Main battery formulas
Shell Grouping (σ)2.05
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp139.5 m
Horizontal dispersion ellipse width at max range, from the verified WoWS dispersion model: $\sigma_H = \left(\dfrac{R}{30}\cdot\dfrac{\text{idealRadius}-\text{minRadius}}{\text{idealDistance}} + \text{minRadius}\right)\cdot 30$ $= \left(\dfrac{15440}{30}\cdot\dfrac{8-1.1}{1000} + 1.1\right)\cdot 30 = 139.5\,\text{m}$
Max Vert Disp83.7 m
Vertical dispersion ellipse height at max range: $\sigma_V = \sigma_H \cdot \text{radiusOnMax}$ $= 139.5 \cdot 0.6 = 83.7\,\text{m}$
Med Horiz Disp43.8 m
50%-hit horizontal radius: $\sigma_{H,50} = \sigma_H \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 139.5 \cdot 0.314\;(\sigma = 2.05) = 43.8\,\text{m}$
Med Vert Disp26.3 m
50%-hit vertical radius: $\sigma_{V,50} = \sigma_V \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 83.7 \cdot 0.314\;(\sigma = 2.05) = 26.3\,\text{m}$
AP Pen Close323.8 mm
Canonical community AP formula (jcw780/wows_shell), evaluated at muzzle velocity: $P = 10^{-7}\cdot K \cdot m^{0.69} \cdot d^{-1.07} \cdot v_0^{1.38}$ $= 10^{-7}\cdot 2672 \cdot 59.85^{0.69} \cdot 0.152^{-1.07} \cdot 768^{1.38} = 323.8\,\text{mm}$. Matches the in-game spec card.
AP Pen Far94.3 mm
Same formula at the ship's max firing range (19.3 km), where the shell has slowed to 314.2 m/s: $P = 10^{-7}\cdot 2672 \cdot 59.85^{0.69} \cdot 0.152^{-1.07} \cdot 314.2^{1.38} = 94.3\,\text{mm}$.
HE penetration30 mm
In-game data: 30 mm = 152 mm caliber / 5.07 (non-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 Radius20
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 alpha10
All 10 barrels bear on the broadside.
Turret turn time4.7 s
180 degrees / 38 deg/s traverse speed = 4.7 s.
HE full-salvo alpha21,500
2,150 HE damage x 10 broadside guns = 21,500.
AP full-salvo alpha32,000
3,200 AP damage x 10 broadside guns = 32,000.
Base HE DPM322,500
21,500 HE full-salvo alpha x 60 / 4 s base reload = 322,500.
Base AP DPM480,000
32,000 AP full-salvo alpha x 60 / 4 s base reload = 480,000.
Installed HE DPM358,333
21,500 HE full-salvo alpha x 60 / 3.6 s installed reload (Main Battery Mod. 3 = -10%) = 358,333.
Installed AP DPM533,333
32,000 AP full-salvo alpha x 60 / 3.6 s installed reload (Main Battery Mod. 3 = -10%) = 533,333.
Base shells/min150
10 broadside guns x 60 / 4 s base reload = 150.
Installed shells/min166.7
10 broadside guns x 60 / 3.6 s installed Artillery reload = 166.7.
Base fires/min13.5
10 HE shells x 60 / 4 s reload x 9% fire chance = 13.5.
Installed fires/min15
10 HE shells x 60 / 3.6 s installed reload x 9% fire chance = 15.
Torpedoes
Torpedo detectability1.3 km
Estimated torpedo reaction time7.7 s
detectability / (speed kt x 2.6 community game-speed factor).
Torpedo speed65 kt
Travel time to max range79.9 s
range / (speed kt x 2.6 community game-speed factor).
Tube count20
4 launchers x 5 tubes.
Per-side salvo10 torpedoes
tube count / 2 (symmetric port/starboard launcher layout; common on cruisers and battleships with deck torpedoes).
Full-salvo damage313,340
All tubes hitting one target: tubes x per-torpedo simulated damage = 20 x 15,667 = 313,340.
Per-side salvo damage156,670
One side firing, all torpedoes hitting: per-side tubes x per-torpedo simulated damage = 10 x 15,667 = 156,670.
AA defense
Close-range AA DPS639
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (24×3.5×0.9) + (142×3.5×0.9) + (37×3.5×0.9) = 639. 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 range6 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index3200
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
Repair Party
Sonar
Defensive AA Fire
Surveillance Radar
Smoke Generator