Main battery formulas
Shell Grouping (σ)1.8
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp185.6 m
Horizontal dispersion ellipse width at max range, from the verified WoWS dispersion model: $\sigma_H = \left(\dfrac{R}{30}\cdot\dfrac{\text{idealRadius}-\text{minRadius}}{\text{idealDistance}} + \text{minRadius}\right)\cdot 30$ $= \left(\dfrac{16385}{30}\cdot\dfrac{10-1.6}{1000} + 1.6\right)\cdot 30 = 185.6\,\text{m}$
Max Vert Disp111.4 m
Vertical dispersion ellipse height at max range: $\sigma_V = \sigma_H \cdot \text{radiusOnMax}$ $= 185.6 \cdot 0.6 = 111.4\,\text{m}$
Med Horiz Disp63.8 m
50%-hit horizontal radius: $\sigma_{H,50} = \sigma_H \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 185.6 \cdot 0.344\;(\sigma = 1.8) = 63.8\,\text{m}$
Med Vert Disp38.3 m
50%-hit vertical radius: $\sigma_{V,50} = \sigma_V \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 111.4 \cdot 0.344\;(\sigma = 1.8) = 38.3\,\text{m}$
AP Pen Close713.2 mm
Canonical community AP formula (jcw780/wows_shell), evaluated at muzzle velocity: $P = 10^{-7}\cdot K \cdot m^{0.69} \cdot d^{-1.07} \cdot v_0^{1.38}$ $= 10^{-7}\cdot 2428 \cdot 560^{0.69} \cdot 0.33^{-1.07} \cdot 870^{1.38} = 713.2\,\text{mm}$. Matches the in-game spec card.
AP Pen Far365.3 mm
Same formula at the ship's max firing range (20.5 km), where the shell has slowed to 535.7 m/s: $P = 10^{-7}\cdot 2428 \cdot 560^{0.69} \cdot 0.33^{-1.07} \cdot 535.7^{1.38} = 365.3\,\text{mm}$.
HE penetration55 mm
55 mm ≈ 330 mm caliber / 6 (standard HE penetration ratio).
AP overmatch23 mm
floor(330 mm caliber / 14.3) = 23 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius120
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 alpha9
All 9 barrels bear on the broadside.
Turret turn time36 s
180 degrees / 5 deg/s traverse speed = 36 s.
HE full-salvo alpha43,200
4,800 HE damage x 9 broadside guns = 43,200.
AP full-salvo alpha87,300
9,700 AP damage x 9 broadside guns = 87,300.
Base HE DPM108,000
43,200 HE full-salvo alpha x 60 / 24 s base reload = 108,000.
Base AP DPM218,250
87,300 AP full-salvo alpha x 60 / 24 s base reload = 218,250.
Installed HE DPM120,000
43,200 HE full-salvo alpha x 60 / 21.6 s installed reload (Main Battery Mod. 3 = -10%) = 120,000.
Installed AP DPM242,500
87,300 AP full-salvo alpha x 60 / 21.6 s installed reload (Main Battery Mod. 3 = -10%) = 242,500.
Base shells/min22.5
9 broadside guns x 60 / 24 s base reload = 22.5.
Installed shells/min25
9 broadside guns x 60 / 21.6 s installed Artillery reload = 25.
Base fires/min7.88
9 HE shells x 60 / 24 s reload x 35% fire chance = 7.88.
Installed fires/min8.75
9 HE shells x 60 / 21.6 s installed reload x 35% fire chance = 8.75.
AA defense
Close-range AA DPS553
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (59×3.5×0.9) + (64×3.5×0.85) + (56×3.5×0.9) = 553. 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 index1949
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
Secondary battery firepower
Secondary DPM (per side)221,538
Sum across all secondary families of (per-side barrels × 60 / reload_s × alpha), where per-side barrels = mounts × barrels-per-mount / 2 (the guns that bear on one broadside target). Per-family: 4×3 139 mm (6/side) × 60/6.5 × 2000 = 110,769 + 6×2 139 mm (6/side) × 60/6.5 × 2000 = 110,769. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2000
Maximum HE damage per shell across secondary HE families. Best on this ship: 2000 from the 139 mm family.
Max HE fire chance10%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 10% from the 139 mm family.
Max HE pen23 mm
Maximum HE armor penetration across secondary HE families (caliber × 1/6 for most nations; 1/4 for German/UK BBs). Shells whose pen falls under a plate's armor thickness shatter for 0 hull damage though fire chance still applies. Best on this ship: 23 mm from the 139 mm family.
Damage Control Party
Main Battery Reload Booster
Sonar
Defensive AA Fire
Repair Party
Catapult Fighter
Engine Boost