Main battery formulas
Shell Grouping (σ)1.4
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp226.2 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (16622/30·(12−2)/1000 + 2)·30 = 226.2 m
Max Vert Disp135.7 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 226.2 × 0.6 = 135.7 m
Med Horiz Disp89.2 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 226.2 × 0.394 (σ=1.4) = 89.2 m
Med Vert Disp53.5 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 135.7 × 0.394 (σ=1.4) = 53.5 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 Far318 mm
Same formula at the ship's max firing range (20.8 km), where the shell has slowed to 471.7 m/s: 1e-7 × 2295 × 721^0.69 × 0.356^-1.07 × 471.7^1.38 = 318 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 Radius175
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 alpha16
All 16 barrels bear on the broadside.
Turret turn time40 s
180 degrees / 4.5 deg/s traverse speed = 40 s.
HE full-salvo alpha84,800
5,300 HE damage x 16 broadside guns = 84,800.
AP full-salvo alpha176,000
11,000 AP damage x 16 broadside guns = 176,000.
Base HE DPM203,520
84,800 HE full-salvo alpha x 60 / 25 s base reload = 203,520.
Base AP DPM422,400
176,000 AP full-salvo alpha x 60 / 25 s base reload = 422,400.
Installed HE DPM226,133
84,800 HE full-salvo alpha x 60 / 22.5 s installed reload (Main Battery Mod. 3 = -10%) = 226,133.
Installed AP DPM469,333
176,000 AP full-salvo alpha x 60 / 22.5 s installed reload (Main Battery Mod. 3 = -10%) = 469,333.
Base shells/min38.4
16 broadside guns x 60 / 25 s base reload = 38.4.
Installed shells/min42.7
16 broadside guns x 60 / 22.5 s installed Artillery reload = 42.7.
Base fires/min9.22
16 HE shells x 60 / 25 s reload x 24% fire chance = 9.22.
Installed fires/min10.24
16 HE shells x 60 / 22.5 s installed reload x 24% fire chance = 10.24.
AA defense
Close-range AA DPS682
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (117×3.5×0.75) + (121×3.5×0.75) + (22×3.5×0.75) = 682. 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 index2487
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 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
Secondary Battery Booster
