Luck

Note: These are not the actual ratios, this is just an example.

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Luck is player stat that reduces a players chance of finding items of normal quality. Reducing the ratio of normal quality drops effectively increases the chance that higher item qualities will drop. For example:

Item Quality	Weighting	Percent
Common	1250	90.5%
Enhanced	100	7.2%
Rare	25	1.8%
Legendary	5	0.36%
Unique	0.8	0.06%
Mythic	0.1	0.007%

Luck subtracts itself from the normal quality pool while retaining all other quality weightings, effectively increasing chance of finding items of higher quality.
Let's say, the player has 1250 Luck, which is enough to "remove" Common from drop pool. The result will be:

Item Quality	Weighting	Percent
Common	0	0%
Enhanced	100	76.4%
Rare	25	19%
Legendary	5	3.8%
Unique	0.8	0.61%
Mythic	0.1	0.076%

As you can see, removing Common from drop pool has led to an x10.5 increase in drop rates of other items.
Please note that "Depending on the enemy grade (25% for Champions, 50% for bosses), there is a chance to simply bypass Commons or Commons+Enhanced respectively. This is not just assuming ~1250 Luck (ie 1/4 or 1/2 of the time you'll get max Luck drops), but rather applying ~1250 Luck to a new pool which just lacks Commons or Commons and Enhanced. Therefore, in those cases you'd have different results if you had 0 Luck and if you had ~1250 from enriched rolls."[1]

Influence vs Bosses

Bosses and some unique named monsters may have two drop tables, one table with improved drop rates and is affected by Luck, and the other is predetermined with fixed drop chances for monster specific Unique and Named items, on which Luck has no effect whatsoever. Therefore, using the above example the non-predetermined drop table will appear:

Item Quality	Weighting	Percent
Common	0	0%
Enhanced	0	0%
Rare	25	80.9%
Legendary	5	16.2%
Unique	0.8	2.6%
Mythic	0.1	0.3%

Item Quality	Weighting	Percent
Common	0	0%
Enhanced	0	0%
Rare	0	0%
Legendary	5	84.7%
Unique	0.8	13.6%
Mythic	0.1	1.7%