Main battery formulas
Shell Grouping (σ)1.7
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp206.5 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (14338/30·(12−2.2)/1000 + 2.2)·30 = 206.5 m
Max Vert Disp123.9 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 206.5 × 0.6 = 123.9 m
Med Horiz Disp73.6 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 206.5 × 0.356 (σ=1.7) = 73.6 m
Med Vert Disp44.2 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 123.9 × 0.357 (σ=1.7) = 44.2 m
Dispersion familyEU BB Disp.
Standard BB dispersion. Used as the baseline for cross-family comparisons.
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 Far456.1 mm
Same formula at the ship's max firing range (19.7 km), where the shell has slowed to 558.6 m/s: 1e-7 × 2434 × 884.8^0.69 × 0.381^-1.07 × 558.6^1.38 = 456.1 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 alpha8
All 8 barrels bear on the broadside.
Turret turn time30 s
180 degrees / 6 deg/s traverse speed = 30 s.
HE full-salvo alpha43,200
5,400 HE damage x 8 broadside guns = 43,200.
AP full-salvo alpha88,000
11,000 AP damage x 8 broadside guns = 88,000.
Base HE DPM78,545
43,200 HE full-salvo alpha x 60 / 33 s base reload = 78,545.
Base AP DPM160,000
88,000 AP full-salvo alpha x 60 / 33 s base reload = 160,000.
Base shells/min14.5
8 broadside guns x 60 / 33 s base reload = 14.5.
Base fires/min3.49
8 HE shells x 60 / 33 s reload x 24% fire chance = 3.49.
AA defense
Close-range AA DPS327
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) + (36×3.5×0.7) + (42×3.5×0.75) = 327. 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 index1068
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)479,314
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) × 60/5 × 3800 = 136,800 + 2×3 152 mm (3/side) × 60/5 × 3800 = 136,800 + 12×1 90 mm (6/side) × 60/3.5 × 2000 = 205,714. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max SAP alpha3800
Maximum SAP damage per shell across secondary SAP families. Best on this ship: 3800 from the 152 mm family.
Max SAP pen42.3 mm
Maximum SAP armor penetration across secondary SAP families. SAP auto-bounces past its ricochet angles but never shatters on plate it can pen, and it starts no fires. Best on this ship: 42.3 mm from the 152 mm family.
Damage Control Party
Repair Party
Exhaust Smoke Generator
Secondary Battery Booster