Main battery formulas
Shell Grouping (σ)1.8
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp230.5 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (16787/30·(12−2.2)/1000 + 2.2)·30 = 230.5 m
Max Vert Disp138.3 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 230.5 × 0.6 = 138.3 m
Med Horiz Disp79.3 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 230.5 × 0.344 (σ=1.8) = 79.3 m
Med Vert Disp47.6 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 138.3 × 0.344 (σ=1.8) = 47.6 m
AP Pen Close814.1 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 × 2434 × 884.8^0.69 × 0.381^-1.07 × 850^1.38 = 814.1 mm. Matches the in-game spec card.
AP Pen Far443.6 mm
Same formula at the ship's max firing range (21 km), where the shell has slowed to 547.5 m/s: 1e-7 × 2434 × 884.8^0.69 × 0.381^-1.07 × 547.5^1.38 = 443.6 mm.
HE penetration64 mm
64 mm ≈ 381 mm caliber / 6 (standard HE penetration ratio).
AP overmatch26 mm
floor(381 mm caliber / 14.3) = 26 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 time30 s
180 degrees / 6 deg/s traverse speed = 30 s.
HE full-salvo alpha52,200
5,800 HE damage x 9 broadside guns = 52,200.
AP full-salvo alpha108,000
12,000 AP damage x 9 broadside guns = 108,000.
Base HE DPM104,400
52,200 HE full-salvo alpha x 60 / 30 s base reload = 104,400.
Base AP DPM216,000
108,000 AP full-salvo alpha x 60 / 30 s base reload = 216,000.
Installed HE DPM116,000
52,200 HE full-salvo alpha x 60 / 27 s installed reload (Main Battery Mod. 3 = -10%) = 116,000.
Installed AP DPM240,000
108,000 AP full-salvo alpha x 60 / 27 s installed reload (Main Battery Mod. 3 = -10%) = 240,000.
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/min4.32
9 HE shells x 60 / 30 s reload x 24% fire chance = 4.32.
Installed fires/min4.8
9 HE shells x 60 / 27 s installed reload x 24% fire chance = 4.8.
AA defense
Close-range AA DPS364
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (66×3.5×0.75) + (34×3.5×0.7) + (41×3.5×0.75) = 364. 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 index1203
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: 2×3 152 mm (3/side) × 60/12 × 2100 = 31,500 + 2×3 152 mm (3/side) × 60/12 × 2100 = 31,500 + 12×1 90 mm (6/side) × 60/4 × 1300 = 117,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2100
Maximum HE damage per shell across secondary HE families. Best on this ship: 2100 from the 152 mm family.
Max HE fire chance7%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 7% 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
Exhaust Smoke Generator
Catapult Fighter
Observation Seaplane
Secondary Battery Booster
