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Not sure why, but when clicking the finger slot with Cyrce’s circlet, a lot of other rings are shown as being better, but they’re not actually recommended. I can only guess this is because the pop-up list has no sockets in Cyrce’s circlet, but not sure.
It does appear that the sockets Circe’s Circlet are “over-weighted”, based on the gems that go IN the sockets.
With your 671 Jester’s, for example, it may be worth doing something regular & familiar with that equipped to see if the throughput is compromised in any major way to draw a conclusion as to whether the Citrines offer any meaningful contribution for more recent content… or if the 671 would ‘cover for them’.
OK; that 671 Jester’s is the second Ring in the set-up, but by marking Circe’s as ‘ignored’ I get this:
While it’s shown as a 0.4% drop in throughput, that may prove to be negligible in real-game setting…
Yeah the list ranking for cyrce’s circlet is unfortunately not that helpful because it doesn’t try all of the gem combinations. The Best in Bags and Best in Slot optimizers will fill the sockets though and give it a fair ranking.
The total amount of secondary stats gained from that combo on cyrce’s circlet is very similar to e.g. your 684 ring – when the total secondary stats are close it all comes down to which combination of those stats is slightly better or worse.