Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp165 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15785/30·(10−0.5)/1000 + 0.5)·30 = 165 m
Max Vert Disp99 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 165 × 0.6 = 99 m
Med Horiz Disp52.7 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 165 × 0.319 (σ=2) = 52.7 m
Med Vert Disp31.6 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 99 × 0.319 (σ=2) = 31.6 m
AP Pen Close603.4 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 × 2365 × 448.8^0.69 × 0.31^-1.07 × 836^1.38 = 603.4 mm. Matches the in-game spec card.
AP Pen Far324.7 mm
Same formula at the ship's max firing range (19.7 km), where the shell has slowed to 533.5 m/s: 1e-7 × 2365 × 448.8^0.69 × 0.31^-1.07 × 533.5^1.38 = 324.7 mm.
HE penetration52 mm
52 mm ≈ 310 mm caliber / 6 (standard HE penetration ratio).
AP overmatch21 mm
floor(310 mm caliber / 14.3) = 21 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius215
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 time36 s
180 degrees / 5 deg/s traverse speed = 36 s.
HE full-salvo alpha45,900
5,100 HE damage x 9 broadside guns = 45,900.
AP full-salvo alpha77,850
8,650 AP damage x 9 broadside guns = 77,850.
Base HE DPM114,750
45,900 HE full-salvo alpha x 60 / 24 s base reload = 114,750.
Base AP DPM194,625
77,850 AP full-salvo alpha x 60 / 24 s base reload = 194,625.
Installed HE DPM127,500
45,900 HE full-salvo alpha x 60 / 21.6 s installed reload (Main Battery Mod. 3 = -10%) = 127,500.
Installed AP DPM216,250
77,850 AP full-salvo alpha x 60 / 21.6 s installed reload (Main Battery Mod. 3 = -10%) = 216,250.
Base shells/min22.5
9 broadside guns x 60 / 24 s base reload = 22.5.
Installed shells/min25
9 broadside guns x 60 / 21.6 s installed Artillery reload = 25.
Base fires/min6.08
9 HE shells x 60 / 24 s reload x 27% fire chance = 6.08.
Installed fires/min6.75
9 HE shells x 60 / 21.6 s installed reload x 27% fire chance = 6.75.
AA defense
Close-range AA DPS486
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (103×3.5×0.85) + (57×3.5×0.9) = 486. 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 index1848
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)272,000
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: 8×2 100 mm (8/side) × 60/3 × 1700 = 272,000. 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 100 mm family.
Max HE fire chance6%
Maximum per-shell fire chance across secondary HE families (before target fire resistance is applied). Best on this ship: 6% from the 100 mm family.
Max HE pen17 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: 17 mm from the 100 mm family.
Damage Control Party
Sonar
Defensive AA Fire
Catapult Fighter
Repair Party
