this page is pretty outdated and has info in it that's just outright wrong
I'm just gonna go ahead and go down the list
Premium accounts have an added bonus to the creation of rare, supreme, and fantastic items over non-premium players.
Premium players do not have a bonus to rare creation. I can vouch for this from my time rare spamming. They have an added bonus for the item to go supreme or fantastic, but if they were non-premium they would instead get a rare. Supreme chance is 1/12 for premium and 1/50 for non-premium, fantastic chance is 1/4750 for premium and 1/5000 for non-premium, if both these fail the item is rare.
When rare items were introduced players were told "You get approximately 1 chance of 50% each hour to create a rare item." What this actually means to game play is unknown. The odds of creating a rare seem to be much higher than improving an item and making it rare.
On average you will get one moment of inspiration per 1 hour and 55 minutes or so. What's really going on server side is you get a window every hour or so, that has a 50% chance to be a rare window, 4% chance to be supreme, and 0.0103 chance to be fantastic (assuming prem for supreme/fantastic). This ends up with a 54.0103% chance of a moment window every hour on average, with 50% of that being rare. It's correct but worded so weirdly and easy to assume by "create a rare item" that supreme is also included in it.
Some items have a chance to retain their rarity when combining with other non-rare items.
This was removed.
If the item is fantastic, you will also get a skill tick, but a much larger one than a supreme.
skill tick is 10x the size
This includes anything you use up to create something else, examples being Sand, Dirt, Planks, Nails and so on. Upon completely consuming the item - through improving with it, or creating an item with it - there is a small chance of its rarity transferring to the item that are being worked on exists.
The chance is 1/parts chance for creation, and the order in which you put in the rare+ parts and normal parts has no effect on the chance of the item being rare. For improving, it's 1/100 chance when the rare material is fully consumed, and will not give a moment of inspiration popup, the item will simply turn rare+.
Tools and Toolbelts
In addition to the damage reduction and enchant decay already listed (should be 10/20/30% reduction but whatever, with weird wurm maths that could be correct for all i know) Rare+ also imp faster (10% rare, 20% supreme, 30% fantastic). Note this is the rarity of the item being imped, not the item imping. They also lose less ql while repairing (1/2 rare, 1/3 supreme, 1/4 fantastic).
In addition to the 3% per rarity level damage reduction, they also add 3% per rarity level glance rate, and 3% per rarity level to power of enchants on the armor (a 104 aosp fantastic armor for example, will return 110% of damage dealt to you. I learnt this sparring against enki in the shrimpalong and i was doing more damage to myself than i was to him due to his fantastic aosp armor)
1/3/5% damage based on rarity, and 10/30/50% extra crit chance based on rarity. the crit chance is pvp only and a percent of the weapons base crit chance. Like, a huge axe is 1% crit chance base, rare 1.1%, supreme 1.3%, fantastic 1.5%. Artifacts have the bonus crit chance removed because they're only fantastic and that'd be op or something.
It's not a flat bonus, Rarity adds 3/6/9% bonus to the amount of speed you get from ql+woa.