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While the game shows percentages, it doesn't *really* work on actual percentage hit/miss rolls. It does some semi-complicated dispersion modelling and the worse you roll, the more dispersion the round has.
I believe that everything always shoots at center of mass. Imagine the rolls dictate that a shot goes a little high and a standing guy would take a plasma bolt to the face. Well, that same shot would pass right over a crouching guy.
Again though, this is a small chance sort of thing. Really just an edge case.
You need to remember that XCOM is a running a voxel engine with what you see being an abstracted isometric overview. When you shoot at something your weapon fires projectiles in a cone based on your accuracy. There's no rolling for hit or miss - you are rolling for a trajectory. Crouching only helps in the edge cases where the bullet was going to barely hit the top of your voxel but won't because you are now a bit shorter.
Its real benefit is for breaking enemy LOS since they can't fire at what they can't see*
*except for certain mods utilizing OXCE enhancements.
And is the enemy's LOS view reduced by distance? I know they can see up to 20 blocks and can have their vision impaired by smoke (all depending what smoke and where the smoke is, etc.), but does crouching reduce that sight number?
(I only ask all this 'cause I've seen you guys breaking stuff down here in the discussions based on the reverse engineering done, and I can't find the data on it myself.)
No, it doesn't.
I only ever crouch these days in mods where there is a substantial bonus to aim associated with it. Or in situations where I can shoot from beyond enemy LOS since the accuracy bonus is also not worth the 12 TU cost.
Crouching has no affect on alien view distance, other than the times when it could remove you from view completely due to sight lines.
Oh, btw, you can find a bunch of mechanical information buried in the articles on this page -
https://www.ufopaedia.org/
Knowledge is power, Commander.
Crouch is a very useful strategic tool, but you have to know how to use it; but if you're asking about it like this, then you're probably not at that level. Figure out how to minimize being seen first.
Beyond that, crouching probably makes a bigger difference on skilled soldiers: those with the TUs to afford it, and the skill to reduce the cost of each shot. Things you can't apply to the Bravery 10 meatshields you pick up.
Generally speaking, you should never move (except out of view), fire, or crouch someone who is in view of an enemy. That can draw reaction fire.
If I'm planning on holding a position for a few turns, then crouching makes sense. Every little bit helps. Otherwise, I've found it better to stay mobile and just stand.
Also, there is a LOS consideration. There are times I could see an enemy standing, and when I crouch, the enemy is no longer in LOS. It stands to reason that ducking behind concealment also removes you from their LOS.