Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp141.7 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15750/30·(8−1.1)/1000 + 1.1)·30 = 141.7 m
Max Vert Disp85 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 141.7 × 0.6 = 85 m
Med Horiz Disp45.3 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 141.7 × 0.32 (σ=2) = 45.3 m
Med Vert Disp27.2 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 85 × 0.32 (σ=2) = 27.2 m
AP Pen Close488.4 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 × 2919 × 152^0.69 × 0.203^-1.07 × 762^1.38 = 488.4 mm. Matches the in-game spec card.
AP Pen Far178.1 mm
Same formula at the ship's max firing range (19.7 km), where the shell has slowed to 366.8 m/s: 1e-7 × 2919 × 152^0.69 × 0.203^-1.07 × 366.8^1.38 = 178.1 mm.
HE penetration34 mm
34 mm ≈ 203 mm caliber / 6 (standard HE penetration ratio).
AP overmatch14 mm
floor(203 mm caliber / 14.3) = 14 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius30
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 time25.7 s
180 degrees / 7 deg/s traverse speed = 25.7 s.
HE full-salvo alpha25,200
2,800 HE damage x 9 broadside guns = 25,200.
AP full-salvo alpha45,000
5,000 AP damage x 9 broadside guns = 45,000.
Base HE DPM137,455
25,200 HE full-salvo alpha x 60 / 11 s base reload = 137,455.
Base AP DPM245,455
45,000 AP full-salvo alpha x 60 / 11 s base reload = 245,455.
Installed HE DPM152,727
25,200 HE full-salvo alpha x 60 / 9.9 s installed reload (Main Battery Mod. 3 = -10%) = 152,727.
Installed AP DPM272,727
45,000 AP full-salvo alpha x 60 / 9.9 s installed reload (Main Battery Mod. 3 = -10%) = 272,727.
Base shells/min49.1
9 broadside guns x 60 / 11 s base reload = 49.1.
Installed shells/min54.5
9 broadside guns x 60 / 9.9 s installed Artillery reload = 54.5.
Base fires/min6.87
9 HE shells x 60 / 11 s reload x 14% fire chance = 6.87.
Installed fires/min7.64
9 HE shells x 60 / 9.9 s installed reload x 14% fire chance = 7.64.
AA defense
Close-range AA DPS498
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (129×3.5×0.9) + (29×3.5×0.9) = 498. 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 index2488
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)108,000
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) × 60/6 × 1800 = 108,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1800
Maximum HE damage per shell across secondary HE families. Best on this ship: 1800 from the 127 mm family.
Max HE fire chance5%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 5% from the 127 mm family.
Max HE pen21 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: 21 mm from the 127 mm family.
Damage Control Party
Defensive AA Fire
Sonar
Smoke Generator
Repair Party
