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A complex is EVE's equivalent of a fantasy MMO's dungeon. It’s a pocket of space that is locked off from the outside world except for an Acceleration Gate (not to be confused with a stargate), kind of like a mission. Inside, you will either find drug runners, criminal hideouts, pirates, or rogue drones. You find complexes either with scan probes (exploration) or in certain COSMOS constellations.
For the COSMOS complexes, see the COSMOS page.
Once upon a time these complexes were static beacons in certain systems, which you could warp to and enter at any time. They respawned 8 hours after being completed (usually by killing the final overseer (a special pirate NPC) or destroying some structure) and at downtime. Since a lot of the gates inside the complexes required keys (found in one of the first rooms), this lead to crazy rushes at downtime to farm keys and control when the plex respawned, as well as a lot of drama, since plexes can be hugely profitable.
A while ago however, CCP removed the static complexes. They still exist, but now you have to probe them down, and they can only be run once before despawning and moving somewhere else. While they were at it they also seem to have unlocked all the gates; the keys still drop but they aren't used anymore.
DED complexes have a difficulty rating ranging from 1 (easiest, can be run in a frigate) to 10 (hardest, requires multiple well-fit battleships). Only complexes of difficulty 6/10 and higher spawn in 0.0, the easier ones can only be found in empire. The harder the complex is, the better loot it drops (obviously).
A DED complex is easily recognized by the popup you get when you initiate warp to it; it has a message from DED with some RP bullshit about what the local pirates are doing in the plex and what the difficulty rating is. If it doesn't have a difficulty rating, it isn't a DED plex but an escalation site (some of which also give you popups when you warp to them).
Loot from DED complexes
Besides the rat bounties you get, the complexes can also drop some extremely expensive stuff, namely deadspace modules of various grades (like faction modules but better; the better ones being on par with the best officer modules), which can be sold on Jita contracts for potentially gigantic sums of money (the best deadspace modules can be worth well over two billion ISK each) and Overseer's Personal Effects, which can be sold to NPC buy orders for instant spacebux.
Generally, 1-3/10 drops frigate-sized, 4-6/10 drops cruiser-sized and 7-10/10 drops battleship-sized modules. There are different names for these, for example the Angel frigate-sized stuff is called Gistii, the cruiser-sized Gistum and the battleship-sized Gist. Each tier has three different grades (or four grades for the battleship-sized gear), namely X (battleship-sized only), A, B and C, with X being best and C worst. X-Type stuff is generally on par with the best officer modules in the game and can (depending on what it is) be insanely expensive. What drops is (in theory) determined by the difficulty rating of the plex, as follows:
However, with CCP being CCP, stuff doesn't really work out perfectly as it should in the game. Here is a handy list of all existing DED complexes and what kind of deadspace modules they actually drop (taken from this list):
DED complexes are not the only place to get this kind of loot. There are also escalation complexes (see below). Loot from these is as follows:
List of guides to DED complexes
See DED Complexes.
Escalation complexes are the other type of complexes, added relatively recently together with exploration. Unlike the DED complexes they were never static to begin with, you've always had to probe for them. They are quite different from the DED complexes; instead of a single site there's a whole chain of sites, with the final site being the one that might drop the delicious deadspace loot. The initial and intermediate sites only rarely drop anything worthwhile; the best you can get is a faction spawn.
Once you've probed out the initial site, you will have to run it. Each site has a trigger of some kind (usually blowing up one of the rats, blowing up a certain structure, or in some cases just bumping into or approaching some object), that may or may not trigger an "escalation". An escalation means you get a temporary bookmark expiring in 24 hours (in your journal, under the "expeditions" tab) a few systems away (usually ranging between 3 and 10 jumps), where a similar complex is located. Running that and tripping whatever the escalation trigger is may or may not give you a further escalation, until you get to the final site (usually the fourth escalation), which then may (or may not) make you space rich.
Types of escalations
Just like DED complexes, escalations vary in difficulty; the easiest ones can only be found in empire. The easiest 0.0 escalations are soloable in a T2 fit, decently skilled battleship, while the most difficult ones require either a capital ship or a very heavily tanked battleship supported by a few priests to finish.
The following sites are common to all factions and are listed in order of difficulty, easiest first (empire sites not included). The difficulty refers to the escalation chain as a whole, not just to the initial site.
In addition to this, each faction has a few unique sites where the difficulty varies.
Loot from escalation complexes
The loot from the escalations is roughly inline with the loot from the DED plexes, at least when it comes to deadspace modules. They do usually not drop overseer effects, although there are exceptions. Do note that only the final site in an escalation chain drops deadspace loot; the initial site usually drops nothing but the intermediate stages may drop faction modules.
The list goes something like this:
The unique sites for each pirate faction (i.e. Domination Fleet Staging Point, Blood Raider Temple Complex etc.) are not easily predictable loot-wise, but usually it's battleship-sized deadspace gear plus some kind of overseer effects.
Some escalation protips
List of guides to escalation complexes
See Escalation Complexes.
This category has the following 11 subcategories, out of 11 total.
Pages in category "Complexes"
The following 186 pages are in this category, out of 186 total.