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You mean lock boxes? I don't think so. I get just as many Blues out of lockboxes on all my characters as any other character.
What can have an effect is the location of the lock boxes, and to an extent the level of the lock. When they first set up Legerdemain, Zones 4 and 5 for each alliance would have more of a chance for Blues and even Purples than say Zone 1 or 2. And I tend to find better loot in the Advanced lock boxes than in the simple or intermediate ones. Not that i have not found Blue items in Simple chests, it just does not seem to happen as much.
When One Tamriel dropped, I think this zone effect on lockbox loot was relaxed somewhat. But still your homes with Advanced locks on the doors, noble houses and the like still give better return on the Blues and Greens.
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PakKat "Everything was going well, until I died"
Gary Gravestink "I am glad you died, I needed the help"
It affects the loot that isn't fence items that you can also find in these boxes (aka set gear). The only thing that affects the quality of the fence items you get is your legerdemain skill. Having it maxed gives you better quality items (that change came with 1T update I think).
This Bosmer was tortured to death. There is nothing left to be done.