Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp96.8 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (10903/30·(8−0.5)/1000 + 0.5)·30 = 96.8 m
Max Vert Disp58.1 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 96.8 × 0.6 = 58.1 m
Med Horiz Disp30.9 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 96.8 × 0.319 (σ=2) = 30.9 m
Med Vert Disp18.6 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 58.1 × 0.32 (σ=2) = 18.6 m
AP Pen Close216.9 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 × 2400 × 23.5^0.69 × 0.12^-1.07 × 825^1.38 = 216.9 mm. Matches the in-game spec card.
AP Pen Far47.6 mm
Same formula at the ship's max firing range (13.6 km), where the shell has slowed to 274.8 m/s: 1e-7 × 2400 × 23.5^0.69 × 0.12^-1.07 × 274.8^1.38 = 47.6 mm.
HE penetration20 mm
20 mm ≈ 120 mm caliber / 6 (standard HE penetration ratio).
AP overmatch8 mm
floor(120 mm caliber / 14.3) = 8 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius10
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 alpha4
All 4 barrels bear on the broadside.
Turret turn time7.2 s
180 degrees / 25 deg/s traverse speed = 7.2 s.
HE full-salvo alpha7,000
1,750 HE damage x 4 broadside guns = 7,000.
AP full-salvo alpha8,400
2,100 AP damage x 4 broadside guns = 8,400.
Base HE DPM233,333
7,000 HE full-salvo alpha x 60 / 1.8 s base reload = 233,333.
Base AP DPM280,000
8,400 AP full-salvo alpha x 60 / 1.8 s base reload = 280,000.
Installed HE DPM262,500
7,000 HE full-salvo alpha x 60 / 1.6 s installed reload (Main Battery Mod. 3 = -10%) = 262,500.
Installed AP DPM315,000
8,400 AP full-salvo alpha x 60 / 1.6 s installed reload (Main Battery Mod. 3 = -10%) = 315,000.
Base shells/min133.3
4 broadside guns x 60 / 1.8 s base reload = 133.3.
Installed shells/min150
4 broadside guns x 60 / 1.6 s installed Artillery reload = 150.
Base fires/min10.67
4 HE shells x 60 / 1.8 s reload x 8% fire chance = 10.67.
Installed fires/min12
4 HE shells x 60 / 1.6 s installed reload x 8% fire chance = 12.
AA defense
Close-range AA DPS438
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (82×3.5×1) + (43×3.5×1) = 438. 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 index1787
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.
Damage Control Party
Smoke Generator
Sonar
Engine Boost