I'll take one more crack at this, then drop it.
I think the misunderstanding is in the terminology. You seem to think the original poster was looking for a ratio of kills to deaths in the arena, which will of course be approximately 1:1. In your calculations there is no averaging done, only a ratio of kills to losses.
I think what he was looking for was an average of "individual" player's k/d, not the arena as a whole. So he could compare his k/d to an average player's k/d.
If you accept that each player has a k/d figure, you can then average those figures.
average individual k/d = pilot1 k/d + pilot2 k/d + pilot3 k/d.../number of pilots
bowser