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Many DKP systems provide disproportionate rewards to people who are able to raid more often. This means that if someone raids less than 1/2 the time of someone else competing for the same gear, that less-often raider will not be able to spend DKP or get that gear until the hardcore player has everything they want. Insert a new hardcore member into the group before that point, and the casual player will never begin getting gear, even potentially after having multiple raids under their casual-belt. Ideally, the ratio of gear to effort should be the same no matter if you raid 3x/week or 1x/month.

A solution is not to use the difference between points earned and points spent, but instead the quotient. Such a system will still allow hardcore members to gain first pick most of the time, but will give less frequent raid members a fair chance too.

Relational DKP systems allow to use the standard rewards - points for attending in-time, boni for first kills and learning runs, point expenditure for bank items. RDKP at the same time are fixed-price systems with their inherent drawback (what happens to loot nobody wants?). Thus each member of a RDKP system has two scores - his earned points, and his spent points. When loot drops, the quotient of (points earned) divided by (points spent) is used to determine the hierarchy. The person with the highest current quotient who wants the item gets it, and gets their points spent score increased by the item value.

Example and comparison to zero sum, fixed price

Traditionally, zero sum, fixed price (ZSFP) systems are considered to be most fair to newbies. In reality that's not true, but let's compare for the sake of simplicity a relational DKP to ZSFP.

Assume that Anna runs 3 raids per week, whereas Bob can take part only once a week. Each run yields 30 points, and the average drop costs 60. After 10 weeks, Anna has earned 900 points, Bob only 300. Anna can have won 9 drops (leaving her with 360 points), and still maintain a lead over Bob (even if he took not a single item), outranking him on every contested item. If by some stroke of luck Bob managed to grab something, his chance to compete for top of the line drops will be even lower.

If the raid was using relational DKP instead, Bob would be able to compete for the second item (after Anna got her first drop). After that, he will at all times be able to compete again when he has won less than one-third of Annas' items. If she had 9 drops, Bob would be guaranteed to have at least 3. If he had three, he would be able to call "first dibs" after she got her 10th (but then would have to wait until she had 12).

Implementation Variations:

As other major DKP systems have variations, Relational DKP systems have their particular flavors as well.

Raid Window
A Raid count or time based system so that all members are looking at the same window (10 raids, or what have you) of evaluation. This brings more junior members up quickly to be on-par w/ the more long-term members since the system only looks over the the last number of raids or period of time.
Decay
A constant decay of both effort and gear points so that older raids count much less to shape loot priority than more recent ones. This is a generalization of the raid window in a sense because given a large enough number of raids the last raid raid in the series will amount for nothing. The advantage of this over a Raid Window is that Priority does not change at all between raids, whereas with a Raid Window it is possible for members to jump in priority a lot (say because a very high quality item received raid window days ago dropped off the raid window).
DKP Floor/Ceiling
Other systems use the DKP value as the threshold trigger, rather than time. As longer term or more hardcore players values get up there in quantity, as with any fixed price system, they see their Priority change less and less per point of DKP. Making it harder and harder to raise their PRI and loosing loot to the newer members. Esp if the initial Gear value is 1. So the solution when a given player's DKP reaches or exceeds the threshold amount reduce the DKP & GR values by a set %. Example: Anna's DKP goes past 300 (the threshold value) and her GR = 120 (Priority = 2.5). At this point reduce both by 1/3, leaving her new values at 200/80 = 2.5. The priority stays the same, but makes the DKP earned mean something more consistent over time, as all players get into this DKP floor/ceiling, yet still having realistic priority values.
Initial Gear values > 1
As found during actual play, bringing in new players into a system that's been in use for some time with an initial Gear value of 1 means they can gain Priority very quickly and shoot past the older more senior players who have gotten some gear. Sometimes this happens after just the first boss kill before loot is even distributed. To mitigate this problem, some adjust the initial value to be higher, like 25 or 50 even. This delays that initial burst of priority with a lower GR value. The best way to adjust this within an already existing system is to change all players by this fixed amount. Thus affecting new players greatly, and older players hardly at all.

Complications/Questions:

What about rotting gear, gear that no one wants to spend the priority on but could use?
If someone gets gear, their points spent increase and their priority drops accordingly.
What about an item that no one wants and is DE'd?
The item is not aquired by anyone and no points are spent. The shard is available for rolling on or can be sent to the guildbank.
So minor upgrades can be disenchanted?
Yes, in this respect relational DKP is a Fixed price system - see the discussion of disenchanting there.
What if someone goes on a large number of raids and the gear they want just doesn't drop?
Their points earned continue to increase, putting that player in prime position to get the gear once it does drop.
What if the officers want to reward out-of-raid attendance in the form of raid points?
They can just increase someone's points which will in effect raise their priority for their next loot situation.

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