Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp100.1 m
Horizontal dispersion ellipse width at max range, from the verified WoWS dispersion model: $\sigma_H = \left(\dfrac{R}{30}\cdot\dfrac{\text{idealRadius}-\text{minRadius}}{\text{idealDistance}} + \text{minRadius}\right)\cdot 30$ $= \left(\dfrac{11348}{30}\cdot\dfrac{8-0.5}{1000} + 0.5\right)\cdot 30 = 100.1\,\text{m}$
Max Vert Disp60.1 m
Vertical dispersion ellipse height at max range: $\sigma_V = \sigma_H \cdot \text{radiusOnMax}$ $= 100.1 \cdot 0.6 = 60.1\,\text{m}$
Med Horiz Disp32 m
50%-hit horizontal radius: $\sigma_{H,50} = \sigma_H \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 100.1 \cdot 0.32\;(\sigma = 2) = 32\,\text{m}$
Med Vert Disp19.2 m
50%-hit vertical radius: $\sigma_{V,50} = \sigma_V \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 60.1 \cdot 0.319\;(\sigma = 2) = 19.2\,\text{m}$
AP Pen Close141.8 mm
Canonical community AP formula (jcw780/wows_shell), evaluated at muzzle velocity: $P = 10^{-7}\cdot K \cdot m^{0.69} \cdot d^{-1.07} \cdot v_0^{1.38}$ $= 10^{-7}\cdot 1445 \cdot 41.4^{0.69} \cdot 0.152^{-1.07} \cdot 792.5^{1.38} = 141.8\,\text{mm}$. Matches the in-game spec card.
AP Pen Far25.6 mm
Same formula at the ship's max firing range (13.2 km), where the shell has slowed to 229.1 m/s: $P = 10^{-7}\cdot 1445 \cdot 41.4^{0.69} \cdot 0.152^{-1.07} \cdot 229.1^{1.38} = 25.6\,\text{mm}$.
HE penetration25 mm
25 mm ≈ 152 mm caliber / 6 (standard HE penetration ratio).
AP overmatch10 mm
floor(152 mm caliber / 14.3) = 10 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
Barrels that can bear on one beam (6 of 14); casemate/wing mounts only fire one side.
Turret turn time36 s
180 degrees / 5 deg/s traverse speed = 36 s.
HE full-salvo alpha12,600
2,100 HE damage x 6 broadside guns = 12,600.
AP full-salvo alpha16,200
2,700 AP damage x 6 broadside guns = 16,200.
Base HE DPM87,907
12,600 HE full-salvo alpha x 60 / 8.6 s base reload = 87,907.
Base AP DPM113,023
16,200 AP full-salvo alpha x 60 / 8.6 s base reload = 113,023.
Base shells/min41.9
6 broadside guns x 60 / 8.6 s base reload = 41.9.
Base fires/min3.35
6 HE shells x 60 / 8.6 s reload x 8% fire chance = 3.35.
AA defense
Close-range AA DPS9
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (3×3.5×0.9) = 9. 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 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index28
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