Too long didn't read version is more successful missions you do in a region, the more advent reinforces it. And they reinforce strength from UFOs on a regular basis (with possibility of emergency reinforcement) hidden behind the scenes which is why you can't avoid regions of high advent strength. That's actually all you really need to know about it. The details are fascinating but you don't have much control over it.
There are three scores we need to talk about here to get a basic grip on the world map, "vigilance," "alert" (same thing as advent strength), and "force level."
1. Each region has a hidden "vigilance" score which is a reflection about how concerned Advent is about you. Every time you win a mission in a region, vigilance goes up by 1 point. There are some types of missions (supply raids, troop ambush, retaliations) which are modified to additionally give vigilance -1, or in other words if you do those specific missions, the net result is vigilance doesn't go up (this is prevent you getting into an overly vicious cycle of high vigilance retal over and over and over simply from winning retaliations, although you can easily still get into this cycle anyways if advent strength is high enough and you give them enough time to find your haven).
Vigilance is local per region, and naturally fades by 1 point per week. It also goes down by 2 points if you lose/skip a mini-retal mission, and 4 points if you lose/skip a full retaliation.
If the vigilance score (mind you, you can't see this anywhere, you only have a guess based on missions you are doing) > advent strength, then advent will do things to try to reinforce the area, by either transferring advent strength from a neighboring region, or reinforcing from off world (UFO comes to reinforce the region).
If vigilance score <= advent strength, they will do nothing special with respect to transferring reinforcements, but it doesn't imply that they will suddenly leave the region or go down on advent strength. It is a mistake to hope that by hiding rebels in a region that advent strength will go down.
There are other ways to mess with vigilance, one is the sabotage statue mission I don't remember how many points it goes up by, but it raises more vigilance than a normal mission would.
2. Advent strength is a score you can see on the map/haven resistance management screen which is a reflection of how strong their actual presence is. This affects the number of aliens you see on missions in that region, but not the type (aka now matter how high you jack up advent strength, you won't see a sectopod on month 2).
Advent strength can be modified in a number of ways, but I want to say right here before you get your hopes up - you CANNOT win this game by depleting global advent strength. It is impossible, especially on higher difficulties. This is because there are limited ways to reduce it, and they are secretly reinforcing on a regular schedule all the time that exceeds your ability to reduce it. So get the silly idea out of your head. I know this is why you asked the strategy board question to begin with, to see if there is some way to game the system and tame them at advent strength level 1. You can't, sorry. You're going to be facing a lot of hot regions especially on higher difficulties, end of the story.
With that being said, advent strength can go down by
a) you doing supply raids. This means they are transferring in strength from an adjacent region. These are very hard to detect, and please stop complaining it's a bug you don't see them. They are literally very hard to detect: they are are 10 times harder to detect than a lib 1 mission, and have a lower duration than a lib1 mission. It is coded as rare into the game. They are also on a cooldown.
b) troop column ambushes. Not that hard to detect, but they are on a cooldown, they reduce alert level by 1 in the region you do them in.
c) you liberate a region. This destroys up to 5 alert levels in the region, but any excess gets spread to other advent regions (not sure how this is decided, whether randomly or to weakest I dunno)
d) you doing UFO raids, similar to supply raid it's the equivalent of them reinforcing by magic (they have limitless troops offworld, and every so often they send new troops to earth, this is why you can't ever get rid of alert for good)
Advent strength (alert) goes up by
a) them reinforcing from adjacent areas. Thus an area will lose one point, and give that point to its neighbor.
b) regularly schedule UFO (offworld reinforcements). It is possible to catch UFOS in missions (it is a 2 chain misison, with the first being "find a lead" which immediately gives you a UFO raid, these are tough.)
c) emergency UFO reinforcements. These are on a higher cooldown than the regular offworld reinforcements, but if you are really making advent mad and wondering where the strength is coming from, these are an additional source of them
d) certain missions have hidden alert modifiers like lib2 and up, so those missions are acting as +2/+3 strength above what you see in the region
e) I think there's one or two dark events that jack up the alert levels in certain regions, I forget which
3. "force level" is a global, hidden score that goes up every 16 days by 1 point. It governs the type of aliens you can see. I don't think there's any way to stop this from happening, even though in the code it's listed as a UFO bringing it in, I think that's just like...thematic dressing, it's not that you can find a force UFO and kill it.
I'll show a bit of ini code below
[LW_Overhaul.X2LWActivityCooldown_UFO]
; How many DAYS between UFOs that level-up aliens worldwide.
+FORCE_UFO_COOLDOWN_DAYS[0]=16
+FORCE_UFO_COOLDOWN_DAYS[1]=16
+FORCE_UFO_COOLDOWN_DAYS[2]=16
+FORCE_UFO_COOLDOWN_DAYS[3]=16
; How many DAYS between UFOs that increase alert levels in a series of adjacent territories. Pretty big difficulty lever here.
+ALERT_UFO_COOLDOWN_DAYS[0]=14
+ALERT_UFO_COOLDOWN_DAYS[1]=12
+ALERT_UFO_COOLDOWN_DAYS[2]=10
+ALERT_UFO_COOLDOWN_DAYS[3]=8
So you see, force ufos just represent a steady increase in quality of aliens over time, and the alert/strength ufos are secretly bringing up the advent strength in multiple territories without you knowing about it for the most part (although again, you CAN raid alert ufos with enough intel, it's just hard and they are happening all the time).
To add a little bit more wrench in all of this, pavonis actually coded in a little bit of randomness in areas you haven't contacted
; Repression works only in uncontacted regions; it is simulating the Resistance without XCOM's assistance. It rolls several d100s once the cooldown is over.
REPRESSION_REGIONAL_COOLDOWN_HOURS_MIN=336
REPRESSION_REGIONAL_COOLDOWN_HOURS_MAX=504
REPRESSION_ADVENT_LOSS_CHANCE=2 ; -1 Alert, +1 Vig
REPRESSION_RECRUIT_REBEL_CHANCE=15 ; +1 rebel
REPRESSION_VIGILANCE_INCREASE_CHANCE=25 ; +1 vig
REPRESSION_REBEL_LOST_CHANCE=10 ; -1 nonfaceless rebel, min of 1
REPRESSION_CLONES_RELEASED_CHANCE=0 ; +1 alert
REPRESSION_2ND_REBEL_LOST_CHANCE=10 ; -1 nonfaceless rebel, min of 1
I don't really care to guess at the details here but the point is advent strength/vigilance is fluctuating in non-contacted regions according to some simulated rules.
4. Although not directly related to the above 3 scores, you should know that advent has some direct counterattacks to your activities called "retaliations." There are "mini-retaliations" and regular "retaliations." These are annoying missions that offer no reward except to not lose your ability to do rebel jobs in that region. (well some minor experience/loot). They trigger based on how many active rebels you have in a haven. Unfortunately even though I have done some code diving and found some hard numbers for the limits, people have reported that they can still get retaliated while below the limit. This may have to do with faceless secretly lowering the limit, or other factors I can't get at just by looking at ini files. The variable they have in the ini file for "mini-retals" is 6 working rebels on a particular job, so theoretically you can use say 5 intel rebels and not get miniretals, although there is player experience to the contrary. Maybe the true limit depends on faceless. The variable they have in the ini files for the regular retals is 5 working rebels of any type.
Having read the journal of a guy who beat ironman/legendary LW2, he kept his working rebels at 4 supplies for most regions, hid the rest, and never got any retals in those regions. So maybe 4 working rebels is what to shoot for if you hate retaliations.
At the end of the day I don't think it's worth studying "the board game" because there simply isn't much you can do about it. Your decisions boil down to can you handle advent strength in a given region, if not, then do missions elsewhere. You expand when you can afford it, but not willy-nilly: you try to get to the avatar objectives. If you are offered the chance to do raids/troop ambushes you take them as you are able. It's a pretty simple decision making process. Knowing about the AI reinforcing doesn't do you much good in this game, because you don't have much ability to react to it. Your decisions are either do I take this mission or not.
As a fun note, if you liberate 16/16 regions, advent invades all 16 regions simultaneously, which drives home the point that you shouldn't be trying to game the alert/chessboard aspect. You should be aiming to get just enough men well enough equipped to zip in and close down the avatar project. If you read the comments of this player who did legend/ironman LW2, you can see his success doesn't have much if anything to do with the chessboard; he only lilberates 1 region the entire game, and keeps 4 rebels on supplies in most regions to avoid annoying retaliation missions.
https://www.reddit.com/r/Xcom/comments/ ... n_writeup/
You will see that he only liberates 1 region in the entire game, and the only way he "plays chess" is to put 4 rebels on supplies rest hide in most regions in order to avoid retaliations. He skips tons of missions, is only able to afford gear to equip one team well, and he aims to end the avatar project instead of liberating many regions/toy with advent strength.