Artifact/Occurrence

ArtifactsSetsStatsDistributionOccurrenceScaling

Occurrence

While the occurrence probability of a specific minor affix is useful, the probability of occurrence of that specific minor affix with respect to the 4 possible minor affixes of an artifact is a more practical application of its distribution.

While the gap between the occurrence probabilities of some minor affixes are relatively large, it is compensated by having 4 minor affix slots, bridging some of the gap between minor affixes that have a low rolling chances. In short, this indicates the probability of an artifact with 4 minor affixes that a specific minor affix is one of them.

The rate of the most common CRIT Rate and CRIT DMG pair is also especially shown to highlight the large decrease of probability as more minor affixes out of the 4 are specified.

Mathematical Treatment

Consider a collection of at most 4 occurrable minor affixes, each respectively with a probability of $p_{1},p_{2},p_{3},p_{4}$. The specific minor affixes occurrence probability is $\prod _{i=1}^{4}{\frac {p_{i}}{1+(\sum _{j=0}^{i-1}-p_{j})}}$

Specific Minor Affixes Occurrence Probabilities

Specific Minor Affix Count	Occurrence Probability
1	${\frac {p_{1}}{1}}$
2	${\frac {p_{1}}{1}}\times {\frac {p_{2}}{1-p_{1}}}$
3	${\frac {p_{1}}{1}}\times {\frac {p_{2}}{1-p_{1}}}\times {\frac {p_{3}}{1-p_{1}-p_{2}}}$
4	${\frac {p_{1}}{1}}\times {\frac {p_{2}}{1-p_{1}}}\times {\frac {p_{3}}{1-p_{1}-p_{2}}}\times {\frac {p_{4}}{1-p_{1}-p_{2}-p_{3}}}$

Minor Affix Occurrences

Flower of Life

Minor Affix	Scaled Chance
ATK	57.8%
DEF	57.8%
HP%	43.2%
ATK%	43.2%
DEF%	43.2%
Energy Recharge%	43.2%
Elemental Mastery	43.2%
CRIT Rate%	34.2%
CRIT DMG%	34.2%
CRIT Rate% & CRIT DMG%	9.2%

Plume of Death

Minor Affix	Scaled Chance
HP	57.8%
DEF	57.8%
HP%	43.2%
ATK%	43.2%
DEF%	43.2%
Energy Recharge%	43.2%
Elemental Mastery	43.2%
CRIT Rate%	34.2%
CRIT DMG%	34.2%
CRIT Rate% & CRIT DMG%	9.2%

Sands of Eon

The distribution is dependent on the main affix.

Minor Affix	Scaled Chance
	HP%	ATK%	DEF%	Elemental Mastery	Energy Recharge%
HP	56.0%	56.0%	56.0%	56.0%	56.0%
ATK	56.0%	56.0%	56.0%	56.0%	56.0%
DEF	56.0%	56.0%	56.0%	56.0%	56.0%
HP%	0	41.6%	41.6%	41.6%	41.6%
ATK%	41.6%	0	41.6%	41.6%	41.6%
DEF%	41.6%	41.6%	0	41.6%	41.6%
Elemental Mastery	41.6%	41.6%	41.6%	0	41.6%
Energy Recharge%	41.6%	41.6%	41.6%	41.6%	0
CRIT Rate%	32.8%	32.8%	32.8%	32.8%	32.8%
CRIT DMG%	32.8%	32.8%	32.8%	32.8%	32.8%
CRIT Rate% & CRIT DMG%	8.3%	8.3%	8.3%	8.3%	8.3%

Goblet of Eonothem

The distribution is dependent on the main affix.

Minor Affix	Scaled Chance
	HP%	ATK%	DEF%	Elemental Mastery	Elemental/Physical DMG Bonus%
HP	56.0%	56.0%	56.0%	56.0%	51.2%
ATK	56.0%	56.0%	56.0%	56.0%	51.2%
DEF	56.0%	56.0%	56.0%	56.0%	51.2%
HP%	0	41.6%	41.6%	41.6%	37.5%
ATK%	41.6%	0	41.6%	41.6%	37.5%
DEF%	41.6%	41.6%	0	41.6%	37.5%
Elemental Mastery	41.6%	41.6%	41.6%	0	37.5%
Energy Recharge%	41.6%	41.6%	41.6%	41.6%	37.5%
CRIT Rate%	32.8%	32.8%	32.8%	32.8%	29.4%
CRIT DMG%	32.8%	32.8%	32.8%	32.8%	29.4%
CRIT Rate% & CRIT DMG%	8.3%	8.3%	8.3%	8.3%	6.7%

Circlet of Logos

The distribution is dependent on the main affix.

Minor Affix	Scaled Chance
	HP%	ATK%	DEF%	Elemental Mastery	CRIT Rate%	CRIT DMG%	Healing Bonus%
HP	56.0%	56.0%	56.0%	56.0%	54.9%	54.9%	51.2%
ATK	56.0%	56.0%	56.0%	56.0%	54.9%	54.9%	51.2%
DEF	56.0%	56.0%	56.0%	56.0%	54.9%	54.9%	51.2%
HP%	0	41.6%	41.6%	41.6%	40.7%	40.7%	37.5%
ATK%	41.6%	0	41.6%	41.6%	40.7%	40.7%	37.5%
DEF%	41.6%	41.6%	0	41.6%	40.7%	40.7%	37.5%
Elemental Mastery	41.6%	41.6%	41.6%	0	40.7%	40.7%	37.5%
Energy Recharge%	41.6%	41.6%	41.6%	41.6%	40.7%	40.7%	37.5%
CRIT Rate%	32.8%	32.8%	32.8%	32.8%	0	32.0%	29.4%
CRIT DMG%	32.8%	32.8%	32.8%	32.8%	32.0%	0	29.4%
CRIT Rate% & CRIT DMG%	8.3%	8.3%	8.3%	8.3%	0	0	6.7%