Your rank is based on your Elo rating. You can look up Elo in Wikipedia for a detailed explanation on how it works, but here's the short version. If you have a low (bad) Elo rating and you kill someone with a high (good) Elo rating, then you will improve substantially and his Elo will worsen. But if the high Elo rating guy kills the low Elo rating guy then neither player will see much if any difference. That's because a good player killing a bad player means little, and a bad player killing a good player is noteworthy.
Why does my rank go up and down so much?
Let's say for arguments sake that a person ranked #100 has an Elo of 2200. A person ranked #3000 has an Elo of 2000. If #3000 plays really well (or get lucky kills on high ranking people) then let's say his Elo increases to 2050. Since there's 3000 people between 2000 and 2200, the ranking can improve many more places than just the 50 Elo points. That's how small changes in Elo can have a large impact on your ranking.
Why does my rank fall when I don't play?
That's because your Elo rating is static if you're not active, and other people are playing and passing you up.
I think the ranking system is stupid!
Maybe it is. It's just for fun. Try not to let it impact your play style.
To wrap it up in a nutshell, kill:death ratio matters not. It's who you kill and not how many. Killing sprees, multi-kills, rewards etc. have no impact on your rating. However I believe that team based objectives (destroying core, returned flag etc.) does improve your Elo rating.
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