Darkcloud! wrote:This is an amazing post, thank you for taking the time to put all this together! I couldn't find a good place to snip it, because it's all so good!
With your points-
I think the pets are definitely being shown to at least 5 people at a time right now, based anecdotally off seeing a pet on my page + seeing who got it + who then posts about having also seen it. Having it up to 20 wouldn't be bad- after all, that's still better then odds you face when a user posts in the adoption forums that they're quitting.
When I mention seeing 2-3 rares, it would be over the course of the delay + pages, so the pool of users would go down as pets are claimed, meaning that the second or third rare that player sees, the chance rate of grabbing it would be (minimally) higher.
I agree that we'll never end up seeing exactly how the pound works, but knowing what the code-method is for choosing who gets the option to try for rares would put to bed a lot of the accusations towards individuals and speculation around botting.
i'm glad you found it usefull ^^
to be totally fair, i cannot confirm all of the math there is correct (as someone has already corrected it), but it was very interesting for me to try and piece it all together.
the amount of people is still a mystery, as we cannot gather that data for the entire pool, thus we can't know if every pet is shown to the same number of people or if it varies per pet.
as for the second/third etc page rares, i don't actually think the chances go up much, if at all. yes, the amount of users gets slightly smaller (though some people can come into the pound a bit late), but so does the pool of pets, especially rares. the 20 pet pull for the second page will likely have a very different pool composition than that of the first page as the percentage of rares gets lower relative to non-rares. while it is probably less drastic of a change with the waves, i still suspect that out of wave one most rares get picked out rather quickly while other rarities don't, leaving wave two rares among a higher relative percentage of below rare.
the change of the pool over time, however, is very user-dependent and probably uncalculable as it would require very large and fast tracking.
bookshelf wrote:interestingly this is not quite true. the odds of seeing a rare pet in a sample of 20 are MUCH higher than the odds of an individual pet being rare (that's the beauty of factorials).
let me try to compute it!
there's currently 1322 pets in the pound, 97 of which are rare (only 7.3%!!).
we can't account for any unnatural distribution or the fact that rare pets are now scattered throughout the first few pages, so assuming your first page of 20 pets is a truly random sample, you can find the probability of seeing a rare pet as follows:
# of ways you can see NO rare pets: c(1225, 20) = 1225!/[(1225-20)!20!] = 2.04 x 10^43 (giant number btw)
# of ways you can see pets: c(1322, 20) = 1322!/[(1322-20)!20!] = 9.46 x 10^43 (even gianter number btw)
now we can take a percentage by taking ways of seeing no rare pets/ways of seeing pets which gives about 22% of seeing no rare pets.
yup, that means there's a 78% chance of seeing at least one rare pet
this makes sense if you think about it because 20 pets is kind of a huge sample. 1322/20 is 66, which is less than 97, suggesting a distribution of more than 1 rare to 20 pets. the reason it's so hard to snag one is because tons of people are seeing the rare at the same time, so you have to be quick to snag it.
this does seem to be quite a big number, so in reality it's probably lower because of the behind-the-scenes manipulation of page distribution. and the new feature that spreads rare pets out is going to further make this number lower because it cuts the pool of rare pets available on the first page down quite a bit.
i also think our perception of pound rarity is skewed because most users probably just don't recognize many rares when they see them. like, did you know this chicken was rare? i certainly would have missed it.
however it's definitely true that the odds of seeing more than one are MUCH MUCH lower than the odds of seeing one. for example the odds of you getting a page of 20 rares is 135114119146959387435/94575315226397539842194003664749840563259356, which ends up being 0.00000000000000000000014% lol. so basically it's never going to happen.
(also, you said it doesn't mean that 13% of the pets on your page are rares: it actually DOES mean that. if the sample of 20 is truly random, it should represent the whole, meaning 13% of the pets on a page of 20 should be rare+ and 87% should be below rare, the same way 13% of the pets on a page of 100 or 200 or whatever number you choose should be rare+. of course it's unlikely you would get that exact distribution but it should be the average)(but then again it's prob not a random sample so)
if anyone wants to check my math please please please feel free!!! math was never my strong suit so i could have made errors.
thank you for the corrections! the last time i did math on this scale was like seven years ago and my brain cannot compute those formulas anymore.
good to know that the percentage is much higher than i initially thought (it did seem suspiciously low to me)!
to the last point - i totally agree that on average it should represent the total percentages, but as i mentioned in my first post, if we get a random 1000 samples out of every possible combination of 20 out of 1300 pets (which is basically your second giant number, much much higher than a 1000), there's no way every one of those samples will get that distribution, which is why it can't be expected that every person out of that 1000 sees 13% of rares on their page. some surely will, and the average distribution might align with the number, but each individual page will vary wildly, so my point was more of a "not every individual page has this percentage". then again, i could be totally wrong here - me and math never got along :3
(and yeah there's probably some coding to prevent wild extremes and such so we can't really know for sure)
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and as for the skewed perception, i very much agree with that.
i know i have missed rares in the pound because my brain didn't register them as such. it once took me a whole minute after the fact to realize a random wishlist pet i saw dated december 2021 was in fact an er re-release and not just an advent pet i missed that year lmao. in the same way, i stared at a store pet bunny which wasn't on my wl and dismissed it as an easter pet i must have already had.
honestly, having every rare on you wl is much bigger of an advantage than looking at the upcoming pound pool as it does actually help you spot them quicker, but i don't see people ganging up against that even though it's a more widely known and used feature.