Ever noticed something counter-intuitive about the way set bonuses are calculated? For example, adding one piece of gold-quality gear to an otherwise fully-purple set can result—though not always—in ZERO change to the set bonuses provided. It always puzzled me, and a recent bug report (link) reminded me of the issue, so I decided to investigate and post my findings here, in an unnecessarily complicated article that will probably never affect most of the playerbase. But to all those interested—enjoy!
To start off, there are two very clear constants governing the stam/mag provided by a standard 1-4pc set bonus (stam/mag is arbitrarily chosen; you could pick a different stat, eg. weapon damage, but the rules are the same):
- A fully-purple set provides 1058
- A fully-gold set provides 1096
It's what happens between those two extremes that gets confusing. In the following example, we start from a baseline of a fully-purple 5pc set, and observe how the set bonus transforms as we add more gold pieces to the set. Notice that at certain intervals, there is no gain in the stat bonus despite the addition of a gold piece, as mentioned in the intro:
- 5 purple pieces - 1058
- +1 gold piece(s) - no change
- +2 gold piece(s) - 1071
- +3 gold piece(s) - no change
- +4 gold piece(s) - 1083
- +5 gold piece(s) - 1096
It gets even more complicated when we
include a 2-handed weapon as part of the 5pc set, meaning it now only comprises of 4 individual items. Once again, we see a "null interval" where adding an additional gold piece does nothing, but this time there's only one:
- 4 purple pieces - 1058
- +1 gold piece(s) - no change
- +2 gold piece(s) - 1071
- +3 gold piece(s) - 1083
- +4 gold piece(s) - 1096
What about a 2pc set, you ask? I tested that with the Tremorscale monster set:
- 2 purple pieces - 1058
- +1 gold piece(s) - 1071
- +2 gold piece(s) - 1096
From these examples, we can draw several common observations:
- When wearing a mix of gold/purple, the resultant stat bonus is NOT a numerical average
- When adding more gold pieces, the change in stat occurs at discrete intervals
- There are only 3 such intervals (eg. 1071, 1083, 1096)
Because these intervals occur at different points depending on how many items comprise the set, I suspected there was some underlying proportionality involved. Since there are 3 intervals, the simplest and most likely hypothesis was that they were distributed evenly-apart, at thirds, along the purple to gold spectrum:
- 33.3% - 1071
- 66.7% - 1083
- 100% - 1096
This seems consistent with the first set of data (5pc set consisting of 5 items). With one gold piece, you are 20% of the way towards full-gold and have not passed the one-third milestone, hence no change. You pass this upon adding 2 gold pieces (40%) and thus bump-up the bonus to 1071. 3 pieces, 60%, no change. 4 pieces, 80%, 1083 due to passing the two-thirds milestone. This framework also holds true for the 4-items data, as well as the Tremorscale data.
The final, conclusive way to verify this hypothesis was to test a 3pc jewelry set, since the theoretical intervals coincide precisely with the number of items involved. For this I chose the
Ancient Grace set, and yes, I actually purchased gold jewelry solely for research purposes. The result:
- 3 purple pieces - 1058
- +1 gold piece(s) - 1071
- +2 gold piece(s) - 1083
- +3 gold piece(s) - 1096
Bingo!
So to summarize these findings in picture format for easier reference:
Note: just a reminder that these interval values (1058 - 1096) apply to max stam/mag set bonuses. If we were considering a different stat—eg. mag/stam/health regen, spell/weapon damage—they would use a different set of numbers (124, 126, 127, 129) but adhere to the same interval points.
PC/NA — Daggerfall Covenant — BGs, Kaalgrontiid
Kalazar Chalhoub — Redguard Nord Stamplar
Kalaron Caemor — Altmer Magsorc
Kalahad Cirith — Dunmer Magden