To go into specifics, the rarities are determined based off of how many of any given pet exists per active account. Meaning the more popular Bunny designs are usually less likely to be rare as they are hoarded by more people during the event. The less popular rabbit designs are less likely to be hoarded which means fewer of them exist. Which is why in 2020 the snow cloud Bunny is only UC. This year there were quite a few really popular designs so I would not be surprised if we got a bunch of UC. The random boxes are hard to judge because the amounts in existence are not selected by the players, however people tend to trade for outcomes they missed instead of spending tokens on them (to save more for Bunnies)
Based on an outdated explanation from Nick in 2009 this is around how the rarities work
Nick wrote:Right now the rarities are:
OMG so rare! (less than 1 pet per 1000 users)
Very rare (less than 1 pet per 80 users)
Rare (less than 1 pet per 25 users)
Uncommon (less than 1 pet per 5.5 users)
Common (less than 1 pet per 3 users)
Very common (more than 1 pet per 3 users)
OMG so common (???)
This of course was from over a decade ago and the rarities have since gone through two major updates (the last one bumped some pets down two rarities, and changed the system so that it only counted active accounts instead of all accounts) unfortunately though a visual scale of the new rarities does not exist.
If you're big on reading
This is the "Understanding Rarities" guide and it goes through all of the variables that can impact a pets Popularity/Rarity