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Building tall
This approach involves personally owning as many holdings as possible in your capital county/duchy.
Depending on your rank and whether or not you're an independent ruler, your capital duchy gets a bonus to levy size and your capital province gets an even larger bonus. Your concillors also get missions that you can assign them in order to boost a province's taxes or levy size.
Imagine that you send your steward to boost taxes for 50% and your marshal to boost levy size for 50%. If you only had 1 castle in that province, you might get an extra 10 gold per year and 500 max levy. But if you had 4 castles in that province, you would get an extra 40 gold per year and 2k max levy.
All those troops would also be affected by your capital's tech, which is undoubtedly higher than other provinces in your realm.
Building wide
This approach involves owning as many provinces as possible.
Basically, the more provinces you own, the more barons you have as direct vassals. The way vassalage works is that a vassal supports his/her liege with a portion of his/her taxes and levy. Let's say that everyone gets taxed 20% of their income and troops by their liege.
Imagine that all barons have 10 gold income and 500 troops. So each baron gives their count 2 gold and 100 troops. If you are the owner of the province, you get all of that.
However, if the owner of the province is a count that's your direct vassal, then you get only 20% of what he gets, which would mean you get 0.4 gold and 20 troops from each of those barons. But what if the owner of the province is not your direct vassal?
If that count is under a duke, then that duke gets 0.4 gold and 20 troops from each of those barons. But as for you, as the king you only get 20% of what your duke gets, which means you get 0.08 gold and 4 troops from each of those barons.
And if you're an emperor, a vassal baron under a vassal count under a vassal duke under a king that's your direct vassal only provides you with 0.016 gold and 0.8 troops...
Each level of vassalage means an extreme reduction in the amount of taxes and levies you get. So it's in your best interest to own as many provinces as possible to have as many barons directly answering to you as possible.
Which is better?
I'm not sure, there are pros and cons to each. I personally prefer building tall.
If a building upgrade says that it adds 40 pikemen, then the garrison increases by exactly 40 pikemen. As for the levy size, if the owner has 10 martial and no other bonuses are applied, then exactly 40 pikemen are added to the levy. If the owner has 20 martial, then 60 pikemen are added to the levy. If the owner has 0 martial, then only 20 pikemen are added. Each point in martial is a 5% change.
As such retinues are always on the map, which costs maintenance. Recruiting them also costs gold & takes some time. To start with (assumming you start small, very sensible while learning the game IMO) you can't use them or at least not get a reasonable number of them. The number you can raise depends on number of holdings, tech, various buildings, etc but basically early game ignore them, late game they will be a major part of your army or even most of it.
There's a whole bunch of advice on which retinues to recruit and how to use them but if you are not at that point yet I wouldn't worry about it for now. ^^
You can do both; directly owning a few heavily upgraded counties (TALL) at the heart of a massave Empire (WIDE). Additionally if you upgrade the buildings in your vassal's counties, or build new settlements in said counties, then you can increase the amount of troops and wealth those produce (as well as the amount you recieve).
thanks guys
At the start you should mostly focus on numbers (light infantry is best for that) to deter factions and speed up sieges. Later in the game when your retinue cap gets bigger and bigger you can have 10K+ heavy troops and so they become very useful.
I usually don't have them join my armies b/c then losses are spread across the entire group and I would rather the losses be concentrated on the mercs since I'm paying the most for them.
If you have 5000 in levies, the AI needs 5000+ before they feel willing to enforce their faction demands, and often you can easily pick them off because the faction members are usually spread across the country, rather than just being a single blob. As a result, you can just bonk their armies on the head one-by-one rather than facing a large mass of foes.