# Game engine weapon dispersion math

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As part of CfgWeapons there is a parameter governing the dispersion/muzzle spread of a weapon called dispersion which is described as "In-game weapon dispersion in radians". There is however no mention of the actual mathematical or statistical properties of how said angular deviation is applied to the projectile vector as it exits the muzzle nor can I find an authoritative reference to how value is used.

Specifically I'm looking for information on:

1. What the value represents (e.g. is it a standard deviation value, CEF, maximum value of a uniform distribution from [0, dispersion], etc)
2. What kind of statistical distribution is used to generate the 'random' variable based on the dispersion parameter (is it a uniform distribution from 0 to max dispersion, single-variate normal, bi-variate normal where the value is applied twice across two axis [e.g. azimuth and elevation], etc)

The closest thing I have found to give a clue as to how the value is used is in this line from the ACE3 mod here:

`dispersion = 0.0046; //0.279508497 = 0.25 * sqrt(0.8^-1); (80%, 5mil. https://en.wikipedia.org/wiki/GAU-8_Avenger#Accuracy) - Luke`

where a CEF 80% value has been used to calculate the standard deviation σ of a bi-variate normal (assuming uncorrelated variables with the same σ). But the relationship of the commented value σ = 0.2795... to the actual value used for the game engine is not clear, the commit that introduced the change doesn't give any hints either.

Most other posts that talk about dispersion do so in a general way without really quantifying how the value works, instead opting to experiment with the value until it roughly matches what the mod author wants.

In addition to the above, are there any other parameters that affect the shot deviation from muzzle vector within the game engine (for players, not AI) that I am unaware of? Ultimately I'm trying to develop a mathematical model of shot precision such that I can run calculations without having to run statistical simulations within the game which is both time consuming and error prone.

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best to reach out to Dedmen or ACE people on arma discord or BI discord

afaik should be gaussian random distribution

these (mostly older) threads may have some more specifics

and might be relevant too