Loyalty formula

[LDiCesare]

According to the manual,

If you place your population to the culture line, you produce culture
and every 2 culture points generate +1 region loyalty. This bonus is
capped at 1/3 of the base regional loyalty (with this value set for your
faction and by game difficulty).

However, very often, when I put pop in the culture line, that doesn't change my loyalty a iota.
I suspect this comes from the fact I have culture buildings in that province. In that case, the culture providing citizens don't add to the loyalty at all.
So either this a bug or the manual should be updated to something like:

"Every other culture point generated in a region provides +1 region loyalty (displayed as welfare in the UI) up to a cap of 1/3 of the base regional loyalty."

That would be more in line with what I see in the game and is completely different from what the manual hints at. Right now, I thought I could gain +30 loyalty out of pop but most of the time I can get nothing, which means I should reconsider most of the buildings I put in most of my core regions.

After more checking, the formula seems to be even more complex.
I have a province with culture output +19 from buildings, welfare is 24. If I put citizens for +33 culture, total 52, my welfare bonus soars to 30, which is my current cap. With one citizen (+5 culture) I go from 24 to 26 welfare (+2 for +5 culture points, ok with manual), but a second citizen brings a total of +10 culture and welfare rises to +27 only (so 10 points gave only 3 welfare). All this on balanced difficulty.

So... What are the real formulas? What does the "welfare" figure in the tooltip mean and how is it computed exactly?

[Pocus]

The culture used is close to the culture calculation for the CDR (culture decadence ratio), i.e the current culture has a weight of 50% and the average culture generated over 25 turns has also a weight of 50%.

And the cap is on any culture provided by population and buildings.

[LDiCesare]

Thank you for the explanation, Pocus.

[PJL1973]

The culture value also depends on loyalty as well (it's basically culture x loyalty per province, added up and averaged out). But in a way it doesn't really matter, all you really need to know is the trend. In other words, if you're in the lowest rung, you just need to improve your rank each turn to get you out of trouble. If you're in the middle rung, as long you stay there it's not an urgent problem. If you're in the top tier, great.

[LDiCesare]

The culture value also depends on loyalty as well (it's basically culture x loyalty per province, added up and averaged out). But in a way it doesn't really matter, all you really need to know is the trend. In other words, if you're in the lowest rung, you just need to improve your rank each turn to get you out of trouble. If you're in the middle rung, as long you stay there it's not an urgent problem. If you're in the top tier, great.

If you're decadent and loyalty is an issue, improving your rank may be impossible to achieve through buildings/assigning citizens to culture. You may be better off conquering 5 token provinces in order to get out of decadence and thereby vastly increase your culture (and loyalty). Becoming glorious is the single best boost you can get to culture and loyalty. Still, I feel that understanding the game mechanics matters a lot. Knowing that culture buildings improve your loyalty and not just the citizens, as the manual implied, is extremely interesting for example.

[Bamilus]

The culture value also depends on loyalty as well (it's basically culture x loyalty per province, added up and averaged out). But in a way it doesn't really matter, all you really need to know is the trend. In other words, if you're in the lowest rung, you just need to improve your rank each turn to get you out of trouble. If you're in the middle rung, as long you stay there it's not an urgent problem. If you're in the top tier, great.

Is this actually true? Wouldn't that be a circular formula? Culture increases loyalty and loyalty increases culture production? The manual says that loyalty over 75 increases "production" but it's not clear production of what.

Or are you specifically referring to the HCV used in the CDR formula, not the culture production? But still, Pocus mentioned culture used in the CDR formula is the one used to determine loyalty, so isn't it still circular? How is this circular formula handled, iteratively?

[loki100]

I *think* the distinction is between raw culture production which is loyalty*inputs (pop/buildings) and could feasibly be any value and the capped amount of culture (1/3 base loyalty - with this affected by more than just culture but reflecting things like pop make up, recent conquest etc) which feeds back into improving loyalty. Its possible for this second value to have no real impact if the region has a low enough base loyalty.

So yes there is a feedback up to a point but once you hit the 1/3 cap culture doesn't produce more loyalty for the region, even though you may want it to help with your position on the CDR?

[Bamilus]

I think that makes sense...so effectively it's a positive feedback loop up until you hit the cap. Meaning the HCV formula used to calculate bonus loyalty would slowly improve the bonus loyalty over time if you increase culture production and that culture production will slowly be increased over time by the resulting loyalty bonus. Confusing, but I get it now.

[LDiCesare]

I have another question.
What is the relationship between health and loyalty?
A smokehouse contributes 2 points of loyalty, but a herbalist 0. That's not written in the description, but you can find out by disabling such buildings.
Is there a list somewhere or complete description of the effects? I've looked at the csv files but couldn't find an obvious link between smokehouse and loyalty.

[loki100]

I have another question.
What is the relationship between health and loyalty?
A smokehouse contributes 2 points of loyalty, but a herbalist 0. That's not written in the description, but you can find out by disabling such buildings.
Is there a list somewhere or complete description of the effects? I've looked at the csv files but couldn't find an obvious link between smokehouse and loyalty.

I think you are reading this the wrong way around. When you disband a building there is a small loyalty hit - now the question is why this happens for the smokehouse and not the herbalist. Did you disband them in the same region? if not the effect may be relative to overall population or something, or may be related to the relative upkeep costs ... as you may gather I'm floundering a wee bit here.

what I am sure of is the direct effects of all the buildings are as listed, as the screen displays the code from the buildings database

[LDiCesare]

Yes, I'm disbanding in the same region. I'm looking for buildings to remove in order to build some better buildings after filling all the slots.

Thus I think you're correct, the good question is:
How does disbanding buildings affect loyalty, exactly?
After more testing, it looks like loyalty hit = upkeep cost of the building.

[loki100]

yes that would be my suspicion, so if you disband something with 1 or 0 upkeep it has no (or v little effect), but thereafter upkeep cost is deducted from loyalty for a few turns.