First of all, love the site! Both of my guilds use it extensively
Average item level is 113 but gear score is 0? Huh?
Average ilvl is 113 but you have 7 green (uncommon) items, so they are not counted as much as rare or epic itels lvl 113.... For example, if a group of 10 ppl with similar gear enters Karazhan, they would have a bit of hard time there, unless they're very skilled. Ok, you have 3 PvP epics, but still...... a score of 0 for gear sounds close enough.
This char has 3 green items and 5 non-pvp epics, so it would be normal that he gets better score. I suggest upgrading those 3 greens into at least some items from heroics, and you're score will be boosted quite a lot.
Gear score was 45. Upgraded from a green 102 head piece and a green 88 leg to blue 115's for both. Gear score went DOWN from 45 to 16. What gives?
This sounds soooo wierd, I'll check it out, but I'm sure it should not ever happen. Maybe you had some good enchant on both of them? Still, it shouldn't go so low. I'll take a look