So the ranking system works like this to my understanding. Their are 5 Tiers ranked Bronze - Silver - Gold - Plat - Diamond and in these there are 5 ranks you need to work from 1 up to 5 then you will be placed in the next tier up. After these there is Onyx which seems to be a number rating which is the top in the world for example if you are rank 1536 then you are 1536 best in the world in that playlist. in not sure what the lowest rank in Onyx is but when you reach the top 200 your rank changes from onyx to Champion which is the top 200 people in the world.
From experience it seems whether you go up or down is hugely based on Win / Loss but it also takes into account something else what that is IDK whether it be KDA or medals earned im not sure. hope this helps.
Please post if I missed something and I will correct it.
EDIT: If you manage to achieve a certain rank such as Champion and you lose it it will only show you current rank from what I understand I was rank 107th in the world for SWAT and took an Xbox screen shot to display. As I knew it would probably go by morning which it did, now I’m 1500 orso.