Main battery formulas
Shell Grouping (σ)1.8
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp102.6 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (10093/30·(8−1.1)/1000 + 1.1)·30 = 102.6 m
Max Vert Disp61.6 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 102.6 × 0.6 = 61.6 m
Med Horiz Disp35.3 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 102.6 × 0.344 (σ=1.8) = 35.3 m
Med Vert Disp21.2 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 61.6 × 0.344 (σ=1.8) = 21.2 m
AP Pen Close219.2 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 × 1830 × 47.7^0.69 × 0.152^-1.07 × 853^1.38 = 219.2 mm. Matches the in-game spec card.
AP Pen Far50.4 mm
Same formula at the ship's max firing range (12.6 km), where the shell has slowed to 294.1 m/s: 1e-7 × 1830 × 47.7^0.69 × 0.152^-1.07 × 294.1^1.38 = 50.4 mm.
HE penetration25 mm
25 mm ≈ 152 mm caliber / 6 (standard HE penetration ratio).
AP overmatch10 mm
floor(152 mm caliber / 14.3) = 10 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius10
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 alpha8
Barrels that can bear on one beam (8 of 14); casemate/wing mounts only fire one side.
Turret turn time22.5 s
180 degrees / 8 deg/s traverse speed = 22.5 s.
HE full-salvo alpha16,800
2,100 HE damage x 8 broadside guns = 16,800.
AP full-salvo alpha24,000
3,000 AP damage x 8 broadside guns = 24,000.
Base HE DPM112,000
16,800 HE full-salvo alpha x 60 / 9 s base reload = 112,000.
Base AP DPM160,000
24,000 AP full-salvo alpha x 60 / 9 s base reload = 160,000.
Base shells/min53.3
8 broadside guns x 60 / 9 s base reload = 53.3.
Base fires/min3.73
8 HE shells x 60 / 9 s reload x 7% fire chance = 3.73.
AA defense
Close-range AA DPS21
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (7×3.5×0.85) = 21. 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 range1 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index21
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 km
Secondary battery firepower
Secondary DPM (per side)118,800
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 76.2 mm (9/side) × 60/5 × 1100 = 118,800. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1100
Maximum HE damage per shell across secondary HE families. Best on this ship: 1100 from the 76.2 mm family.
Max HE fire chance4%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 4% from the 76.2 mm family.
Max HE pen13 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: 13 mm from the 76.2 mm family.
Damage Control Party