Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp122.4 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (12952/30·(8−1.1)/1000 + 1.1)·30 = 122.4 m
Max Vert Disp73.4 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 122.4 × 0.6 = 73.4 m
Med Horiz Disp39.1 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 122.4 × 0.319 (σ=2) = 39.1 m
Med Vert Disp23.5 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 73.4 × 0.32 (σ=2) = 23.5 m
Dispersion familyCruiser Disp.
Standard cruiser dispersion baseline.
AP Pen Close290.2 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 × 2445 × 59^0.69 × 0.152^-1.07 × 762^1.38 = 290.2 mm. Matches the in-game spec card.
AP Pen Far89.3 mm
Same formula at the ship's max firing range (17.8 km), where the shell has slowed to 324.4 m/s: 1e-7 × 2445 × 59^0.69 × 0.152^-1.07 × 324.4^1.38 = 89.3 mm.
HE penetration25 mm
25 mm ≈ 152 mm caliber / 6 (standard HE penetration ratio).
AP overmatch10 mm
floor(152 mm caliber / 14.3) = 10 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius15
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 alpha15
All 15 barrels bear on the broadside.
Turret turn time22.5 s
180 degrees / 8 deg/s traverse speed = 22.5 s.
HE full-salvo alpha33,000
2,200 HE damage x 15 broadside guns = 33,000.
AP full-salvo alpha48,000
3,200 AP damage x 15 broadside guns = 48,000.
Base HE DPM198,000
33,000 HE full-salvo alpha x 60 / 10 s base reload = 198,000.
Base AP DPM288,000
48,000 AP full-salvo alpha x 60 / 10 s base reload = 288,000.
Base shells/min90
15 broadside guns x 60 / 10 s base reload = 90.
Base fires/min10.8
15 HE shells x 60 / 10 s reload x 12% fire chance = 10.8.
AA defense
Close-range AA DPS368
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (58×3.5×0.9) + (38×3.5×0.85) + (23×3.5×0.9) = 368. 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 index1228
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)72,000
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: 4×2 127 mm (4/side) × 60/6 × 1800 = 72,000. 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
Sonar
Defensive AA Fire
Catapult Fighter
