This article will try to debunk the commonly used terms of Dispersion & Sigma to describe a ships accuracy. While the World of Warships Wiki actually does a great job at describing these two terms in depth (Check it out here), I want to try and make it a little easier to understand as well as ‘correct’ a few terms that are used as well as provide some clarification.

### Dispersion

In short, dispersion is the value used to describe the horizontal (and vertical – though the only value listed in port is horizontal) distance in which shells are expected to disperse at a range. The value in port represents the maximum horizontal dispersion for the maximum range of the ship. An example of this is the Montana has a maximum dispersion of 296m at 23.65km. So in this instance, when you fire your Montana shells at a broadside target locked (very important) ship at max range, the left most shell and the right most shell will be, at max, 296m apart.1 This does not mean that there will always be a horizontal spread that large, just that it can and certainly will happen.

The vertical values, how far apart the shells that land short and long are, are not published by WarGaming. While sites like https://gamemodels3d.com/games/worldofwarships do have a value published here, no measurement unit is given and since the value given for horizontal dispersion is not that given in game, I cannot give any other information on it.

### Sigma

This term describes the tendency of the shells to group towards the center, or your point of aim. The World of Warships Wiki states that this distribution of shells is Gaussian or a ‘Normal’ distribution – think bell curve. In game, a ship with a sigma of 1.7 will have a less dense clustering of shells near the point of aim than a ship with a sigma of 2.0. For those that shoot, think of a gun with a 1 MOA accuracy versus a .5 MOA accuracy. While both can put a shot in the bullseye, the .5 MOA gun will have a tighter group of 5 shots at the same distance compared to the 1 MOA gun. In short, sigma is just a fancy word for consistency.

### My Issues with the Wiki Page

Warning: This section will be on the more technical side. If you’ve made it this far and don’t want to read the ‘boring’ technical stuff, continue to the conclusion.

For you brave folk, my issues will be addressed in the order that they appear in the article. My first issue came with the following statement:

The in-port value describes dispersion in terms of one probable error, i.e. it gives a value where 50% of the fired shells will land around the point of aim.

https://wiki.wargaming.net/en/Ship:Gunnery_and_Aiming

Statistically, this statement means that – given that the distribution is considered normal – 50% of shells will land on target with the other 50% splitting to either side of that. This is actually incorrect. What it should say is that 68.2% of the shells will land around the point of aim (1 standard deviation on either side – FYI – in statistics a standard deviation is often noted as σ or sigma). Further, in a normal distribution, the 50% value denotes that 50% of all shells, in this case, land to the left of the point of aim, while the other 50% land to the right.

The next issue I have with the Wiki article is with the scatter graph and bar graph showing the horizontal distribution of a Fuzo’s [sic] shells landing at max range. With the information that is presented in those two infographics, it shows that the maximum horizontal dispersion of the Fuso is not the 226m that is stated by WarGaming, but rather, something that is closer to 900m.

Both this issue, and the previous issue that I have, when taken apart and reassembled, actually means that, if the first statement is true and the data for Fuso was compiled, plotted and analyzed correctly, the term Maximum Distribution used by the game is a lie. What it really means, based on the above information is that at least half of all shells will land within an ellipse that has a minor axis length (based on the dispersion ellipse infographic- https://wiki.gcdn.co/images/thumb/3/3b/ShipDispersion.jpg/700px-ShipDispersion.jpg) of 226m. That still means that half of all shots will whiff outside of that. In terms of a Fuso on Fuso shoot out at max range, that means that less than half of your shells (Fuso’s historical length is 205.13m) will land within the length of the ship. Further, given that the findings were that the max distribution value is equal to 1 standard deviation, we can determine that only 38.2% of shells will fall within that horizontal value, NOT 50%.

This brings up a lot more questions than answers in the grand scheme of things in regards to stated dispersion of ships and what it truly means. For now though, I’ll leave said what as been said and continue.

The final issue I have with the wiki article is probably the simplest. In the dispersion graph depicting the growth of the maximum dispersion of ships as range increased, it is stated that these are curves. Not only are they clearly lines, but the formulas that follow are clearly those of lines and not curves (with curves, you would expect to see an exponent on one of the values, in this case, likely R).

### Conclusion

Overall, I hope this clears up dispersion and sigma for most of you – those that only read the first few sections. There are a lot of mechanics in this game, all of which make it unique, some of which make it frustrating, and I hope to educate as many as are interested in nuances that make this game so dynamic. So I hope you are one step closed to being more informed. For the rest, particularly those that read the previous section, I’d be happy to answer and questions or comments posted either here or on my Discord server.

#### References

1. A detailed breakdown of actual data collected by players disproves this statement, but that has yet to be verified.

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