 AP full-salvo alpha x 60 / 26 s base reload = 186,923.
Base shells/min23.1
10 broadside guns x 60 / 26 s base reload = 23.1.
Base fires/min5.31
10 HE shells x 60 / 26 s reload x 23% fire chance = 5.31.
AA defense
Close-range AA DPS90
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (10×3.5×0.75) + (23×3.5×0.7) + (3×3.5×0.75) = 90. 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 range3.5 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index228
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)133,215
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: 14×1 150 mm (7/side) × 60/8.57 × 1800 = 88,215 + 6×1 88 mm (3/side) × 60/4 × 1000 = 45,000. 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 150 mm family.
Max HE fire chance10%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 10% from the 150 mm family.
Max HE pen38 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: 38 mm from the 150 mm family.
Damage Control Party
Repair Party
Secondary Battery Booster