Main battery formulas
Shell Grouping (σ)1.8
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp200.8 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (17163/30·(10.5−1.6)/1000 + 1.6)·30 = 200.8 m
Max Vert Disp120.5 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 200.8 × 0.6 = 120.5 m
Med Horiz Disp69 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 200.8 × 0.344 (σ=1.8) = 69 m
Med Vert Disp41.4 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 120.5 × 0.344 (σ=1.8) = 41.4 m
AP Pen Close855.7 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 × 2390 × 1746^0.69 × 0.457^-1.07 × 732^1.38 = 855.7 mm. Matches the in-game spec card.
AP Pen Far519.6 mm
Same formula at the ship's max firing range (21.5 km), where the shell has slowed to 509.9 m/s: 1e-7 × 2390 × 1746^0.69 × 0.457^-1.07 × 509.9^1.38 = 519.6 mm.
HE penetration77 mm
77 mm ≈ 460 mm caliber / 6 (standard HE penetration ratio).
AP overmatch32 mm
floor(460 mm caliber / 14.3) = 32 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius400
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 alpha6
All 6 barrels bear on the broadside.
Turret turn time45 s
180 degrees / 4 deg/s traverse speed = 45 s.
HE full-salvo alpha38,700
6,450 HE damage x 6 broadside guns = 38,700.
AP full-salvo alpha94,500
15,750 AP damage x 6 broadside guns = 94,500.
Base HE DPM89,308
38,700 HE full-salvo alpha x 60 / 26 s base reload = 89,308.
Base AP DPM218,077
94,500 AP full-salvo alpha x 60 / 26 s base reload = 218,077.
Installed HE DPM99,231
38,700 HE full-salvo alpha x 60 / 23.4 s installed reload (Main Battery Mod. 3 = -10%) = 99,231.
Installed AP DPM242,308
94,500 AP full-salvo alpha x 60 / 23.4 s installed reload (Main Battery Mod. 3 = -10%) = 242,308.
Base shells/min13.8
6 broadside guns x 60 / 26 s base reload = 13.8.
Installed shells/min15.4
6 broadside guns x 60 / 23.4 s installed Artillery reload = 15.4.
Base fires/min5.95
6 HE shells x 60 / 26 s reload x 43% fire chance = 5.95.
Installed fires/min6.62
6 HE shells x 60 / 23.4 s installed reload x 43% fire chance = 6.62.
AA defense
Close-range AA DPS639
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (119×3.5×0.75) + (81×3.5×0.7) + (49×3.5×0.75) = 639. 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 range5 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index2133
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: 10×2 127 mm (10/side) × 60/6 × 1800 = 180,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1800
Maximum HE damage per shell across secondary HE families. Best on this ship: 1800 from the 127 mm family.
Max HE fire chance5%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 5% from the 127 mm family.
Max HE pen21 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: 21 mm from the 127 mm family.
Damage Control Party
Repair Party
Catapult Fighter
Observation Seaplane
Secondary Battery Booster
Engine Boost