Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp168.6 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (14360/30·(10−1.6)/1000 + 1.6)·30 = 168.6 m
Max Vert Disp101.2 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 168.6 × 0.6 = 101.2 m
Med Horiz Disp53.9 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 168.6 × 0.32 (σ=2) = 53.9 m
Med Vert Disp32.3 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 101.2 × 0.319 (σ=2) = 32.3 m
Dispersion familyCruiser Disp.
Standard cruiser dispersion baseline.
AP Pen Close452.6 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 × 2409 × 122^0.69 × 0.203^-1.07 × 925^1.38 = 452.6 mm. Matches the in-game spec card.
AP Pen Far144.2 mm
Same formula at the ship's max firing range (19.7 km), where the shell has slowed to 403.9 m/s: 1e-7 × 2409 × 122^0.69 × 0.203^-1.07 × 403.9^1.38 = 144.2 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 Radius25
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 time22.5 s
180 degrees / 8 deg/s traverse speed = 22.5 s.
HE full-salvo alpha25,650
2,850 HE damage x 9 broadside guns = 25,650.
AP full-salvo alpha43,200
4,800 AP damage x 9 broadside guns = 43,200.
Base HE DPM118,385
25,650 HE full-salvo alpha x 60 / 13 s base reload = 118,385.
Base AP DPM199,385
43,200 AP full-salvo alpha x 60 / 13 s base reload = 199,385.
Installed HE DPM131,538
25,650 HE full-salvo alpha x 60 / 11.7 s installed reload (Main Battery Mod. 3 = -10%) = 131,538.
Installed AP DPM221,538
43,200 AP full-salvo alpha x 60 / 11.7 s installed reload (Main Battery Mod. 3 = -10%) = 221,538.
Base shells/min41.5
9 broadside guns x 60 / 13 s base reload = 41.5.
Installed shells/min46.2
9 broadside guns x 60 / 11.7 s installed Artillery reload = 46.2.
Base fires/min5.4
9 HE shells x 60 / 13 s reload x 13% fire chance = 5.4.
Installed fires/min6
9 HE shells x 60 / 11.7 s installed reload x 13% fire chance = 6.
AA defense
Close-range AA DPS435
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (54×3.5×0.9) + (52×3.5×0.85) + (35×3.5×0.9) = 435. 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 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)136,000
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: 4×2 120 mm (4/side) × 60/3 × 1700 = 136,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1700
Maximum HE damage per shell across secondary HE families. Best on this ship: 1700 from the 120 mm family.
Max HE fire chance7%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 7% from the 120 mm family.
Max HE pen20 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: 20 mm from the 120 mm family.
Damage Control Party
Sonar
Defensive AA Fire
Repair Party