Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp219.4 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15943/30·(12−2)/1000 + 2)·30 = 219.4 m
Max Vert Disp131.7 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 219.4 × 0.6 = 131.7 m
Med Horiz Disp70.1 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 219.4 × 0.32 (σ=2) = 70.1 m
Med Vert Disp42.1 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 131.7 × 0.32 (σ=2) = 42.1 m
AP Pen Close610.7 mm
Canonical community AP formula (jcw780/wows_shell), evaluated at muzzle velocity: 1e-7 × Krupp × mass^0.69 × caliber_m^-1.07 × v0^1.38 = 1e-7 × 2295 × 721^0.69 × 0.356^-1.07 × 757^1.38 = 610.7 mm. Matches the in-game spec card.
AP Pen Far323.1 mm
Same formula at the ship's max firing range (19.9 km), where the shell has slowed to 477.2 m/s: 1e-7 × 2295 × 721^0.69 × 0.356^-1.07 × 477.2^1.38 = 323.1 mm.
HE penetration89 mm
89 mm ≈ 356 mm caliber / 4 (improved HE penetration: German BBs, Yamato-class, and a handful of others).
Improved HE PenYes
This ship's HE shells use a 1/4 (~0.25) caliber-to-pen ratio instead of the standard 1/6 (~0.167) - 0.25 in this case. Lets HE pen ~89mm armor instead of ~59mm. Hits every German cruiser (150mm CL, 203mm CA) and BB (350mm+), British heavy cruisers / Lion / Nelson, a handful of other premiums.
AP overmatch24 mm
floor(356 mm caliber / 14.3) = 24 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius90
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 time45 s
180 degrees / 4 deg/s traverse speed = 45 s.
HE full-salvo alpha61,000
6,100 HE damage x 10 broadside guns = 61,000.
AP full-salvo alpha105,000
10,500 AP damage x 10 broadside guns = 105,000.
Base HE DPM124,068
61,000 HE full-salvo alpha x 60 / 29.5 s base reload = 124,068.
Base AP DPM213,559
105,000 AP full-salvo alpha x 60 / 29.5 s base reload = 213,559.
Base shells/min20.3
10 broadside guns x 60 / 29.5 s base reload = 20.3.
Base fires/min8.34
10 HE shells x 60 / 29.5 s reload x 41% fire chance = 8.34.
AA defense
Close-range AA DPS656
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (112×3.5×0.75) + (15×3.5×0.75) + (108×3.5×0.7) + (22×3.5×0.75) = 656. 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 range4.5 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index1662
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)136,732
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: 8×2 134 mm (8/side) × 60/6.67 × 1900 = 136,732. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1900
Maximum HE damage per shell across secondary HE families. Best on this ship: 1900 from the 134 mm family.
Max HE fire chance8%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 8% from the 134 mm family.
Max HE pen22 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: 22 mm from the 134 mm family.
Damage Control Party
Repair Party
Sonar
Secondary Battery Booster
