Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp135.7 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (14885/30·(8−1.1)/1000 + 1.1)·30 = 135.7 m
Max Vert Disp81.4 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 135.7 × 0.6 = 81.4 m
Med Horiz Disp43.4 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 135.7 × 0.32 (σ=2) = 43.4 m
Med Vert Disp26 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 81.4 × 0.319 (σ=2) = 26 m
AP Pen Close257.7 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 × 1862 × 45.5^0.69 × 0.15^-1.07 × 960^1.38 = 257.7 mm. Matches the in-game spec card.
AP Pen Far52 mm
Same formula at the ship's max firing range (18.6 km), where the shell has slowed to 301 m/s: 1e-7 × 1862 × 45.5^0.69 × 0.15^-1.07 × 301^1.38 = 52 mm.
HE penetration38 mm
38 mm ≈ 150 mm caliber / 4 (improved HE penetration: German BBs, Yamato-class, and a handful of others).
Improved HE PenYes
This ship's HE shells use a 1/4 (~0.25) caliber-to-pen ratio instead of the standard 1/6 (~0.167) - 0.253 in this case. Lets HE pen ~37mm armor instead of ~25mm. Hits every German cruiser (150mm CL, 203mm CA) and BB (350mm+), British heavy cruisers / Lion / Nelson, a handful of other premiums.
AP overmatch10 mm
floor(150 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 alpha9
All 9 barrels bear on the broadside.
Turret turn time23.7 s
180 degrees / 7.6 deg/s traverse speed = 23.7 s.
HE full-salvo alpha15,300
1,700 HE damage x 9 broadside guns = 15,300.
AP full-salvo alpha35,100
3,900 AP damage x 9 broadside guns = 35,100.
Base HE DPM153,000
15,300 HE full-salvo alpha x 60 / 6 s base reload = 153,000.
Base AP DPM351,000
35,100 AP full-salvo alpha x 60 / 6 s base reload = 351,000.
Base shells/min90
9 broadside guns x 60 / 6 s base reload = 90.
Base fires/min7.2
9 HE shells x 60 / 6 s reload x 8% fire chance = 7.2.
Torpedoes
Torpedo detectability1.3 km
Estimated torpedo reaction time7.8 s
detectability / (speed kt x 2.6 community game-speed factor).
Torpedo speed64 kt
Travel time to max range36.1 s
range / (speed kt x 2.6 community game-speed factor).
Tube count6
2 launchers x 3 tubes.
Per-side salvo3 torpedoes
tube count / 2 (symmetric port/starboard launcher layout; common on cruisers and battleships with deck torpedoes).
Full-salvo damage76,200
tube count x per-torpedo simulated damage (all torpedoes hitting).
Per-side salvo damage38,100
per-side salvo x per-torpedo simulated damage.
AA defense
Close-range AA DPS235
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) + (8×3.5×0.85) + (13×3.5×0.9) = 235. 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 index807
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)66,000
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 88 mm (4/side) × 60/4 × 1100 = 66,000. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max HE alpha1100
Maximum HE damage per shell across secondary HE families. Best on this ship: 1100 from the 88 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 88 mm family.
Max HE pen15 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: 15 mm from the 88 mm family.
Damage Control Party
Sonar
Defensive AA Fire