The Priest links theirself to a single ally they have a clear line of fire to using one action point; this does not necessarily end their turn. The ally gains +1 Mobility, +10 Aim, +25 crit chance, and 4 ablative HP, but if the Priest dies the beneficiary also dies. The Priest can only maintain one Holy Warrior boost at a time, and the link is non-lethally broken if either individual is put into Stasis for any reason. 1 turn cooldown.
Holy Warrior
The Priest links theirself to a single ally they have a clear line of fire to using one action point; this does not necessarily end their turn. The ally gains +2 Mobility, +10 Aim, +25 crit chance, and 6 ablative HP, but if the Priest dies the beneficiary also dies. The Priest can only maintain one Holy Warrior boost at a time, and the link is non-lethally broken if either individual is put into Stasis for any reason. 1 turn cooldown.
Slightly more Mobility and slightly more ablative HP, but otherwise the same as with basic Priests. The primary difference with Advanced Priests is actually...
Sustain
The first time the soldier should have died in a mission, they instead enter Stasis with 1 HP remaining. This Stasis ends at the start of their team's next turn. Each individual Priest has only a 50% chance of actually having Sustain.
... that Sustain is vastly more common on Advanced Priests. With Basic Priests, Holy Warrior is usually to your benefit. With Advanced Priests, you should basically assume Holy Warrior won't result in a double-kill, because a coin-flip isn't anything to plan around. Sustain triggering will still wipe the boosts, so if you're going to go for a kill on the Priest you should ideally do that before delivering damage to their beneficiary, but still.
Also, I mentioned in the Faceless post that beginning-of-turn resolution is handled inconsistently by the game. This same issue applies to the Stasis from Sustain ending, and in this case it's a much more frustrating, janky issue, in that usually an ADVENT Priest who triggers Sustain is guaranteed to get a chance to act, with the only surefire ways of preventing them from doing something being Templar with Bladestorm standing next to them, a Bladestorm Ranger carrying the Katana standing next to them, or, assuming no other enemies are in the area or stumble into the area first, a Covering Fire soldier on Overwatch and equipped with a Stock so even a miss will do damage and thus finish them...
... but sometimes the game will decide that the Sustain-derived Stasis should end and then Poison, Acid, or Burn should do damage, and voila! The Priest is dead with no chance to act!
As such, afflicting Priests of any tier with Poison or Acid is a surprisingly good idea, even if the absolute best-case scenario is fairly rare. (You generally don't want to Burn a Priest: they'll be stuck with no choice but to take a shot at your soldiers, and the vast majority of the time you'd rather they use one of their special abilities)
Mostly, though, once Advanced Priests are a thing you should plan around assuming you can't kill them in one turn without Overwatch or Bladestorm support.
Additionally, Advanced Priests have picked up a new trick...
Mind Control
Attempts to take control of a single biological enemy for 2 turns: this takes the Priest's Psi stat+50 and subtracts the target's Will to determine the chance to succeed. The Priest cannot initiate Mind Control if they have a Holy Warrior link and vice-versa, and the Mind Control is lost if either unit is put into Stasis for any reason. 2 turn cooldown.
...Mind Control.
Weirdly enough, gaining Mind Control doesn't actually do a lot to make Advanced Priests more threatening. Their Psi score is low enough that it doesn't actually succeed very often (It will generally be about a coin flip chance to succeed), and indeed you should worry about Mind Control from Sectoids if you're going to worry about it at all. It does at least mean they're less prone to giving you a free double-kill -they much prefer wasted attempts at Mind Control to using Holy Warrior- but overall they're... actually a bit easier than basic Priests, relative to other enemies in their respective tiers. You fight them basically the same, as well. Indeed, since Mind Control is so prone to failure, any temptation you might have to slap Mind Shields onto people in response to Priests being on the field is dubious to give into: that Item slot would probably be better served being filled by something more relevantly helpful.
... even considering Priests are utterly oblivious to Mind Shields and will happily waste a turn trying to Mind Control an immune individual.

That said, Advanced Priests picking up Mind Control is one of the more reliably relevant reasons to pursue Bond Level 2, so you can use Stand By Me to neuter it. The Warlock is unreliable in showing up early (Though of course if your run rolled him as your first Chosen you should prioritize anti-Mind Control tools heavily), and while Sectoids going for the Mindspin are a lot more likely to get a successful Mind Control than Advanced Priests, Sectoids tend to get distracted by Psi Zombie potential and if you've got Rangers or Templar about are much easier to kill than an Advanced Priest. Advanced Priests, meanwhile, rate Mind Control as their preferred action by a wide margin: they're willing to do other things first, but usually their first turn will be spent on a Mind Control attempt. They prioritize this enough they'll often ignore the option to shoot people in the open! (Where Sectoids will almost always take a shot if they start a turn with a clear shot from their current position) As such, while an Advanced Priest will succeed in Mind Control less often than a Sectoid, they'll try more often, generally putting them ahead in successful Mind Controls in practice.
Overall, Advanced Priests popping in are still generally a relief compared to Advanced Officers doing so, though. They far prefer to use their abilities over shooting, and none of their abilities will cause your troops long-term problems the way being shot does. Mind Control is easily canceled by attacking them, even if Sustain triggers, and Holy Warrior potentially giving you a double-kill can easily take a tough situation and make it far easier to untangle, as opposed to Mark Target on Officers very possibly leading to a bunch of extra-accurate shots taken at your squad before you get a chance to do anything.
Also worth noting is that pod leaders always going before their podmates opens up the potential for completely wasted Holy Warriors once Priests are allowed to follow around other pod leaders, where the Priest goes last, puts up Holy Warrior, and then you just shoot the Priest until they die or Sustain triggers. Whoops!
Elite
HP: 13/16/18/18
Armor: 0
Defense: 0/10/15/15
Dodge: 15/20/20/25
Aim: 75/75/80/80
Mobility: 12 (8/16)
Damage: 5-6 (+2)
Shred: 0
Crit Chance: 0/0/10%/10%
Will: 75
Psi: 40
Tech: 125
Yes, even the Elite Priest has a measly 40 Psi. Unless you're playing on Rookie, Sectoids are always going to be the more reliably relevant psionic threat, all the way into the endgame.
Stasis
Stuns a target enemy, but also makes it immune to all effects until the user's team's next turn. 2 turn cooldown, always ends the turn.
Strictly speaking Elite Priests could be compared to Advanced Priests in terms of Stasis having not improved while Holy Warrior and Sustain have gotten improved, but by the time Elite Priests are around it's generally too easy to punish/cancel out Mind Control and Holy Warrior before they can really threaten you, whereas Stasis can end up taking out of action a key squad member with absolutely nothing you can do about it. Maybe you were planning on your Darkclaw-equipped Sharpshooter spamming Bluescreen Rounds-backed shots at a Sectopod to trivialize it, and whoops that soldier got Stasised and the rest of your squad happens to be ill-equipped to take out a Sectopod and you're thus in actual trouble!
That specific example is a bit of a rarity, but the point is that Elite Priests tossing out a Stasis can irrevocably ruin your plans with no way to respond, just suck it up and cope with being down a soldier for a turn, where their other possible actions can be undone/made to backfire, or are just straight damage attempts that are only going to kill someone if they're already injured or other enemies get in damage. (ie the Priest shooting someone) This applied to every tier of Priest, but it's overall most relevant to Elite Priests in practice, given how progression works: among other points, if you don't have tools for dealing with Mind Control by the time Elite Priests show up, it more or less has to be a deliberate choice to neglect Bonds, Mind Shields, Psi Operatives, Flashbangs... where for Advanced Priests you might genuinely spend a bit unable to arrange anti-Mind Control tools beyond 'kill the Priest'.
The example I used also touches on unique gear, and that's very relevant: if you bring two Rangers into a fight in the midgame, very possibly they can both carry out the same duties, where one being Stasised is a minor thing. In the late game, only one of them is going to be carrying the Katana, and if that one ends up Stasised the other Ranger can't take up the slack if you needed perfectly accurate Slashes and/or Armor-piercing Slashes.
They're still willing to use Stasis in incredibly bad ways, of course, but with Elite Priests I genuinely dread the possibility of them using Stasis on the exact right soldier, where for earlier Priests it's usually a mild relief to see Stasis starting, because the worst-case scenarios can be really bad, and are overall a lot more likely to occur, since squad members are so powerful, the game is balanced around their power, and they're not interchangeable in their power. That is, a Katana-equipped Bladestorm Ranger is a terror, and a Darkclaw-equipped Sharpshooter with maximum Pistol skills is also a terror, but they solve different kinds of problems, and if I need them both to disentangle the current situation, then having either be hit by Stasis is a serious problem!
Whereas early in the game there's a large extent to which most problems are solved about as well by any class, with exact gear differences being minimal and not very important to boot.
Holy Warrior
The Priest links theirself to a single ally they have a clear line of fire to using one action point; this does not necessarily end their turn. The ally gains +3 Mobility, +15 Aim, +25 crit chance, and 8 ablative HP, but if the Priest dies the beneficiary also dies. The Priest can only maintain one Holy Warrior boost at a time, and the link is non-lethally broken if either individual is put into Stasis for any reason. 1 turn cooldown.
Another point of Mobility, another couple points of ablative HP, and 5 more points of Aim.
+15 Aim is still low enough the vast majority of enemies can't hit 100% accuracy without flanking a target from high ground, which is more of that frustrating "the RNG can always choose to save you from yourself even when you screwed up" design I've touched on before. Admittedly, there's at least the potential for it to end up combined with an Officer's Mark Target?
Ah well. I do at least appreciate an attempt to have a special ability tier with unit quality. I haven't complained about how eg Officers Marking a Target never gets any better, but this is a bit of an issue with some of the units that tier up, where an ability doesn't scale at all, or scales very mildly. Holy Warrior doesn't scale enough, I feel, but it certainly scales more than some of these.
Sustain
The first time the soldier should have died in a mission, they instead enter Stasis with 1 HP remaining. This Stasis ends at the start of their team's next turn. Each individual Priest has only a 66% chance of actually having Sustain.
By the time Elite Priests are running around, you may well have the Katana, making it much less of a pain to deal with Sustaining Priests. Just drop your Bladestorm Ranger carrying a Katana next to them if they trigger Sustain, and it's more or less guaranteed they'll die without acting.
I'm not sure how I feel about Elite Priests having high enough odds on rolling Sustain the expected result of any given Priest kill is Sustain triggering, but not actually bumping them up to 100%. On the one hand, Elite Priests being guaranteed to trigger Sustain would be incredibly frustrating. On the other hand, you still basically have to play as if every Elite Priest has Sustain, and will just be pleasantly surprised roughly 1/3rd of the time, which feels a bit too much like the 'enemies can virtually always miss even when you screwed up and 100% deserve to be shot' design I flatly do not like.
To be fair, Advanced Priests being coin-flip odds had a rather similar outcome...
... but if Elite Priests were 100% Sustain, I'd just read the prior tiers as operating on chance mechanics so Sustain is scaling in some sense with tier. Can't start from Sustain always triggering and go up from there, except in a few pretty obviously dumb ways like letting it trigger multiple times.
And I've never been able to think of a design benefit to Sustain always being a chance, never a guarantee.
It's possible there's a subtle benefit I haven't explicitly thought up, though. War of the Chosen is good enough about that I hate to discount the possibility.
Mind Control
Attempts to take control of a single biological enemy for two turns: this takes the Priest's Psi stat+50 and subtracts the target's Will to determine the chance to succeed. The Priest cannot initiate Mind Control if they have a Holy Warrior link and vice-versa, and the Mind Control is lost if either unit is put into Stasis for any reason. 2 turn cooldown.
As Elite Priests still have the same Psi score as Advanced Priests, their Mind Control is only better inasmuch as they are tougher targets, making it more likely that shooting them to cancel it will be a risky option. Indeed, while War of the Chosen eliminates guaranteed Will boosts from progressing, you'll on average be less likely to be hit successfully by a Mind Control from an Elite Priest than an Advanced Priest in practice due to Will boosts from Covert Ops and the increasing probability of Focus PCSes ending up passed out to some of your soldiers.
I'm not sure why they didn't get a 10 or 20 point boost to their Psi score, honestly. It's a strange decision in the context of how the game constructs itself. Their durability increase genuinely does help, but it's not really enough.
Indeed, Elite Priests are a sufficiently small boost in threat level you could be forgiven for failing to realize that there are three tiers of Priest.On a different topic, Priests make for fairly iffy Domination targets, more so than you might expect.
Holy Warrior's double-kill effect still triggers even when you are using it on an X-COM soldier, and one of the big utilities of Domination is to have a disposable distraction to absorb fire for your long-term troops. This use is rather defeated if the Dominated target dying is risking instantly losing one of your soldiers, making Dominating them for Holy Warrior bonuses a risky plan.
Mind Control can actually be used even while Dominated, surprisingly, but Priests always have a sad enough Psi score there's basically no enemies they're actually reliable at taking over. A lot of enemies are immune to Mind Control, too, so it's pretty easy to end up never having a good opportunity to use it. Even when you have a decent target, temporary Mind Control is an awkward affair all-around anyway; you'd often rather just shoot a potential Mind Control victim, honestly.
That leaves Stasis as a strongly desirable ability to take advantage of. It's a very good ability, but it's hampered a little by the fact that Dominating a Priest means you probably already have access to Stasis through the Psi Operative. Not necessarily, mind, but usually. Stasis is not an ability you're liable to spam; even a second Stasis tends to be redundant unless you're pretty specifically dealing with an Alien Ruler. If you pull three or more pods it can be a lifesaver, so that's also something to keep in mind, but overall the odds are tilted away from it actually being all that great to have, especially since Psi Operative Stasis can be used in a turn alongside other abilities, so there's not even an action economy advantage being gained.
In practice the primary draw to Dominating a Priest is sidestepping Sustain. If you clear the mission without the Priest dying or exiting Domination, great! You didn't have to deal with it at all! Whereas if the Priest does end up taking lethal damage, it most likely happened during the enemy turn. In that case, what happens is the Priest enters Stasis, exits your control, and then your turn rolls around and they exit Stasis, leaving them an easy target to finish off with their 1 HP and Sustain used up. If you habitually ignore Psi Operatives and also hate planning around Priest Sustain, consider giving Psi Operatives a second chance, and Dominate Priests whenever you can to minimize the annoyance factor.
If you don't care about sidestepping Sustain that way, though, they're a pretty underwhelming choice for Domination.
The Priest Autopsy is, unfortunately, pretty junk-y. It allows you to build an Item that is effectively Sustain in Item form... but if it's triggered the Item is lost forever... and it requires Priest corpses to produce each copy. I'm sure there's people who swear by it, but it's frustratingly niche and you're generally better off giving people Items that reduce the likelihood of them hitting 0 HP, rather than giving them an Item that lets them survive it one time. Resistance classes -your most difficult soldiers to replace- particularly keenly feel Item slot pressure, since only Skirmishers can ever hit 2 slots at all and Reapers don't even necessarily get an Item slot in the first place, so even though they're the obvious choices for passing Sustain out to... it's difficult to justify doing so, outside maybe Tactical Rigging Skirmishers.
I never bother to burn actual lab time on their Autopsy, and even once it's hit Instant I rarely bother to build Sustaining Spheres. There's few situations where they're clearly a worthwhile way of burning the Item slot, and when I've given into the temptation I've always been a bit too aware that a different Item would've helped prevent things from reaching the point of needing the Sustaining Sphere's protection.
I'm a little surprised this Autopsy wasn't used as an excuse to force soldiers to always start bleeding out the first time they'd have died, honestly. It would've made a kind of conceptual sense, and base XCOM 2 is designed so in the long haul your soldiers being guaranteed to not instantly die is the expected result. I'm okay with War of the Chosen making death more a realistic consequence into the late game, personally, but still surprised.
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Narratively, Priests are confusing, ambiguous, and a bit frustrating.
Their name, by itself, is a little weird, out of line with how base-game ADVENT forces tend to get named, but not jarringly so. But then Tygan's intro when you first encounter a Priest refers to them as 'so-called Priests', and their pod activation animations actually do seem to be shooting for a vaguely religious undertone, with Priests reaching to the sky or crouching with their head bowed down in possible prayer. So... the game is maybe signaling they're actually priests in the sense of being persons of importance in an actual religious context? Are they purveyors of an Ethereal-focused religion the game never actually unambiguously refers to as existing? Notably, Tygan talks about ADVENT sending them 'into battle', which is not actually a direct statement that Priests normally perform non-combat duties, but seems likely to be intended to imply such.
But then we don't get info on what such a religion might be, and the only strong secondary support for the notion of there being an official ADVENT religion is a portion of Chosen dialogue. (Lots of Warlock dialogue, and a notable fraction of the Assassin's dialogue, specifically; the Hunter never, to my awareness, refers to the Ethereals as gods or anything of the sort) You won't find centers of worship in ADVENT city center maps, for example, and the new post-mission dialogue from the Speaker and newswoman never touch on religious topics at all. (They never label X-COM as 'heretics' or anything else with religious connotations) Particularly confusing is that you can find what appears to be a church with the ADVENT icon fallen from a position you might normally see a cross at...
... but this is specifically a blown-apart church on a Retaliation map, seeming to imply worship of an ADVENT-specific religion in... a resistance camp that ADVENT is currently trying to murder every resident of?
Chimera Squad seems to firm up the notion of there being an official ADVENT religion, as Sacred Coil is ADVENT loyalists clinging to the cause with zeal while doing things like calling themselves Sacred Coil, but it still doesn't touch on the nature of this religion, and it also doesn't explain why an ADVENT Priest would be... psychic.
Further confusing the issue is that it's actually a semi-widespread cliche for sci-fi to shove religious imagery and terminology together with psychic powers. I... don't really get why it's a cliche... but it is, so it's possible War of the Chosen is calling the psychic ADVENT soldiers Priests purely because of a weird genre convention, rather than intending it to signal anything of substance in-universe. At which point Tygan calling them 'so-called Priests' may be leaning on the fourth wall, poking fun at genre conventions, rather than meant as an indication they're actual religious figures.
Overall, I'm inclined to think they're meant to be actually religious figures, but that itself raises questions about what kind of religion they might be preaching, as well as who they're supposed to be preaching to. ADVENT Priests could be just intended to be preaching to their fellow hybrids, after all, which would be consistent with Skirmishers referring to the Ethereals as false gods while no such religious terminology gets used by the Speaker or anyone else talking to ADVENT civilians. But the game never actually clarifies whether there's a broader ADVENT state religion or not, or even strongly hints in any particular direction.
The fact that Priests are psychic per se also raises a bunch of other problematic questions. The goal of the Avatar project is to take the most psychically sensitive members of the human population and use them as a foundation to make humanoid bodies with strong psychic abilities. So... where do Priests fit into this? Are they prototypes, disseminated into the field as disposable soldiers when the Ethereals rejected them as inadequate? Shouldn't producing psychically capable line troops be eating into the Ethereal's stocks of psychically sensitive human flesh, given the game seems to be treating 'harvesting DNA from psychically sensitive humans' not as a gathering of information (They wouldn't need to kill anyone if they just wanted to study DNA samples, and in fact killing people would be a counterproductive action to a ludicrous extent if that was how this worked, as one of the more blatant examples), but instead as wringing out some limited quantity of psionic potential to then be concentrated in the bodies they're trying to build?
Then there's Tygan's introduction containing another extremely confusing line, where he refers to Priests as having implants that 'enhance whatever latent psionic potential they once possessed'. They have psychic potential. They use it to fight you. So why does Tygan refer to their psionic potential in the past tense? Are we supposed to think Priests are converted humans who had the majority of their psionic ability drained, and then given implants to somehow enhance whatever remains into battlefield-relevant abilities? Or did someone mean for a radically different sentence to go there, and War of the Chosen was rushed enough that nobody stopped the process and went back to double-check with the writer prior to recording the line?
As the final bit of murky confusion, Priests are presented as a psychic command-and-control unit... which is how Officers are explained, too. So, uh, what's the difference supposed to be? I can come up with workable theories, such as guessing that Officers rely on the psionic network to issue orders psychically while Priests can do so even if the psionic network is down or jammed or whatever, but the game itself doesn't clarify the distinction at all.
To be fair, most enemies aren't explained much. But most units aren't closely tied into a lot of important elements of the setting and story the way Priests are. It's a little frustrating that the narrative of XCOM 2 never addresses how your average ADVENT citizen views Sectoids walking the streets naked, but it's very much off to the side of the story and setting. Priests obviously connect directly to the Avatar Project and myriad elements that flow from it, as well as potentially hooking pretty directly into the nature of ADVENT society, so it's a lot more problematic how little coverage they get.
Probably a side effect of War of the Chosen being rushed, admittedly. A detail that's easy to overlook is that when you complete an Autopsy, your support staff will have some additional dialogue about the Autopsied subject... unless its content new to War of the Chosen, in which case they're silent. I suspect if they'd had more time, this kind of thing would've gotten filled in, and we might've gotten eg Shen asking Tygan about what Priests actually do in random Avenger conversations, like how regular animals largely being missing is referred to in random Avenger conversations.
But it still means players are left with an extremely confusing unit and inadequate info on it, narratively.
Aesthetically, I actually like Priests. They're difficult to confuse for another unit, for one: their white color scheme is seen on only one other ADVENT human-type enemy, and then there's enough other differences -like the Psi Amp- that it's unlikely you'll confuse the two. Particularly notable is their firearm, which is the same base shape as the rifle used by literally every base-game ADVENT human-type soldier, but is painted more white than black. I can contrast this with Stun Lancers, where their rifle is exactly the same as a Trooper's, color included; if Stun Lancers had gotten red paint on their rifle, or something, it would be a lot easier to avoid mixing them up with Troopers, same as Priests having a white rifle makes it hard to confuse them for Shieldbearers.
For another, Priests are one of the clearer examples of War of the Chosen showing more recognition of the fact that ADVENT forces ought to look cool, likable, and so on, if ADVENT is to be perceived by in-universe citizens in the way the narrative wants us to think they're perceived. Instead of being blatantly a stock sinister bad guy soldier visual, Priests actually look more like what one might expect to see generic good guy soldiers dressed like. The only significant obstacle in that regard is the manner in which the helmet conceals their face, and War of the Chosen is somewhat hamstrung in that regard by the base game insisting ADVENT soldiers are obviously not fully human if you aren't hiding eg their eyes under a helmet. It'd be better if the base game hadn't mishandled that whole thing in the first place, but War of the Chosen isn't in a good position to back up and course-correct on that topic, especially given it was already struggling to achieve its myriad ambitions. So the helmet point is understandable, in this case.
Especially since fiction wanting to so reliably use no helmet or face-revealing helmets for 'good guy' characters is something I find frustrating. I'd be perfectly happy with a game depicting shiny, cool, helmeted soldiers, because helmets are there to, you know, try to prevent people from getting killed. I have severe issues with how normalized it is that only bad people try to protect their soldiers' lives with helmets and full armor and so on.
Anyway, there's another reason I appreciate the Priest aesthetic, but I'm... not going to be touching on that for a while. Just keep in mind they have Psi Amps, just like your Psi Operatives.
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See you them.