Note: These are not the actual ratios, this is just an example. Please see item qualities for actual figures.
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:
All qualities' values are added, and the sum is used to determine the "ratio." In this example, the sum (maximum Luck) is 5000.
This data set only determines the quality of the generated item. This chart is interpreted "of all items dropped, approximately 89% of them will be normal quality". There are different, unrelated mechanics that determine if and what items will drop.
Luck subtracts itself from the normal quality pool while retaining all other quality ratios. This is luck increases your chance of finding better items. Consider the example above, and the player has 2000 luck. The formulae is simple:
4450 - 2000 = 2450
Luck is calculated on a per drop basis. When the item generation function is executed, the luck stat is referenced from the player unit in the algorithm described above to determine the items quality. Removing items with +luck affixes between kills does alter these ratios.
Influence vs Bosses
Luck has little influence against boss drops. In general, all bosses share a common treasure table which determines what loot, how much and what quality is dropped. Of these drops, the minimum quality of 2 drops will be rare and 1 will be legendary. Therefore, using the above example the drop table will appear:
Not all loot drop by bosses has a minimum rare quality, but most of it is. Therefore luck against drop bosses has little effect in the majority as common quality items are already negated.
Luck is a mysterious property that has no in game or outside insight into how the mechanic actually works. The above description is a similar explanation provided by Flagship Studios. It has also been confirmed by the Revival Team who broke and modified the Single Player version of the game. Luck does not influence any other game play factor other than reducing the quantity of normal quality items dropped.