Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp51.8 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (10520/30·(4−0.5)/1000 + 0.5)·30 = 51.8 m
Max Vert Disp31.1 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 51.8 × 0.6 = 31.1 m
Med Horiz Disp16.6 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 51.8 × 0.32 (σ=2) = 16.6 m
Med Vert Disp9.9 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 31.1 × 0.318 (σ=2) = 9.9 m
AP Pen Close238.8 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 × 1933 × 51^0.69 × 0.15^-1.07 × 835^1.38 = 238.8 mm. Matches the in-game spec card.
AP Pen Far89.7 mm
Same formula at the ship's max firing range (14.5 km), where the shell has slowed to 410.7 m/s: 1e-7 × 1933 × 51^0.69 × 0.15^-1.07 × 410.7^1.38 = 89.7 mm.
HE penetration38 mm
38 mm ≈ 150 mm caliber / 4 (improved HE penetration: German BBs, Yamato-class, and a handful of others).
Improved HE PenYes
This ship's HE shells use a 1/4 (~0.25) caliber-to-pen ratio instead of the standard 1/6 (~0.167) - 0.253 in this case. Lets HE pen ~37mm armor instead of ~25mm. Hits every German cruiser (150mm CL, 203mm CA) and BB (350mm+), British heavy cruisers / Lion / Nelson, a handful of other premiums.
AP overmatch10 mm
floor(150 mm caliber / 14.3) = 10 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius15
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 time12.9 s
180 degrees / 14 deg/s traverse speed = 12.9 s.
HE full-salvo alpha7,200
1,800 HE damage x 4 broadside guns = 7,200.
AP full-salvo alpha14,800
3,700 AP damage x 4 broadside guns = 14,800.
Base HE DPM72,000
7,200 HE full-salvo alpha x 60 / 6 s base reload = 72,000.
Base AP DPM148,000
14,800 AP full-salvo alpha x 60 / 6 s base reload = 148,000.
Base shells/min40
4 broadside guns x 60 / 6 s base reload = 40.
Base fires/min4.8
4 HE shells x 60 / 6 s reload x 12% fire chance = 4.8.
Torpedoes
Torpedo detectability1.2 km
Estimated torpedo reaction time8.9 s
detectability / (speed kt x 2.6 community game-speed factor).
Torpedo speed52 kt
Travel time to max range55.5 s
range / (speed kt x 2.6 community game-speed factor).
Tube count8
2 launchers x 4 tubes.
Per-side salvo8 torpedoes
8 (centerline launchers train across - full salvo to either side).
Full-salvo damage94,936
tube count x per-torpedo simulated damage (all torpedoes hitting).
Per-side salvo damage94,936
per-side salvo x per-torpedo simulated damage.
AA defense
Close-range AA DPS201
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (28×3.5×1) + (31×3.5×0.95) = 201. 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 range3.5 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index549
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
Damage Control Party
Smoke Generator
Engine Boost