Main battery formulas
Shell Grouping (σ)1.95
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp220.6 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15771/30·(12−2.2)/1000 + 2.2)·30 = 220.6 m
Max Vert Disp132.3 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 220.6 × 0.6 = 132.3 m
Med Horiz Disp71.8 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 220.6 × 0.325 (σ=1.95) = 71.8 m
Med Vert Disp43.1 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 132.3 × 0.326 (σ=1.95) = 43.1 m
AP Pen Close759.2 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 × 2550 × 800^0.69 × 0.38^-1.07 × 820^1.38 = 759.2 mm. Matches the in-game spec card.
AP Pen Far404.2 mm
Same formula at the ship's max firing range (21.7 km), where the shell has slowed to 519.3 m/s: 1e-7 × 2550 × 800^0.69 × 0.38^-1.07 × 519.3^1.38 = 404.2 mm.
HE penetration95 mm
95 mm ≈ 380 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(380 mm caliber / 14.3) = 26 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 alpha8
All 8 barrels bear on the broadside.
Turret turn time36 s
180 degrees / 5 deg/s traverse speed = 36 s.
HE full-salvo alpha35,200
4,400 HE damage x 8 broadside guns = 35,200.
AP full-salvo alpha92,800
11,600 AP damage x 8 broadside guns = 92,800.
Base HE DPM81,231
35,200 HE full-salvo alpha x 60 / 26 s base reload = 81,231.
Base AP DPM214,154
92,800 AP full-salvo alpha x 60 / 26 s base reload = 214,154.
Installed HE DPM90,256
35,200 HE full-salvo alpha x 60 / 23.4 s installed reload (Main Battery Mod. 3 = -10%) = 90,256.
Installed AP DPM237,949
92,800 AP full-salvo alpha x 60 / 23.4 s installed reload (Main Battery Mod. 3 = -10%) = 237,949.
Base shells/min18.5
8 broadside guns x 60 / 26 s base reload = 18.5.
Installed shells/min20.5
8 broadside guns x 60 / 23.4 s installed Artillery reload = 20.5.
Base fires/min6.28
8 HE shells x 60 / 26 s reload x 34% fire chance = 6.28.
Installed fires/min6.97
8 HE shells x 60 / 23.4 s installed reload x 34% fire chance = 6.97.
AA defense
Close-range AA DPS471
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (51×3.5×0.75) + (83×3.5×0.7) + (51×3.5×0.75) = 471. 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 index1478
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)253,540
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: 4×2 105 mm (4/side) × 60/3.35 × 1200 = 85,970 + 4×2 105 mm (4/side) × 60/3.35 × 1200 = 85,970 + 4×2 150 mm (4/side) × 60/7.5 × 1700 = 54,400 + 2×2 150 mm (2/side) × 60/7.5 × 1700 = 27,200. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1700
Maximum HE damage per shell across secondary HE families. Best on this ship: 1700 from the 150 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 150 mm family.
Max HE pen38 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: 38 mm from the 150 mm family.
Damage Control Party
Repair Party
Catapult Fighter
Observation Seaplane
Secondary Battery Booster
Sonar