Main battery formulas
Shell Grouping (σ)1.6
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp193.5 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (13011/30·(12−2.2)/1000 + 2.2)·30 = 193.5 m
Max Vert Disp116.1 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 193.5 × 0.6 = 116.1 m
Med Horiz Disp71.4 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 193.5 × 0.369 (σ=1.6) = 71.4 m
Med Vert Disp42.9 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 116.1 × 0.37 (σ=1.6) = 42.9 m
AP Pen Close498.1 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 × 2100 × 390^0.69 × 0.305^-1.07 × 840^1.38 = 498.1 mm. Matches the in-game spec card.
AP Pen Far202.4 mm
Same formula at the ship's max firing range (17.9 km), where the shell has slowed to 437.4 m/s: 1e-7 × 2100 × 390^0.69 × 0.305^-1.07 × 437.4^1.38 = 202.4 mm.
HE penetration59 mm
59 mm ≈ 356 mm caliber / 6 (standard HE penetration ratio).
AP overmatch24 mm
floor(356 mm caliber / 14.3) = 24 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius40
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 alpha13
All 13 barrels bear on the broadside.
Turret turn time60 s
180 degrees / 3 deg/s traverse speed = 60 s.
HE full-salvo alpha49,400
3,800 HE damage x 13 broadside guns = 49,400.
AP full-salvo alpha102,700
7,900 AP damage x 13 broadside guns = 102,700.
Base HE DPM104,000
49,400 HE full-salvo alpha x 60 / 28.5 s base reload = 104,000.
Base AP DPM216,211
102,700 AP full-salvo alpha x 60 / 28.5 s base reload = 216,211.
Base shells/min27.4
13 broadside guns x 60 / 28.5 s base reload = 27.4.
Base fires/min8.21
13 HE shells x 60 / 28.5 s reload x 30% fire chance = 8.21.
AA defense
Close-range AA DPS139
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (8×3.5×0.75) + (45×3.5×0.75) = 139. 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 index476
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 firepower
Secondary DPM (per side)504,000
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: 18×1 120 mm (9/side) × 60/3 × 2800 = 504,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max SAP alpha2800
Maximum SAP damage per shell across secondary SAP families. Best on this ship: 2800 from the 120 mm family.
Max SAP pen34.2 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: 34.2 mm from the 120 mm family.
Damage Control Party
Repair Party
Secondary Battery Booster