Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp192.2 m
Horizontal dispersion ellipse width at max range, from the verified WoWS dispersion model: $\sigma_H = \left(\dfrac{R}{30}\cdot\dfrac{\text{idealRadius}-\text{minRadius}}{\text{idealDistance}} + \text{minRadius}\right)\cdot 30$ $= \left(\dfrac{15029}{30}\cdot\dfrac{10-2.8}{1000} + 2.8\right)\cdot 30 = 192.2\,\text{m}$
Max Vert Disp153.8 m
Vertical dispersion ellipse height at max range: $\sigma_V = \sigma_H \cdot \text{radiusOnMax}$ $= 192.2 \cdot 0.8 = 153.8\,\text{m}$
Med Horiz Disp61.4 m
50%-hit horizontal radius: $\sigma_{H,50} = \sigma_H \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 192.2 \cdot 0.319\;(\sigma = 2) = 61.4\,\text{m}$
Med Vert Disp49.1 m
50%-hit vertical radius: $\sigma_{V,50} = \sigma_V \cdot \text{GetHalfHitsRatio}(\sigma)$ $= 153.8 \cdot 0.319\;(\sigma = 2) = 49.1\,\text{m}$
AP Pen Close859.3 mm
Canonical community AP formula (jcw780/wows_shell), evaluated at muzzle velocity: $P = 10^{-7}\cdot K \cdot m^{0.69} \cdot d^{-1.07} \cdot v_0^{1.38}$ $= 10^{-7}\cdot 2711 \cdot 1020^{0.69} \cdot 0.41^{-1.07} \cdot 806^{1.38} = 859.3\,\text{mm}$. Matches the in-game spec card.
AP Pen Far425.8 mm
Same formula at the ship's max firing range (20.7 km), where the shell has slowed to 484.6 m/s: $P = 10^{-7}\cdot 2711 \cdot 1020^{0.69} \cdot 0.41^{-1.07} \cdot 484.6^{1.38} = 425.8\,\text{mm}$.
HE penetration68 mm
68 mm ≈ 410 mm caliber / 6 (standard HE penetration ratio).
AP overmatch28 mm
floor(410 mm caliber / 14.3) = 28 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius150
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 alpha8
All 8 barrels bear on the broadside.
Turret turn time47.4 s
180 degrees / 3.8 deg/s traverse speed = 47.4 s.
HE full-salvo alpha52,000
6,500 HE damage x 8 broadside guns = 52,000.
AP full-salvo alpha100,800
12,600 AP damage x 8 broadside guns = 100,800.
Base HE DPM97,500
52,000 HE full-salvo alpha x 60 / 32 s base reload = 97,500.
Base AP DPM189,000
100,800 AP full-salvo alpha x 60 / 32 s base reload = 189,000.
Base shells/min15
8 broadside guns x 60 / 32 s base reload = 15.
Base fires/min4.5
8 HE shells x 60 / 32 s reload x 30% fire chance = 4.5.
AA defense
Close-range AA DPS302
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (100×3.5×0.75) + (15×3.5×0.75) = 302. 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 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index1011
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.
Secondary battery dispersion
Secondary dispersion typeImproved (40%) + Standard
This ship's secondary families don't share one dispersion bracket. Each family is listed below with its own slope; max dispersion = secondary range (km) × that family's slope + 30 m.
127 mm × 4 dispersion typeStandard
Max dispersion = range (km) × 57 + 30 for this family. Slope is set per gun model.
127 mm × 4 max disp @ 5 km315 m
5 km × 57 + 30 = 315 m.
140 mm × 18 dispersion typeImproved (40%, German battlecruiser type)
Max dispersion = range (km) × 33 + 30 for this family. Slope is set per gun model.
140 mm × 18 max disp @ 5 km195 m
5 km × 33 + 30 = 195 m.
Secondary battery firepower
Secondary DPM (per side)262,800
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: 4×2 127 mm (4/side) × 60/5 × 2100 = 100,800 + 18×1 140 mm (9/side) × 60/8 × 2400 = 162,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2400
Maximum HE damage per shell across secondary HE families. Best on this ship: 2400 from the 140 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 140 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 140 mm family.
Damage Control Party
Repair Party
Catapult Fighter
Observation Seaplane
Secondary Battery Booster