Main battery formulas
Shell Grouping (σ)1.6
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp204.5 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (14136/30·(12−2.2)/1000 + 2.2)·30 = 204.5 m
Max Vert Disp122.7 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 204.5 × 0.6 = 122.7 m
Med Horiz Disp75.5 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 204.5 × 0.369 (σ=1.6) = 75.5 m
Med Vert Disp45.3 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 122.7 × 0.369 (σ=1.6) = 45.3 m
Dispersion familyEU BB Disp.
Standard BB dispersion. Used as the baseline for cross-family comparisons.
AP Pen Close707.5 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 × 2600 × 525^0.69 × 0.32^-1.07 × 830^1.38 = 707.5 mm. Matches the in-game spec card.
AP Pen Far287.9 mm
Same formula at the ship's max firing range (19.4 km), where the shell has slowed to 432.6 m/s: 1e-7 × 2600 × 525^0.69 × 0.32^-1.07 × 432.6^1.38 = 287.9 mm.
HE penetration55 mm
In-game data: 55 mm = 320 mm caliber / 5.82 (non-standard HE penetration ratio).
AP overmatch22 mm
floor(320 mm caliber / 14.3) = 22 mm (AP auto-penetrates plating this thick or less).
AP AOE Radius55
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 alpha10
All 10 barrels bear on the broadside.
Turret turn time36 s
180 degrees / 5 deg/s traverse speed = 36 s.
HE full-salvo alpha47,000
4,700 HE damage x 10 broadside guns = 47,000.
AP full-salvo alpha95,000
9,500 AP damage x 10 broadside guns = 95,000.
Base HE DPM104,444
47,000 HE full-salvo alpha x 60 / 27 s base reload = 104,444.
Base AP DPM211,111
95,000 AP full-salvo alpha x 60 / 27 s base reload = 211,111.
Base shells/min22.2
10 broadside guns x 60 / 27 s base reload = 22.2.
Base fires/min7.78
10 HE shells x 60 / 27 s reload x 35% fire chance = 7.78.
AA defense
Close-range AA DPS288
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (56×3.5×0.75) + (18×3.5×0.7) + (37×3.5×0.75) = 288. 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 range4 km
Longest-reaching aura across AA-only + dual-purpose auras.
AA threat index991
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)387,429
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: 2×3 135 mm (3/side) × 60/5 × 3000 = 108,000 + 2×3 135 mm (3/side) × 60/5 × 3000 = 108,000 + 10×1 90 mm (5/side) × 60/3.5 × 2000 = 171,429. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max SAP alpha3000
Maximum SAP damage per shell across secondary SAP families. Best on this ship: 3000 from the 135 mm family.
Max SAP pen38 mm
Maximum SAP armor penetration across secondary SAP families. SAP auto-bounces past its ricochet angles but never shatters on plate it can pen, and it starts no fires. Best on this ship: 38 mm from the 135 mm family.
Damage Control Party
Repair Party
Secondary Battery Booster