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One central issue of many Loot systems (Fixed price systems in particular) is that they provide disproportionate rewards to people who are able to raid more often. This means that if someone raids maybe half as frequently as more hardcore raid members competing for the same gear, that less-often raider will never be able to get highend gear until the hardcore players have all they want. For some raids this effect is OK (because regular members are crucial to progress), other raids may feel that the ratio of gear to effort should be the same, no matter whether somebody raids 3x/week or 1x/month. In standard Fixed price systems the loot order is determined by the current DKP totals - in effect by the difference between DKP earnt and spent by each player.

A solution to the problem is not to use the difference, but rather the quotient. Each member of a relational DKP (RDKP) system has two scores - his earned points, and his spent points (sometimes also called EP "Effort Points" and GP "Gear 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.

Advantages

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. It allows to use the standard rewards - points for attending in-time, bonuses 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 minor upgrade / sidegrade loot?). Similar to Zero-sum DKP this system also allows newer members to get a few good items fast, but after that keeps a good balance between casual and hardcore players in the same guild: a hardcore player that raids twice as much as a casual player will receive twice as many items.

The end result is a system that is fair, simple to understand, and friendly to new raid members.

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 RDKP 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. In ZSFP, Anna can win 9 drops (leaving her with 360 points), and still claim first pick 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 able to claim 3 items over her. 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).

Variations

As other major DKP systems have variations, Relational DKP systems have their particular flavors as well. One major issue of RDKP is that its memory must not be too good, lest it becomes unfair to longterm members. After a few months, it becomes very difficult for members to significantly change their ratio, because the amount of points earned in a single run is rather small compared to the sums involved in the calculation. Thus most RDKP include some kind of Tax mechanism.

Raid Window
The most basic method to make the systems memory finite is to simply forget points earned or spent after a certain time (e.g. 10 raids). This brings more junior members up quickly to be on-par with more long-term members.
Decay
A more sophisticated approach is to regularly remove a certain percentage of point spent and earned. For example, each week, all members could have their scores reduced by 2%. In a sense, this is a generalization of the raid window, because given a large enough number of raids the last raid in the series will amount for nothing. The advantage of this over a Raid Window is that the loot priority does not change 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 just dropped out).
DKP Floor/Ceiling
Instead to apply the decay automatically on a regular basis, it's possible to have it take place only when a certain threshold is reached. The threshold could be for example 1000 DKP, so whenever one of a members current score reaches this value, both scores get reduced by maybe 33%. This approach is very similar to Decay, but is easier to administer (if not using some DKP tool which automatically supports taxes).
Initial Gear values > 1
When new raid members start with an initial "points spent" value of 1, they will after their first run automatically have precedence over all veterans. This effect may not be desired. Thus frequently new members start with some points spent, usually about the value of one or two drops.

Complications/Questions:

What about rotting gear, gear that no one wants to spend the full price on but could use (situational gear, off-spec, PvP, resistance etc.)?
This is a common problem with all fixed price systems. Either disenchanting of minor upgrades/sidegrades may take place, or some danger to the fixed price nature arises. For details on this problem, see the discussion in the Fixed price article.
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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