Main battery formulas
Shell Grouping (σ)1.9
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp209.1 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (17380/30·(10−2.8)/1000 + 2.8)·30 = 209.1 m
Max Vert Disp167.3 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 209.1 × 0.8 = 167.3 m
Med Horiz Disp70.6 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 209.1 × 0.338 (σ=1.9) = 70.6 m
Med Vert Disp56.5 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 167.3 × 0.338 (σ=1.9) = 56.5 m
AP Pen Close880.5 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 × 2650 × 1020^0.69 × 0.41^-1.07 × 834^1.38 = 880.5 mm. Matches the in-game spec card.
AP Pen Far434.7 mm
Same formula at the ship's max firing range (21.7 km), where the shell has slowed to 500.1 m/s: 1e-7 × 2650 × 1020^0.69 × 0.41^-1.07 × 500.1^1.38 = 434.7 mm.
HE penetration68 mm
68 mm ≈ 410 mm caliber / 6 (standard HE penetration ratio).
AP overmatch28 mm
floor(410 mm caliber / 14.3) = 28 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius250
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 alpha12
All 12 barrels bear on the broadside.
Turret turn time45 s
180 degrees / 4 deg/s traverse speed = 45 s.
HE full-salvo alpha78,000
6,500 HE damage x 12 broadside guns = 78,000.
AP full-salvo alpha145,200
12,100 AP damage x 12 broadside guns = 145,200.
Base HE DPM139,701
78,000 HE full-salvo alpha x 60 / 33.5 s base reload = 139,701.
Base AP DPM260,060
145,200 AP full-salvo alpha x 60 / 33.5 s base reload = 260,060.
Installed HE DPM154,967
78,000 HE full-salvo alpha x 60 / 30.2 s installed reload (Main Battery Mod. 3 = -10%) = 154,967.
Installed AP DPM288,477
145,200 AP full-salvo alpha x 60 / 30.2 s installed reload (Main Battery Mod. 3 = -10%) = 288,477.
Base shells/min21.5
12 broadside guns x 60 / 33.5 s base reload = 21.5.
Installed shells/min23.8
12 broadside guns x 60 / 30.2 s installed Artillery reload = 23.8.
Base fires/min6.45
12 HE shells x 60 / 33.5 s reload x 30% fire chance = 6.45.
Installed fires/min7.15
12 HE shells x 60 / 30.2 s installed reload x 30% fire chance = 7.15.
AA defense
Close-range AA DPS469
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (133×3.5×0.85) + (28×3.5×0.75) = 469. 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 index1594
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)201,300
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: 6×2 127 mm (6/side) × 60/7.5 × 2100 = 100,800 + 2×2 127 mm (2/side) × 60/6 × 2100 = 42,000 + 3×3 155 mm (4.5/side) × 60/12 × 2600 = 58,500. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2600
Maximum HE damage per shell across secondary HE families. Best on this ship: 2600 from the 155 mm family.
Max HE fire chance10%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 10% from the 155 mm family.
Max HE pen26 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: 26 mm from the 155 mm family.
Damage Control Party
Repair Party
Catapult Fighter
Observation Seaplane
Secondary Battery Booster