Main battery formulas
Shell Grouping (σ)1.65
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp207.8 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (17198/30·(10−2.8)/1000 + 2.8)·30 = 207.8 m
Max Vert Disp166.3 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 207.8 × 0.8 = 166.3 m
Med Horiz Disp75.4 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 207.8 × 0.363 (σ=1.65) = 75.4 m
Med Vert Disp60.3 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 166.3 × 0.363 (σ=1.65) = 60.3 m
AP Pen Close971.1 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 × 2831 × 1460^0.69 × 0.46^-1.07 × 780^1.38 = 971.1 mm. Matches the in-game spec card.
AP Pen Far571.7 mm
Same formula at the ship's max firing range (21.5 km), where the shell has slowed to 531.3 m/s: 1e-7 × 2831 × 1460^0.69 × 0.46^-1.07 × 531.3^1.38 = 571.7 mm.
HE penetration115 mm
115 mm ≈ 460 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 ~115mm armor instead of ~76mm. Hits every German cruiser (150mm CL, 203mm CA) and BB (350mm+), British heavy cruisers / Lion / Nelson, a handful of other premiums.
AP overmatch32 mm
floor(460 mm caliber / 14.3) = 32 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius400
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 alpha65,700
7,300 HE damage x 9 broadside guns = 65,700.
AP full-salvo alpha133,200
14,800 AP damage x 9 broadside guns = 133,200.
Base HE DPM131,400
65,700 HE full-salvo alpha x 60 / 30 s base reload = 131,400.
Base AP DPM266,400
133,200 AP full-salvo alpha x 60 / 30 s base reload = 266,400.
Installed HE DPM146,000
65,700 HE full-salvo alpha x 60 / 27 s installed reload (Main Battery Mod. 3 = -10%) = 146,000.
Installed AP DPM296,000
133,200 AP full-salvo alpha x 60 / 27 s installed reload (Main Battery Mod. 3 = -10%) = 296,000.
Base shells/min18
9 broadside guns x 60 / 30 s base reload = 18.
Installed shells/min20
9 broadside guns x 60 / 27 s installed Artillery reload = 20.
Base fires/min6.3
9 HE shells x 60 / 30 s reload x 35% fire chance = 6.3.
Installed fires/min7
9 HE shells x 60 / 27 s installed reload x 35% fire chance = 7.
AA defense
Close-range AA DPS224
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (5×3.5×0.85) + (49×3.5×0.85) + (24×3.5×0.75) = 224. 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 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index785
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 range3.1 km
Secondary battery firepower
Secondary DPM (per side)178,800
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: 6×2 127 mm (6/side) × 60/7.5 × 2100 = 100,800 + 4×3 155 mm (6/side) × 60/12 × 2600 = 78,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha2600
Maximum HE damage per shell across secondary HE families. Best on this ship: 2600 from the 155 mm family.
Max HE fire chance10%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 10% from the 155 mm family.
Max HE pen26 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: 26 mm from the 155 mm family.
Damage Control Party
Repair Party
Catapult Fighter
Observation Seaplane
Secondary Battery Booster