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So infact it is nothing but a tag currently. "Rare" items drop as often as "uncommon" or "common" items. The reason why "common" items seem to dominate the spot here is basically because once developers found out that it has a hot ZERO in terms of influence on the drop rates they stopped giving a shoot about tagging their items accordingly so they just grabbed the default which is "common".
The only thing actually rare about "Rare" is the amount of items being tagged as such.
Thats at least the case for your requested items. There are infact items on Steam that have actual probabilities based on rarities but those are just the ones received from actually playing the game such as wearables on Unturned.
For further information read through this:
https://partner.steamgames.com/doc/features/inventory/itemtags
https://www.steamcardexchange.net/index.php?gamepage-appid-374320
Since the number of tests is very large, it can be considered that the number of presented items completely correlates with the number of dropped out.
I read carefully what is written in the documentation. There we are talking about setting up tags and chances of IN-GAME items.
The following quote refers directly to the icons and cards: "Some features like Trading Cards can be set up entirelessly in the Steamworks portal."
Therefore, we will wait for the person who is engaged in the development of games and saw this page live. I'm trying to reach out to a few people.
An external source which does not provide ANY sort of source and infact claims not to be partnered or anything with Valve and furthermore not claiming 100% rock-solid facts but guesses.
Which is essentially what I've done multiple times because I once was at exactly your position. The average human being would think that there has to be something about those rarities but - and you will learn that sooner or later - there is not.
Anyways. Why exactly are you asking when you seem to be sure to know it better anyways? No offense here but I am sure that you got my response a lot of times already given your footnote...
Now guess what: you got that answer a few times already because it is basically what the situation IS. For emoticons and backgrounds there is no such thing as rarity. It is just fancying up those items. Which is basically the reason why the market is pretty much equal for "rare" and "common" emoticons.
You didn't even follow the link.
Then I will explain what this example is:
current number of "common" quality backgrounds from Dark Souls 3 on the market is (635 + 618 + 439) = 1695
"uncommon" = 433
"rare" = 169
Total number of all items = 2297
Assuming that the images themselves are about the same attractiveness (people do not want to keep themselves something specific), we get that the number of items offered on the market corresponds to the number of items created in a long period of time.
This is followed by the numbers:
"rare" = 169 / 2297 ~= 7%
"uncommon" = 433 / 2297 ~= 19%
"common" = 100 - (19 + 7) ~= 74%
Thus, the assumption that items have the same rarity is refuted.