Army composition at battle/siege start

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Knight at Arms
Does anyone know if things other then order in party menu are affecting how many units of given type will spawn at start of the battle if armies are bigger than battle limit?

I recently fought in siege (2300 my army vs 1100 defenders) and no archers spawned for me, only infantry.

If only the party menu order is taken into account it should change.

I think that army composition in field battle should be calculated by how much % specific group is in whole army. For example:
1000 man army
700 infantry
200 ranged
100 Cavalry

500 spawns into battlefield. They should be chosen by calculation like this:

x - number of units from specific group in army
y - total number of units in army
z - total number of units spawned in battlefield (for one side)

Calculation: x * z / y

In the example this calculation gives us:

350 infantry
100 ranged
50 cav

With this we have some part of every type of unit with us and no situation like You spawn 500 recruits while the enemy 200 archers. It could be done on combination of tier and group to calculate exactly how many units of given type and tier should spawn.
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