Artifact stats, explained properly
Artifacts are the part of the game with the most arithmetic and the least explanation. On a private server you can spawn them freely — which makes understanding them more useful, not less.
The two kinds of statistic
Every artifact has one main statistic and up to four substatistics. The main stat is fixed by the slot and grows on a known curve as the piece is levelled. Substats are the random part.
The flower always gives flat HP and the feather always gives flat attack. Those two are not choices. The sands, goblet and circlet each roll their main stat from a weighted table, which is why a specific goblet is the usual bottleneck.
How substats actually roll
A five-star piece starts with three or four substats and gains one at every fourth level, to a maximum of five upgrade events. A piece that started with three substats spends its first upgrade adding a fourth, so it gets four increases spread across four stats; a piece that started with four gets five increases.
Each increase is a roll on that substat, and each roll picks one of four possible magnitudes. This is why two artifacts with identical substat names can differ enormously: the same number of rolls landing at the bottom of the range versus the top.
Which numbers matter
Critical rate and critical damage dominate almost every damage calculation, and the reason is multiplicative rather than aesthetic: they multiply the whole damage figure, while attack is added to a base that is already large.
The usual guidance is to keep critical damage around twice critical rate. That ratio is not magic — it is where an additional point of either is worth about the same, so it is the point at which you stop having an obvious answer to which to improve.
Elemental mastery matters only for characters whose damage comes from reactions. On a character who does not trigger reactions it does literally nothing, and it is the most commonly wasted substat.
Why spawning artifacts is more interesting than it sounds
On the official game, testing a build means committing months of resin to find out whether a theory works. On a private server the same test costs a command, so you can answer the question directly: build the piece you were considering, and look at the number.
That is the genuinely useful thing about a sandbox. Not having everything, but being able to check something before spending real time on it.