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If you've just taken the region there's a temporary debuff (icon visible on the region screen, tooltip will tell you how long it has left) which you can't really do much about but will go away eventually. You then have the usual issues - distance from capital (reduced via Stewardship), religious differences (Piety) and cultural difference (Stewardship again). So long term you'll want to raise both piety and stewardship. Outside of that there are several buildings that give a flat loyalty bonus (predominantly in the military and stewardship trees), and some fortifications can give a boost to loyalty when built.
There's also a few RGD's that will help - Show of Authority and Religious Procession give a one time boost to Stewardship and Piety, with an ongoing bonus to production for a few turns. Grant Land can also help - the baron grants a loyalty boost, though of course you need the 'remove civilised' RGD to get rid of him once the situation has stabilised.
some of the problems may be short term - there are malus such as 'recently conquered' which are time related and possibly 'unrest' Plague and unrest in neighbouring regions are a pain too
beyond things that push down loyalty are population volume with this amplified if they are of a different religion/culture. These are variable, so for eg Shia pop in a Sunni realm are a minor problem, Sunni pop in a catholic realm are a major problem (& heretics are a pain)
On the benefits side, there are quite a lot of buidings that either lower unrest or reduce the chance of revolt.
Having said all that, local authority is a key, and that can be improved by stewardship.
But, my personal view, is you need to resolve the religion problem first. There are lots of reasons for this - see the sections in the manual - but converting them will help improve loyalty. So in this respect, yes an army helps (but may also solve the problem by killing pops), but its mainly via clergy and piety buildings. You may need to promote some catholic freemen to clergy to help (which may well demand a couple of RGD).
so its slow, and even once you have suceeded you'll find you have an unbalanced region and may need to disband buildings so you can develop commerce etc
broadly in Spain, the net effect is military victories are relatively easy, holding onto to the gains much less so
I generally leave at least 3 units in any area I just took while the main stack rolls on, but not sure exactly the interaction between troops and revolt %.
Ending the war helps, so do + loyalty buildings (always a high priority anyway, especially when its on top of other resources - love a farmers market and the town buildings), + religion if they need converting, + stewardship in the mix and I think (though don't know fir sure), things like roads and harbours may help with distance from capital.
Keeping them healthy and fed doesn't hurt either.
Restore order RGD of course - but you have to have taken over the province - holy procession, ordinate, ennoble and peasant to freedman can all help as you get the 'right' religion in my experience.
Also, don't neglect National Authority...
So everything really :D
0 - 5000 education -> 1 legacy point per turn
5001 - 15000 education -> 2 legacy points per turn
and so on
Education is the weighted average of piety and stewardship. It's skewed towards the smaller of those values. It's calculated as follows:
It is more efficient if those values are close to earch other. For example, if you have 1000 piety and 1000 stewardship, you get 1000 education:
But if you have 1900 piety and 100 stewardship (the same total) you get only 550 education:
So, if both stewardship and piety are close, you get more education for each additional point of stewardship or piety. If they are far apart, you get less education for each point.
I started a campaign with Halych, it's been really great learning the game with them, I recommend. But early on I'm trying to cut corners by taking my Priests and Nobles off of Piety and Stewardship. Correct me if I'm wrong, but the only downside to taking my Priest off Piety is the chance of Heretics, after all the National Religion is Christian and these bastards are Pagans. The risk to taking my Nobles off of Stewardship is the risk of revolts. Am I right in saying that my Priests and Nobles have such a negligible effect on legacy early on that it's not even something I should factor in and that the risk to both heresy and revolts are far more significant?
specific to nobles - watch the ratio stewardship-income, if that dips below 50% you are likely to get thieves and they tend to escalate. Clearing them out takes a few buildings that are of relatively little use for anything else.
so its not really the impact on education-legacy that matters, as you say early game that is pretty minor, its that you can end up with long term problems.
other wee bit, in the main a pop in stewardship or piety will save you more than that single building slot