Free Supply

[bs_grom]

How do free supply buildings work?
My army with food usage 8 ate 8 food.
When I built a Roman Camp building with 10 free supply it caused it to eat 4 food.

[Pocus]

That's because food and supply are not equivalent, there is a conversion ratio, 1 food provides 5 supply. Check your national panel, in the summed traits section you might have a different ratio.
Be sure also to check that you speak of food and not supplies, or the reverse, I believe the tooltip on units is about supplies, not food.

[bs_grom]

I ran some tests playing Romans on suicide difficulty. Romans because legionary units can build Roman Camp. I also checked armies with different food usage values and I am 99% sure that armies consume exactly as much food as the food usage value of the army. The armies were stationed in regions that did not form provinces to count. I set the food growth so that the growth was zero. Every time an army had food usage 8/7 the region would lose 8/7 food. When the army was stationed in a region with Roman Camp, it consumed 6/5 food respectively and when it was in a region with Preserved Foodstore, it consumed 4/3. I haven't checked the Logistics Depot building, but based on these two buildings, I put forward a thesis that the Supply value from these Roman Camp 10 and Preserved Foodstore 20 buildings, when divided by 5, gives 2 and 4, respectively, i.e. as many p as less food armies used. Exactly as it should be for the supply value, i.e. one Food equals 5 Supply. However, the army eats food of normal value, i.e. if food usage 8, it will eat 8 food in the region where it is stationed. If the assumption was that the army should be the value as in the supply of buildings, then the value of the supply of buildings should be increased 5 times to match the value of the supply usage of the army. And ideally, it would also display the value in food and not in supply because it's confusing. At the moment, knowing how supply buildings work, I don't know if they are profitable, I'd have to think about it, but it seems quickly that a building that gives food is much more profitable because it is cheaper and gives more food all the time, supply only works when there is an army and has little value less than any even the cheapest building with food.
I also renew the request for the return of bonuses to the Supply usage of steppe, forest and mountain desert units so that their food consumption in these areas is lower because the barbarians need it especially at the beginning when their provinces have one population.

[Mevelios]

If the assumption was that the army should be the value as in the supply of buildings, then the value of the supply of buildings should be increased 5 times to match the value of the supply usage of the army.

There's no such assumption there though, right? The preserved foodstore is indeed worth only four food for armies, you can't station a large number of squads in low food regions. It's good at making money if you need some desperately; it's handy in desertic or arid regions (unless the qanat is amongst your available buildings), yet you could argue since there's nothing else to build, hard to ignore it.

A simple orchard is more valuable in feeding your standing armies in every way, even if you have to build a delicacy shop to force the import of one of its related bonuses. The real exception is during sieges since free supply doesn't suffer from the besieged malus; still I only resort to such buildings in desertic or arid areas. BTW, got a doubt there: is free supply shared between neighbouring regions (in the case you'd be invading a neighbour), or provinces (when armies are stationed in times of peace)?

Unless I'm mistaking it for something else, army logistic bonuses are what you're looking for to lower your armies' consumption. Military expertise can provide one (was it starting 6 or 8 ratio?), otherwise your ruler starting the very good military (rating displayed as double +) or with the logistician trait (the anvil icon IIRC).

And ideally, it would also display the value in food and not in supply because it's confusing.

I'd turn it around; the display of the value in food is misleading when you're slightly over the given value (6 supply or 1.20 food consumption gets rounded down), ending up in supply shortage for drawn-out sieges or recently conquered/low production regions. Otherwise I've had several supply shortages for which I can't pinpoint the cause - and it's unrelated to a bad foraging roll!