Average item level theorycrafting questions

I'm researching how average gear item level works in WoW (acknowledging accuracy and relevancy could change in Legion), and I can't get the math to come out in any way that makes sense.

Check out the following armories (Thanks to @Veryscary and @raziel83 for posting these).

http://us.battle.net/wow/en/character/stormscale/Veryscarý/advanced
http://us.battle.net/wow/en/character/malganis/Ijustreroll/advanced
http://us.battle.net/wow/en/character/malganis/Ghman/advanced

No matter how I do the math, I can't get the average item level to come out to what Blizzard shows.

I found some interesting notes from years past that further cloud the situation.

First, this poster claims that average item level throws out your best and worst piece of gear when calculating your number.

http://www.wowhead.com/forums&topic=176708/average-item-level#p2439477

...But this doesn't seem to be wholly true, given the impact on ilvl that the Bottled Tornado has.

Next, the following post says that calculations differ depending on whether you fill every slot. If that's true, then would it be better to leave a slot empty in some cases?

https://greenleewow.wordpress.com/2012/06/17/how-does-item-level-work/

This would probably only apply to the lower brackets (19-29) which would suffer the least impact from having an empty slot.

I'd appreciate any insights you have on how Blizzard calculates average ilvl.
 

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