Old post that Sancus wrote regarding Luck stat:
Luck works in buckets of 10. The benefits of luck are constant within that range. That means having 1 luck is the same as having 9. Having 32 luck is the same as having 39.
With 1 to 9 luck, 45% of your critical hits are lucky critical hits. With any luck >=10, 50% of your critical hits are lucky critical hits. The critical damage added by luck is a random roll between a minimum and maximum crit amount as shown by the table:
As an example, let's say you have a 400% crit damage modifier, cast a 10,000 damage nuke, and have no other modifiers. Normally it'd do 10,000 damage on a non-crit and 50,000 on a crit. With 50 luck, on a lucky crit, the minimum damage you could do would be 53,000, and the maximum would be 53,500. Any value between those values, inclusive of them, is possible.
The DPS Increase numbers are based on a Magician at a 100% crit rate. It varies significantly depending on crit rate.