Main battery formulas
Shell Grouping (σ)2
Shell grouping (sigma); shown in-game as Shell Grouping.
Max Horiz Disp177 m
Horizontal dispersion ellipse width at max range. (R/30·(idealRadius−minRadius)/idealDistance + minRadius)·30 = (15360/30·(10−1.6)/1000 + 1.6)·30 = 177 m
Max Vert Disp106.2 m
Vertical dispersion ellipse height at max range = max horizontal × radiusOnMax = 177 × 0.6 = 106.2 m
Med Horiz Disp56.6 m
50%-hit horizontal radius = max horizontal × GetHalfHitsRatio(σ) = 177 × 0.32 (σ=2) = 56.6 m
Med Vert Disp33.9 m
50%-hit vertical radius = max vertical × GetHalfHitsRatio(σ) = 106.2 × 0.319 (σ=2) = 33.9 m
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 Far289.8 mm
Same formula at the ship's max firing range (19.2 km), where the shell has slowed to 434.7 m/s: 1e-7 × 2600 × 525^0.69 × 0.32^-1.07 × 434.7^1.38 = 289.8 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 Radius175
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 alpha8
All 8 barrels bear on the broadside.
Turret turn time22.5 s
180 degrees / 8 deg/s traverse speed = 22.5 s.
HE full-salvo alpha37,600
4,700 HE damage x 8 broadside guns = 37,600.
AP full-salvo alpha77,600
9,700 AP damage x 8 broadside guns = 77,600.
Base HE DPM104,930
37,600 HE full-salvo alpha x 60 / 21.5 s base reload = 104,930.
Base AP DPM216,558
77,600 AP full-salvo alpha x 60 / 21.5 s base reload = 216,558.
Installed HE DPM116,289
37,600 HE full-salvo alpha x 60 / 19.4 s installed reload (Main Battery Mod. 3 = -10%) = 116,289.
Installed AP DPM240,000
77,600 AP full-salvo alpha x 60 / 19.4 s installed reload (Main Battery Mod. 3 = -10%) = 240,000.
Base shells/min22.3
8 broadside guns x 60 / 21.5 s base reload = 22.3.
Installed shells/min24.7
8 broadside guns x 60 / 19.4 s installed Artillery reload = 24.7.
Base fires/min7.81
8 HE shells x 60 / 21.5 s reload x 35% fire chance = 7.81.
Installed fires/min8.66
8 HE shells x 60 / 19.4 s installed reload x 35% fire chance = 8.66.
Torpedoes
Torpedo detectability1.7 km
Estimated torpedo reaction time9.1 s
detectability / (speed kt x 2.6 community game-speed factor).
Torpedo speed72 kt
Travel time to max range42.8 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 damage115,398
tube count x per-torpedo simulated damage (all torpedoes hitting).
Per-side salvo damage57,699
per-side salvo x per-torpedo simulated damage.
AA defense
Close-range AA DPS464
Sum across every AA aura on this ship of (aura.continuous_damage x 3.5 x aura.hit_probability). Here: (71×3.5×0.9) + (30×3.5×0.85) + (48×3.5×0.9) = 464. 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 index1566
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)408,304
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: 3×4 152 mm (6/side) × 60/9.6 × 3650 = 136,875 + 10×2 90 mm (10/side) × 60/4.2 × 1900 = 271,429. Assumes every shell hits (real hit rate is lower; the Brawl matchup tool on the Compare page folds in dispersion + target armor).
Max SAP alpha3650
Maximum SAP damage per shell across secondary SAP families. Best on this ship: 3650 from the 152 mm family.
Max SAP pen42.3 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: 42.3 mm from the 152 mm family.
Damage Control Party
Repair Party
Sonar
Defensive AA Fire
Exhaust Smoke Generator
Secondary Battery Booster
