[Mass Combat] Discipline, Law, Order and Preventing Atrocities

[Icelander]

A PC is acting as the overall commander of an army of around 3,500 men and some 1,500 sailors serving on land. I've been using Mass Combat rules at least to benchmark things, though I usually make things more complicated and call for rolls against many more skills, all the way down the chain of command.*

As the PC-Affiliated Forces (PCAF) are liberating territory that the polity they are fighting for can make a historical political claim to rule and the cities they take are meant to become part of the new country they are building, it has been decided to keep the men under tight discipline around civilians, judiciously enforce law and order** and prevent atrocities as much as possible.

I'm looking for good guidelines on how difficult this is. How much of your force needs to be devoted to non-combat shore patrol, traffic control and law enforcement to make rapes and murders statistical outliers rather than the expected activity of a conquering army?

What kind of Administration, Law, Leadership, Propaganda, etc. checks are involved? What skill takes the place of Tactics or Operations for planning military police operations that are ultimately meant to protect both your own troops and the civilian populace?

Usually I guesstimate this sort of thing and it doesn't harm anyone, as long as I personally find it plausible. For this question, however, I'm lacking a fundamental basis for guesstimates, which is that I don't really have a good intuitive sense for what percentage of military personnel in a low TL army will attempt to rape and murder civilians when given an opportunity?

I'd like to have some kind rule of thumb that used Troop Quality as a benchmark for levels of discpline for individual units, which would have a huge impact on this number. I'd modify it by situation, morale, leadership, opportunity, weather, enemy activity, etc. Obviously, unhappy, frightened and poorly led troops with little to do but face unpredictable attacks by partisans that are almost indisguisable from other civilians will be far more likely to commit crimes against the local populace than highly motivated troops competently led and kept busy out-maneuevering an enemy army in the field.

I also imagine that factors like Disloyal, Fanatic, Impetuous and other such modifiers can have a strong impact. To take a random example, I imagine Fanatics are less likely to run riot out of greed, lust or frustration, but more likely to have religious or ethnic hatred that lead them to commit atrocities. And both Levies and Mercenaries might be more prone to looting, which often leads to worse atrocities, than troops who chose a military life and specifically chose an organisation where they are expected to show loyalty beyond a desire to secure the next pay packet. And so on.

On the other hand, I can't apply any of the ad hoc modifiers to the percentage of troops who are risk factors without having some basic idea of what that percentage should be.

How many in an Average Troop Quality unit of TL 2-4 soldiers will seize upon a chance to rob, rape or murder one or more civilians during an assault on a city that was held by the enemy?

*Often limiting the skill of the character with supreme command over logistics, intelligence or operational planning by using an average of effective skill levels for his staff and the officers in charge of units.
**At the very least, a rough approximation of it that allows civilians to trade with the invading soldiers without being raped, tortured and murdered.