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Loot rolls

An enemy's level or a dungeon's kind picks the tier range. Treasure piles multiply the base rarity chances by 1.3, and bosses by 2.5. These multipliers do not multiply gold.
Luck shifts the odds by 1% per point either side of 50.
Rare and Legendary gear is rarer early on and more common as a character grows.
The longer you go without a Legendary, the better your chance of one. It resets when one drops.
Each Legendary has a home enemy family, and hunting that family improves your chance of finding it.
Every possible item bonus is listed on Affixes and curses. Weapons can carry a named technique, and garments roll their own pool.
A Perfect Rare has every bonus at its maximum value. About 1 Legendary in 10 is Exalted, with one extra bonus.
About 1 Rare or Legendary in 12 is Cursed: an extra bonus plus a drawback. A temple's Cure Disease priest lifts the curse for a quarter of the piece's price (minimum 300 gold), and you keep the bonus. One cursed Legendary weapon in four is Damned and cannot be lifted.

Sources (29)