Rare item creation

[whathuh]

To find the rarities, I looked it up in the Affic Calculator. 
Your assumption is wrong.  The alvl can be higher than the ilvl.  Generally speaking, the alvl cannot be higher than max(qlvl, ilvl).
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I looked up on the affix calculator and found out that there is a reason for my claw having an alvl higher than my ilvl. The ilvl is still 1 on the claw, but rare weapons can't have less than a max alvl of 14. Also, an ilvl 60 war sword (dropped by normal baal) can't have the Berzerker's and Sounding prefix. For some reason, the alvl on rare weapons is much lower than the ilvl. To get an alvl of 50, you'd need it to be an ilvl of 63.