What the ellipse shows
Shells from a salvo do not land on a point — they scatter inside an ellipse whose size grows with range. The horizontal axis comes from the ship's maximum dispersion at that distance; the vertical axis is the same figure shortened by the ship's dispersion angles. Sigma controls how tightly shells cluster toward the middle of that ellipse rather than how big it is, which is why a high-sigma ship with a wide ellipse can still feel accurate.
Ballistics and armor penetration
Alongside the ellipse the simulator integrates the shell's trajectory to give flight time, impact angle and AP penetration at range, using the shell's own Krupp value, mass and drag from the game data. The integration runs in your browser as a WebAssembly module, so changing range or ship redraws the curves without a round trip to a server.
Impact angle matters as much as raw penetration: the steeper a shell arrives, the better it defeats deck armor and the worse it fares against a well-angled belt.
Build modifiers
Aiming Systems Modification and the other accuracy-affecting upgrades can be toggled on so the ellipse reflects the ship as you actually play it, not the stock hull. Comparing two ships at the same range with the same modifiers is the fastest way to see which one will reliably land a citadel volley.