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Way to gloss over the Wizard's all-important victory, there Conan. "Fighters lost?! Let's talk about races!"
S'all good. You fought valiantly...which I suppose is self-evident...being fight-ers and all.
And just for anyone who fell for your false title and misleading lead...
WIZARDS WIN! THEEEEEEE WIZARDS WIN!!
*ehem* Carry on. You were saying about races?
EDIT: About the races...if you're going to add in aasimar, and I can't really see why you would, thereby using "what's in the DMG" then it would seem only fair (though I despise them) to include Eladrin as well. They are both presented in the DMG. Separately out Drow (which I completely agree you should do), would seem to further support the inclusion of the other "example sub-race in the DMG."
Personally, I'd go with the smaller option...and, granted I don't quite follow/know about all of this polling/statistical business...but I don't see why any race should/would be getting a "by."
OK, so then, the base 4 get the "bye/by/buy." Human, Elf, Dwarf, Halfling. That makes sense.
So, the obvious pairings would then become:
Dragonborn v. Tiefling
Half-elf v. Half-Orc
Drow v. Eladrin
Gnome v. ...?...Aasimar? [using DMG races but not supplements]
If you don't pull anything from the DMG, then you could just have:
Dragonborn/Tiefling
Half-elf/Half-orc
Drow/Gnome
...but then you only get/using 10...which I gather you don't want.
Dominate Person. Now my wizard can rewrite the laws of reality AND hit things really hard with pointy bits of metal. The fighter just didn't stand a chance.
I think overthinking the races, and planning the rankings, will pre-judge the results too much.
If it's elf vs. the winner of drow/eladrin, or half elf vs. half orc, or halfling vs gnome, I think there really won't be a real competition. I say mix it up! no byes! random seeds! shorter round times! blood on the floor!