Secondary Dispersion in WoWs Legends: How the Formula Actually Works.

What "secondary dispersion" actually controls

When a secondary shell leaves your gun, the game doesn't fire it at a precise point. It samples a position inside a dispersion ellipse centered on the aimpoint, and the size of that ellipse is what we mean by "max dispersion at this range". A tighter ellipse means more shells land inside the target's silhouette. A looser ellipse means more shells fall short or wide.

For your main battery this is something you can feel directly. You aim, you fire, you watch where the shells go. For secondaries you don't aim at all, so the dispersion is a hidden variable that quietly decides whether your brawl is dealing damage or just lighting up the ocean with splashes.

The formula

For every ship except two, the max-dispersion-in-meters of the secondary battery is a simple linear function of secondary firing range:

The slope is the one number that distinguishes the ten brackets the live game uses. Standard ships use slope 57: at a typical 5 km secondary range that gives 5 × 57 + 30 = 315 m of spread. Bismarck-family ships (the "German battlecruiser" type) use slope 33, so at their longer 7.5 km range they spread 7.5 × 33 + 30 = 277.5 m, which is actually tighter than a Standard ship at much shorter range. Range pushes the dispersion up; slope pushes it down.

The brackets

Every ship in the game falls into one of these brackets. The "@ 6 km" column shows what max dispersion would be at a 6 km secondary range, for comparing the brackets on a level playing field.

The exception: Arkansas and Graf Zeppelin

Two ships in the entire game don't use the +30 constant: Arkansas (in its Founding Edition form) and Graf Zeppelin. They share a unique formula:

That's the tightest secondary cone in the game by a wide margin. At Graf Zeppelin's 5.5 km secondary range that comes out to just 94 m of spread. A Bismarck at the same range would scatter shells across 211 m, more than twice as wide. This is the only formula in the game where the slope is in single digits.

The other unusual thing about these two ships is that the formula is implemented differently in the game's data. Every other ship sits on one of the ten "regular" brackets via a single per-gun parameter; Arkansas and Graf Zeppelin route through a different mount-tier configuration that swaps in the alternate constant. Mechanically the effect is the same: tighter secondary fire.

What this means for builds

• Secondary range matters more than the chip implies. Adding 1 km of secondary range adds slope × 1 meters to max dispersion, but it also adds 1 km of reach. For a tight bracket like Improved (40%), that's only +33 m of dispersion for +1 km of guaranteed-fire range. Almost always worth it.
• Sigma is fixed at 1 across nearly every secondary battery. That means each shell is drawn from a uniform distribution inside the dispersion ellipse, no center-bias. The whole bubble is the playable area. Range and slope are the only meaningful levers.
• Watch for slope ties at different ranges. Two ships with the same bracket but different secondary ranges will have meaningfully different dispersion. A 5 km Standard ship (315 m) and a 6 km Standard ship (372 m) feel different at the same engagement range, even though they're "the same bracket."
• The CV secondaries are not the same animal. Most carriers have so little surface gunnery that the bracket barely matters; their dispersion never gets a chance to fire. Lexington and Shokaku are the two carriers that actually carry tightened secondaries (Improved ~20% bracket, slope 45). That's interesting trivia. It doesn't change how you play them.

How to read the chip on a ship page

Every ship's Secondary Battery card shows two related rows: Secondary dispersion type (the bracket name) and Max secondary dispersion @ X km (the computed value at that ship's range). The little ƒ icon next to either row expands to show the formula being applied, so you can see exactly why your particular ship lands where it does. For a worked example see Bismarck's spec card. Her 7.5 km secondary range × slope 33 + 30 = 277.5 m.

Where this fits

Secondary dispersion is one slice of the gunnery picture. For the main-battery dispersion model (the one that controls your aimed shells), see AP Penetration Explained. For the anti-air mechanics that share the same ATBA mounts on dual-purpose guns, see How AA Actually Works. The full Codex lives at /wowslegends/codex/.