Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp94.8 m
Horizontal dispersion ellipse width at max range, from the verified WoWS dispersion model: $\sigma_H = \left(\dfrac{R}{30}\cdot\dfrac{\text{idealRadius}-\text{minRadius}}{\text{idealDistance}} + \text{minRadius}\right)\cdot 30$ $= \left(\dfrac{10645}{30}\cdot\dfrac{8-0.5}{1000} + 0.5\right)\cdot 30 = 94.8\,\text{m}$
Max Vert Disp56.9 m
Vertical dispersion ellipse height at max range: $\sigma_V = \sigma_H \cdot \text{radiusOnMax}$ $= 94.8 \cdot 0.6 = 56.9\,\text{m}$
Med Horiz Disp30.3 m
50%-hit horizontal radius: $\sigma_{H,50} = \sigma_H \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 94.8 \cdot 0.32\;(\sigma = 2) = 30.3\,\text{m}$
Med Vert Disp18.2 m
50%-hit vertical radius: $\sigma_{V,50} = \sigma_V \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 56.9 \cdot 0.32\;(\sigma = 2) = 18.2\,\text{m}$
AP Pen Close202.1 mm
Canonical community AP formula (jcw780/wows_shell), evaluated at muzzle velocity: $P = 10^{-7}\cdot K \cdot m^{0.69} \cdot d^{-1.07} \cdot v_0^{1.38}$ $= 10^{-7}\cdot 1987 \cdot 31.75^{0.69} \cdot 0.127^{-1.07} \cdot 808^{1.38} = 202.1\,\text{mm}$. Matches the in-game spec card.
AP Pen Far41.3 mm
Same formula at the ship's max firing range (13.3 km), where the shell has slowed to 255.5 m/s: $P = 10^{-7}\cdot 1987 \cdot 31.75^{0.69} \cdot 0.127^{-1.07} \cdot 255.5^{1.38} = 41.3\,\text{mm}$.
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 alpha6
All 6 barrels bear on the broadside.
Turret turn time15 s
180 degrees / 12 deg/s traverse speed = 15 s.
HE full-salvo alpha10,800
1,800 HE damage x 6 broadside guns = 10,800.
AP full-salvo alpha14,100
2,350 AP damage x 6 broadside guns = 14,100.
Base HE DPM175,135
10,800 HE full-salvo alpha x 60 / 3.7 s base reload = 175,135.
Base AP DPM228,649
14,100 AP full-salvo alpha x 60 / 3.7 s base reload = 228,649.
Installed HE DPM196,364
10,800 HE full-salvo alpha x 60 / 3.3 s installed reload (Main Battery Mod. 3 = -10%) = 196,364.
Installed AP DPM256,364
14,100 AP full-salvo alpha x 60 / 3.3 s installed reload (Main Battery Mod. 3 = -10%) = 256,364.
Base shells/min97.3
6 broadside guns x 60 / 3.7 s base reload = 97.3.
Installed shells/min109.1
6 broadside guns x 60 / 3.3 s installed Artillery reload = 109.1.
Base fires/min8.76
6 HE shells x 60 / 3.7 s reload x 9% fire chance = 8.76.
Installed fires/min9.82
6 HE shells x 60 / 3.3 s installed reload x 9% fire chance = 9.82.
Torpedoes
Torpedo detectability1.3 km
Estimated torpedo reaction time8.1 s
detectability / (speed kt x 2.6 community game-speed factor).
Torpedo speed62 kt
Travel time to max range62 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 damage125,336
All tubes hitting one target: tubes x per-torpedo simulated damage = 8 x 15,667 = 125,336.
Per-side salvo damage125,336
One side firing, all torpedoes hitting: per-side tubes x per-torpedo simulated damage = 8 x 15,667 = 125,336.
AA defense
Close-range AA DPS20
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (6×3.5×0.95) = 20. 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 range3.1 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index62
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
Damage Control Party
Smoke Generator
Torpedo Reload Booster
Engine Boost