Dispersion

This page is a work in progress.

In World of Warships, dispersion curves determine the maximum possible variation between any two shells fired at the same location. All ships possess both horizontal dispersion, which scales with firing range, and vertical dispersion, which is a fixed number for any given ship. These can be combined to create a dispersion ellipse - this representation, along with the sigma value of a ship's guns, can give players an objective picture of how precise and accurate their ship is.

Horizontal Dispersion
Horizontal dispersion for all ships in World of Warships is defined as a function of the range at which you fire. Every single ship in WoWS sees a linear increase in horizontal dispersion as range increases. Generally, battleships possess the largest dispersion curves at a given range, cruisers possess a tighter dispersion curve, and destroyers have the smallest (ie. destroyers are usually more accurate than cruisers, which are usually more accurate than battleships). On websites such as wowsft.org, the official wiki, and the development blog, the given 'dispersion' statistic is the horizontal dispersion at a ships' base maximum firing range.

Vertical Dispersion
Like horizontal dispersion, all ships in WoWS are subject to some degree of randomness in their vertical spread as well. This is affected by sigma as well, but is not nearly as well-understood and defined as the maximum horizontal dispersion (and their curves) which are given by Wargaming. Maximum vertical dispersion for most ships is a fixed value which does not scale with range - that is to say, it is a constant.

The effect of range increases on vertical dispersion
Because increasing your range does not increase your maximum vertical dispersion, increasing a ship's maximum range will actually increase its accuracy on the vertical plane, at less than maximum range. For example: assume a theoretical ship with 20km maximum range and 200m vertical dispersion, to make the math easy. Also assume that vertical dispersion increases linearly with range (thus, for this exact theoretical ship, a shot at 10km will have 100m vertical dispersion). If you increase her maximum range to 23.2km using Gun Fire Control System Modification 2, she will now have 200m vertical dispersion at 23.2km. That means that the same shot at 10km will instead have 86.2m of vertical dispersion, instead of 100m, because 10km is only 43.1% of the way up to her maximum range.

The apparent relationship between velocity and vertical dispersion
Many players that frequent sites which display dispersion ellipses and statistics will notice ships appearing to have a strong correlation between vertical dispersion and muzzle velocity, along with a falloff of vertical dispersion with range.
 * 1) Why does vertical dispersion appear to vary with range and velocity, then, when it's supposed to be a constant?
 * 2) * While it is technically true that vertical dispersion appears to change, it's also a failure of interpretation of data. It's not particularly easy to represent a ship's dispersion ellipse in 3 dimensions, so the most common method for creating an ellipse is to create its projection on the 2D horizontal plane - that is, what would your dispersion look like if there was no ship in the way. Vertical dispersion is a constant on the vertical plane, but appears to have some variation when projected on the horizontal plane. A ship with very high velocity will experience much larger deviation in where their shells land given the exact same vertical dispersion on the vertical plane. As shells slow down in flight due to drag, this deviation tightens, which results in that negative correlation many ships have between their range and apparent vertical dispersion.
 * 3) What does this mean, practically? Do ships with very high muzzle velocity actually suffer from decreased accuracy?
 * 4) * Most ships have very similar vertical dispersion on the vertical plane. This is important because the targets you are firing at are generally vertical - they rise some ways up out of the water, and your shells impact ships mostly on their sides, at a mostly horizontal angle. Rarely (and only at great range) will you be firing at a ship and actually worry about a ship's silhouette on the horizontal plane. This means that you should interpret dispersion ellipses projected on the horizontal plane with a grain of salt - they do illustrate relatively how accurate a ship might be compared to another, but not exactly how well it may perform in a game.
 * 5) * Ships with faster shells generally have to lead less and the target is offered less time to react to incoming shells. Regardless of dispersion, these ships have a much easier time actually putting their point of aim on the enemy ships - the most important factor for landing shells consistently.

Ship cross-sectional hit area
A key point to take home about understanding dispersion ellipses on popular statistics sites such as jcw780's ballistics calculator is that they are purely a convenient visual representation of how accurate a ship is in a vacuum. When you are firing at a ship, since shells generally don't have ballistics that result in impacts at greater than 45 degrees (more vertical than horizontal), the actual hitbox of a ship is specifically the cross-section of it that your shells intersect - a mostly vertical plane. A useful visualization for actually understanding dispersion ellipses is to cast a 'shadow' of the ship you are firing at against the sea, using the angle of impact of your shells. This will give you a projection of a target on the horizontal plane along with your dispersion ellipse also on the horizontal plane.

The Aiming Plane and the effect of Locking On
When you "lock on" to a ship in World of Warships, the game aids your firing and aiming in a few distinct ways:
 * 1) Your dispersion tightens to the listed maximums that are on every ship's stats sheet.
 * 2) * The reason this effect exists was stated to be to prevent mods from bypassing skills like Priority Target.
 * 3) Your camera tracks the ship you are locked on to.
 * 4) * This is an obvious aid as you no longer have to follow the ship around using your cursor as it travels across your screen, and instead you are free to use your cursor to aim at a point relative to the ship rather than at a specific point on the water.
 * 5) The game creates an "aiming plane" which is perpendicular to the terminal ballistic trajectory of your shells.
 * 6) * This primarily helps you fire at ships that are behind islands, but also is a huge aid in firing at ships that are not moving in straight lines. The jist of it is that once you are locked on to a target, your "aiming plane" is now sticky to your target, allowing you to lead ships into and out of your screen while having a primarily horizontal point of view. For example, if you are locked on to a target and are aiming fairly high and ahead of the target, your shells will still go to where your crosshair intersects the aiming plane (which is stuck to your target), rather than what your crosshair is actually looking at exactly.

Dispersion at extremely short ranges
Dispersion curve formulas are listed with a constant and a range coefficient in the chart above - battleships in particular appear to have quite a large constant in their formulas which should make them unusually inaccurate at very close range. As of patch 0.4.1, dispersion curves are ignored between 0.2km and 4km, and all ships enjoy significantly improved accuracy at these ranges.