Main battery formulas
Shell Grouping (σ)1.8
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp200.6 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (16195/30·(10−2.8)/1000 + 2.8)·30 = 200.6 m
Max Vert Disp160.5 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 200.6 × 0.8 = 160.5 m
Med Horiz Disp69 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 200.6 × 0.344 (σ=1.8) = 69 m
Med Vert Disp55.2 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 160.5 × 0.344 (σ=1.8) = 55.2 m
AP Pen Close669.1 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 × 2200 × 1000^0.69 × 0.41^-1.07 × 790^1.38 = 669.1 mm. Matches the in-game spec card.
AP Pen Far302.2 mm
Same formula at the ship's max firing range (20.2 km), where the shell has slowed to 444.1 m/s: 1e-7 × 2200 × 1000^0.69 × 0.41^-1.07 × 444.1^1.38 = 302.2 mm.
HE penetration68 mm
68 mm ≈ 410 mm caliber / 6 (standard HE penetration ratio).
AP overmatch28 mm
floor(410 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 alpha10
All 10 barrels bear on the broadside.
Turret turn time45 s
180 degrees / 4 deg/s traverse speed = 45 s.
HE full-salvo alpha65,000
6,500 HE damage x 10 broadside guns = 65,000.
AP full-salvo alpha124,000
12,400 AP damage x 10 broadside guns = 124,000.
Base HE DPM130,000
65,000 HE full-salvo alpha x 60 / 30 s base reload = 130,000.
Base AP DPM248,000
124,000 AP full-salvo alpha x 60 / 30 s base reload = 248,000.
Base shells/min20
10 broadside guns x 60 / 30 s base reload = 20.
Base fires/min6
10 HE shells x 60 / 30 s reload x 30% fire chance = 6.
AA defense
Close-range AA DPS142
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (49×3.5×0.75) + (5×3.5×0.75) = 142. 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 index458
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.
Secondary battery dispersion
Secondary dispersion typeImproved (40%) + Standard
This ship's secondary families don't share one dispersion bracket. Each family is listed below with its own slope; max dispersion = secondary range (km) × that family's slope + 30 m.
120 mm × 4 dispersion typeStandard
Max dispersion = range (km) × 57 + 30 for this family. Slope is set per gun model in the binary.
120 mm × 4 max disp @ 5 km315 m
5 km × 57 + 30 = 315 m.
140 mm × 16 dispersion typeImproved (40%, German battlecruiser type)
Max dispersion = range (km) × 33 + 30 for this family. Slope is set per gun model in the binary.
140 mm × 16 max disp @ 5 km195 m
5 km × 33 + 30 = 195 m.
Secondary battery firepower
Secondary DPM (per side)192,000
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: 4×1 120 mm (2/side) × 60/5 × 2000 = 48,000 + 16×1 140 mm (8/side) × 60/8 × 2400 = 144,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2400
Maximum HE damage per shell across secondary HE families. Best on this ship: 2400 from the 140 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 140 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 140 mm family.
Damage Control Party
Repair Party
Secondary Battery Booster