Artifact/Occurrence

==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	Scaled Chance	Scaled Chance	Scaled Chance 	Scaled Chance
Minor Affix 	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	Scaled Chance	Scaled Chance	Scaled Chance 	Scaled Chance 	Scaled Chance
Minor Affix 	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	Scaled Chance	Scaled Chance	Scaled Chance 	Scaled Chance	Scaled Chance	Scaled Chance
Minor Affix 	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%
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