Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp226.4 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (17030/30·(12−1.7)/1000 + 1.7)·30 = 226.4 m
Max Vert Disp135.8 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 226.4 × 0.6 = 135.8 m
Med Horiz Disp72.4 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 226.4 × 0.32 (σ=2) = 72.4 m
Med Vert Disp43.4 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 135.8 × 0.32 (σ=2) = 43.4 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 Far520.8 mm
Same formula at the ship's max firing range (21.3 km), where the shell has slowed to 510.8 m/s: 1e-7 × 2390 × 1746^0.69 × 0.457^-1.07 × 510.8^1.38 = 520.8 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 alpha8
All 8 barrels bear on the broadside.
Turret turn time30 s
180 degrees / 6 deg/s traverse speed = 30 s.
HE full-salvo alpha51,600
6,450 HE damage x 8 broadside guns = 51,600.
AP full-salvo alpha126,000
15,750 AP damage x 8 broadside guns = 126,000.
Base HE DPM112,582
51,600 HE full-salvo alpha x 60 / 27.5 s base reload = 112,582.
Base AP DPM274,909
126,000 AP full-salvo alpha x 60 / 27.5 s base reload = 274,909.
Installed HE DPM124,839
51,600 HE full-salvo alpha x 60 / 24.8 s installed reload (Main Battery Mod. 3 = -10%) = 124,839.
Installed AP DPM304,839
126,000 AP full-salvo alpha x 60 / 24.8 s installed reload (Main Battery Mod. 3 = -10%) = 304,839.
Base shells/min17.5
8 broadside guns x 60 / 27.5 s base reload = 17.5.
Installed shells/min19.4
8 broadside guns x 60 / 24.8 s installed Artillery reload = 19.4.
Base fires/min7.51
8 HE shells x 60 / 27.5 s reload x 43% fire chance = 7.51.
Installed fires/min8.32
8 HE shells x 60 / 24.8 s installed reload x 43% fire chance = 8.32.
AA defense
Close-range AA DPS764
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (71×3.5×0.75) + (99×3.5×0.75) + (77×3.5×0.7) + (49×3.5×0.75) = 764. 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 range5.2 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index2998
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)291,892
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) × 60/3.7 × 1800 = 291,892. 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 chance9%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 9% 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
