Main battery formulas
Shell Grouping (σ)1.8
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp227.4 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (16743/30·(12−2)/1000 + 2)·30 = 227.4 m
Max Vert Disp136.5 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 227.4 × 0.6 = 136.5 m
Med Horiz Disp78.2 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 227.4 × 0.344 (σ=1.8) = 78.2 m
Med Vert Disp46.9 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 136.5 × 0.344 (σ=1.8) = 46.9 m
AP Pen Close732.1 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 × 2250 × 879^0.69 × 0.381^-1.07 × 836^1.38 = 732.1 mm. Matches the in-game spec card.
AP Pen Far368.5 mm
Same formula at the ship's max firing range (20.9 km), where the shell has slowed to 508.3 m/s: 1e-7 × 2250 × 879^0.69 × 0.381^-1.07 × 508.3^1.38 = 368.5 mm.
HE penetration95 mm
95 mm ≈ 381 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) - 0.249 in this case. Lets HE pen ~95mm armor instead of ~63mm. Hits every German cruiser (150mm CL, 203mm CA) and BB (350mm+), British heavy cruisers / Lion / Nelson, a handful of other premiums.
AP overmatch26 mm
floor(381 mm caliber / 14.3) = 26 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 alpha9
All 9 barrels bear on the broadside.
Turret turn time45 s
180 degrees / 4 deg/s traverse speed = 45 s.
HE full-salvo alpha56,700
6,300 HE damage x 9 broadside guns = 56,700.
AP full-salvo alpha107,100
11,900 AP damage x 9 broadside guns = 107,100.
Base HE DPM136,080
56,700 HE full-salvo alpha x 60 / 25 s base reload = 136,080.
Base AP DPM257,040
107,100 AP full-salvo alpha x 60 / 25 s base reload = 257,040.
Installed HE DPM151,200
56,700 HE full-salvo alpha x 60 / 22.5 s installed reload (Main Battery Mod. 3 = -10%) = 151,200.
Installed AP DPM285,600
107,100 AP full-salvo alpha x 60 / 22.5 s installed reload (Main Battery Mod. 3 = -10%) = 285,600.
Base shells/min21.6
9 broadside guns x 60 / 25 s base reload = 21.6.
Installed shells/min24
9 broadside guns x 60 / 22.5 s installed Artillery reload = 24.
Base fires/min7.56
9 HE shells x 60 / 25 s reload x 35% fire chance = 7.56.
Installed fires/min8.4
9 HE shells x 60 / 22.5 s installed reload x 35% fire chance = 8.4.
AA defense
Close-range AA DPS536
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (90×3.5×0.75) + (90×3.5×0.75) + (24×3.5×0.75) = 536. 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 index1583
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
Catapult Fighter
Observation Seaplane
Secondary Battery Booster