Main battery formulas
Shell Grouping (σ)2.05
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp179.5 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15650/30·(10−1.6)/1000 + 1.6)·30 = 179.5 m
Max Vert Disp107.7 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 179.5 × 0.6 = 107.7 m
Med Horiz Disp56.3 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 179.5 × 0.314 (σ=2.05) = 56.3 m
Med Vert Disp33.8 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 107.7 × 0.314 (σ=2.05) = 33.8 m
AP Pen Close576.6 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 × 2311 × 405^0.69 × 0.305^-1.07 × 855^1.38 = 576.6 mm. Matches the in-game spec card.
AP Pen Far198.4 mm
Same formula at the ship's max firing range (19.6 km), where the shell has slowed to 394.7 m/s: 1e-7 × 2311 × 405^0.69 × 0.305^-1.07 × 394.7^1.38 = 198.4 mm.
HE penetration76 mm
76 mm ≈ 305 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 ~76mm armor instead of ~50mm. Hits every German cruiser (150mm CL, 203mm CA) and BB (350mm+), British heavy cruisers / Lion / Nelson, a handful of other premiums.
AP overmatch21 mm
floor(305 mm caliber / 14.3) = 21 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 alpha8
All 8 barrels bear on the broadside.
Turret turn time25.7 s
180 degrees / 7 deg/s traverse speed = 25.7 s.
HE full-salvo alpha25,200
3,150 HE damage x 8 broadside guns = 25,200.
AP full-salvo alpha61,600
7,700 AP damage x 8 broadside guns = 61,600.
Base HE DPM84,000
25,200 HE full-salvo alpha x 60 / 18 s base reload = 84,000.
Base AP DPM205,333
61,600 AP full-salvo alpha x 60 / 18 s base reload = 205,333.
Installed HE DPM93,333
25,200 HE full-salvo alpha x 60 / 16.2 s installed reload (Main Battery Mod. 3 = -10%) = 93,333.
Installed AP DPM228,148
61,600 AP full-salvo alpha x 60 / 16.2 s installed reload (Main Battery Mod. 3 = -10%) = 228,148.
Base shells/min26.7
8 broadside guns x 60 / 18 s base reload = 26.7.
Installed shells/min29.6
8 broadside guns x 60 / 16.2 s installed Artillery reload = 29.6.
Base fires/min5.87
8 HE shells x 60 / 18 s reload x 22% fire chance = 5.87.
Installed fires/min6.52
8 HE shells x 60 / 16.2 s installed reload x 22% fire chance = 6.52.
AA defense
Close-range AA DPS465
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (81×3.5×0.9) + (27×3.5×0.85) + (41×3.5×0.9) = 465. 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 index2108
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)334,251
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: 10×2 128 mm (10/side) × 60/3.4 × 1500 = 264,706 + 3×3 150 mm (4.5/side) × 60/6.6 × 1700 = 69,545. 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
Sonar
Defensive AA Fire
Engine Boost
Secondary Battery Booster
Repair Party