Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp131.7 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15555/30·(8−0.5)/1000 + 0.5)·30 = 131.7 m
Max Vert Disp79 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 131.7 × 0.6 = 79 m
Med Horiz Disp42.1 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 131.7 × 0.32 (σ=2) = 42.1 m
Med Vert Disp25.2 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 79 × 0.319 (σ=2) = 25.2 m
AP Pen Close227.4 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 × 2200 × 32.5^0.69 × 0.127^-1.07 × 808^1.38 = 227.4 mm. Matches the in-game spec card.
AP Pen Far58.4 mm
Same formula at the ship's max firing range (19.4 km), where the shell has slowed to 301.6 m/s: 1e-7 × 2200 × 32.5^0.69 × 0.127^-1.07 × 301.6^1.38 = 58.4 mm.
HE penetration21 mm
21 mm ≈ 127 mm caliber / 6 (standard HE penetration ratio).
AP overmatch8 mm
floor(127 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 alpha12
Barrels that can bear on one beam (12 of 16); casemate/wing mounts only fire one side.
Turret turn time6 s
180 degrees / 30 deg/s traverse speed = 6 s.
HE full-salvo alpha25,200
2,100 HE damage x 12 broadside guns = 25,200.
AP full-salvo alpha31,200
2,600 AP damage x 12 broadside guns = 31,200.
Base HE DPM472,500
25,200 HE full-salvo alpha x 60 / 3.2 s base reload = 472,500.
Base AP DPM585,000
31,200 AP full-salvo alpha x 60 / 3.2 s base reload = 585,000.
Installed HE DPM521,379
25,200 HE full-salvo alpha x 60 / 2.9 s installed reload (Main Battery Mod. 3 = -10%) = 521,379.
Installed AP DPM645,517
31,200 AP full-salvo alpha x 60 / 2.9 s installed reload (Main Battery Mod. 3 = -10%) = 645,517.
Base shells/min225
12 broadside guns x 60 / 3.2 s base reload = 225.
Installed shells/min248.3
12 broadside guns x 60 / 2.9 s installed Artillery reload = 248.3.
Base fires/min15.75
12 HE shells x 60 / 3.2 s reload x 7% fire chance = 15.75.
Installed fires/min17.38
12 HE shells x 60 / 2.9 s installed reload x 7% fire chance = 17.38.
AA defense
Close-range AA DPS504
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (119×3.5×0.9) + (41×3.5×0.9) = 504. 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 index2358
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
Sonar
Defensive AA Fire
Engine Boost
Repair Party