Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp200.7 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (18180/30·(10−1.6)/1000 + 1.6)·30 = 200.7 m
Max Vert Disp120.4 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 200.7 × 0.6 = 120.4 m
Med Horiz Disp64.1 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 200.7 × 0.319 (σ=2) = 64.1 m
Med Vert Disp38.5 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 120.4 × 0.32 (σ=2) = 38.5 m
AP Pen Close916.9 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 × 2900 × 900^0.69 × 0.406^-1.07 × 850^1.38 = 916.9 mm. Matches the in-game spec card.
AP Pen Far531.8 mm
Same formula at the ship's max firing range (22.7 km), where the shell has slowed to 572.8 m/s: 1e-7 × 2900 × 900^0.69 × 0.406^-1.07 × 572.8^1.38 = 531.8 mm.
HE penetration68 mm
68 mm ≈ 406 mm caliber / 6 (standard HE penetration ratio).
AP overmatch28 mm
floor(406 mm caliber / 14.3) = 28 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius150
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 time25.7 s
180 degrees / 7 deg/s traverse speed = 25.7 s.
HE full-salvo alpha40,200
6,700 HE damage x 6 broadside guns = 40,200.
AP full-salvo alpha72,600
12,100 AP damage x 6 broadside guns = 72,600.
Base HE DPM90,677
40,200 HE full-salvo alpha x 60 / 26.6 s base reload = 90,677.
Base AP DPM163,759
72,600 AP full-salvo alpha x 60 / 26.6 s base reload = 163,759.
Installed HE DPM100,921
40,200 HE full-salvo alpha x 60 / 23.9 s installed reload (Main Battery Mod. 3 = -10%) = 100,921.
Installed AP DPM182,259
72,600 AP full-salvo alpha x 60 / 23.9 s installed reload (Main Battery Mod. 3 = -10%) = 182,259.
Base shells/min13.5
6 broadside guns x 60 / 26.6 s base reload = 13.5.
Installed shells/min15.1
6 broadside guns x 60 / 23.9 s installed Artillery reload = 15.1.
Base fires/min6.63
6 HE shells x 60 / 26.6 s reload x 49% fire chance = 6.63.
Installed fires/min7.38
6 HE shells x 60 / 23.9 s installed reload x 49% fire chance = 7.38.
AA defense
Close-range AA DPS225
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (15×3.5×0.75) + (33×3.5×0.7) + (40×3.5×0.75) = 225. 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 index894
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 range3.1 km
Secondary battery firepower
Secondary DPM (per side)301,500
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: 12×2 100 mm (12/side) × 60/4 × 1400 = 252,000 + 3×3 152 mm (4.5/side) × 60/12 × 2200 = 49,500. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2200
Maximum HE damage per shell across secondary HE families. Best on this ship: 2200 from the 152 mm family.
Max HE fire chance12%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 12% from the 152 mm family.
Max HE pen25 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: 25 mm from the 152 mm family.
Damage Control Party
Repair Party
Main Battery Reload Booster
Catapult Fighter
Observation Seaplane
Secondary Battery Booster
Engine Boost