What to expect in cup hunting (frequency and timeframe) :

gladiator/wanderer : 11 (from 400 rounds, 1 in every 36 rounds)
bloodstain/noblesse : 8 (from 120 rounds, 1 in every 15 runs)
maiden/viridescent : 8 (from 120 rounds, 1 in every 15 runs)
blizzard/depth : 5 (from 100 rounds, 1 in every 20 runs)
fury/thundersoother : 4 (from 100 rounds, 1 in every 25 runs)
pale flame : 2 (from 40 rounds, 1 in every 20 runs)
crimson : 1 (from 30 rounds)
*these are the numbers of usable artifacts
*domain runs are done per 40 resin
*this amount is achieved in AR56 / 235 days
In conclusion, each domain gives relatively about the same amount,
except for world/weekly bosses.
Frequency in a domain also gives a relatively higher chance.
Note
Domains rarely ever give a matching elemental cup, so it’s better to farm somewhere else. Example: Crimson Witch (a pyro set) would unlikely give a pyro cup unless you have farmed more than an entire month’s worth of resin, which could have been spent on other domains.
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