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Item rarity is a color-coded system, displaying the relative chances/difficulty of obtaining that item.
For craftable items, this is mostly cosmetic in nature. Procedural weapons show their rarity in more functional ways. Example - an uncommon melee weapon will often possess some kind of secondary effect, such as poisoning foes, or setting them on fire. Legendary weapons are a class of their own, drawing from a preset pool of weapons, and having even more notable (and unpredictable) effects. Rarity is likely the best indicator of how much better an item is compared to similar items at the same level. The Essential rarity is used for the Matter Manipulator and its subsequent unlockables (Wiring Mode and Paint Mode, respectively), as well as the Inspection Tool. Although not used for typical inventory items, manually-generated items through the use of admin commands can have the Essential rarity applied to them, as well as the other rarity classifications.