Complex probability calculations for obtaining skins

[Pandawee]

Hello "my name" on PS4 is Pandawee ( ADC me *-* ), this is my first post here so I hope I'm doing everything right and forgive the English of the Google translator.
I am a PS4 player and have been playing DST for many years almost every day. Over time I saw the game go through several changes and additions.
I love to collect skins and believe me if it wasn't for the system of unraveling skins I would have a bigger shoe collection than my girlfriend.
 I usually buy everything the game launches but  I had to gather my team of scientists to do some analysis.
Technically the chance of dropping items of a greater rarity decreases as more items are added, the items that we can acquire via money from the packages are great but items that are 
not obtainable in this way end up becoming "even rarer" and the As content was added, my hopes of acquiring some of them were greatly reduced.
Don't get it wrong, I always want a lot more content, just like all the players, and I think Klei should launch more items that are not only obtained by packages. But would it be possible to
 reduce the chance of dropping an item that you have already dropped to an acceptable level?
I get a lot of repeated items, last halloween despite saving all my clothes to change I didn't get anything, just like many console players. And that was repeated in the last halloweens that I played too.
So although this is not a priority, after all the company has a thousand more important things to do, there is a possibility that in the distant future it will be possible to obtain items like 
Glommy Head Guise or the pots and so many others that "RARELY!" do we see on PS4? And as for the items that were obtainable just by buying Klei's 
physical products, are there any plans for us on the console to redeem?
Thank you for your attention in this long, long, long text full of misspellings and regrets.

[Marco BR]

Welcome to the forum my friend  , we played for a long time together and i can say that he really studied these probabilities a lot, with the addition of content and a greater number of skins being implemented, the chances end up decreasing, but on the other hand, almost all new skins  added are "elegant" also becoming difficult to obtain, balancing things a bit ... in the last time I’m seeing more players winning roseate and triumphant skins, maybe the odds adjust to the amount of skins available to drop,  our maybe i'm wrong  hahahahahaah

[Pandawee]

Always have spaces for shoes and pink polo shirts my friend dshkgjkjsdhg

[CarlZalph]

I know you can set the font size for the text on here, but with that size I am not going to copy paste it into another program without the formatting.

If you're wondering what the stats are for drops tiers, then JoeW posted those a bit back.

[Pandawee]

22 hours ago, CarlZalph said:

I know you can set the font size for the text on here, but with that size I am not going to copy paste it into another program without the formatting.

If you're wondering what the stats are for drops tiers, then JoeW posted those a bit back.

The statistics are not updated with the new additions. Sorry for formatting.

[Tom_P_Moleman]

From a mathematical point of view, you are absolutely right, as the drop rates do chance with the addition of new items.

BUT, as a software dev myself I would have chosen a slightly different approach though. 

In a first step I'd retrieve a random 'rarity-level', whereas the outcome always would be x% for 'Common', y% for 'Distinguished' etc.

And then in a second step I'd fetch any random item from within the entire pool of items with the given 'rarity-level' from above.

 

This way you'll always be given the same chance for retrieving any 'Common/...' item no matter how many items of that kind exist in total. 

BR Tom

[CarlZalph]

1 hour ago, Pandawee said:

The statistics are not updated with the new additions. Sorry for formatting.

I assume the probabilities between the console and PC versions are the same, since they've both been updated past this update:

But the important bit:

Common: 52.7%
Classy: 26.0%
Spiffy: 13.0%
Distinguished: 6.0%
Elegant: 2.3%

Use this percentage and you can find the odds of getting any one item by using the total item count in that pool.

For example, a specific elegant would be: 0.023*(1/#elegants)

[Pandawee]

When I say that the statistics are not up to date, I refer to the fact that with new variables the equation changes. I will try to explain it in the following way, we assume that you bought a tray of twelve eggs and in it came a single egg of another color. Once a day you make an egg and refill the tray. But always with eggs of the same color. The probability that you will remove that colored egg one day is not one to eleven, it is random but within this range of 12 eggs. Now think that you bought two more trays of 12 eggs each with one colored egg each, the probability that you will take a colored egg does not change but the probability that you will get that first colored egg has decreased significantly.

 

So as new items arrive, 2.3% are still valid, but when it comes to obtaining a specific item, they reduce more and more.

[Tom_P_Moleman]

1 hour ago, Pandawee said:

Once a day you make an egg and refill the tray. But always with eggs of the same color. The probability that you will remove that colored egg one day is not one to eleven, it is random but within this range of 12 eggs.

So, if you'd always replace the egg you've eaten with a raw one of the same colour, you'll always end up with the exact same probability for each colour variant per se, as upfront you are always likely to get a 'white egg' in 11 out of 12 cases and a 'brown egg' in 1 of 12 cases. With more potential egg-boxes being available these percentages won't change either, but the chances for retrieving one specific egg changes drastically.

=> This is what I'd ensure as well if I had to come up with the drop-retrieval algorithm as explained above. And those percentage-values posted by Klei (and quoted by @CarlZalph above) are exactely that.

No matter how many 'Common' items would exist in total, you'll always get any with a percentage of 52.7.

So just like @CarlZalph also already mentioned, with the addition of new items merely the likelyhood for one specific item changes.

Equation: PercentageForRetrievingSpecificItemOfAGivenRarityLevel = PercentageForRarityLevel * (1 / AmountOfOverallItemsOfThatRarityLevel)

These 'statistics' are still up to date, as these would refer to retrieving any item of a given rarity level though. Klei never stated anything different apart from that afaik. 

[zVince]

I do not know how it works but for me only comes common skin

[Pandawee]

3 hours ago, Tom_P_Moleman said:

So, if you'd always replace the egg you've eaten with a raw one of the same colour, you'll always end up with the exact same probability for each colour variant per se, as upfront you are always likely to get a 'white egg' in 11 out of 12 cases and a 'brown egg' in 1 of 12 cases. With more potential egg-boxes being available these percentages won't change either, but the chances for retrieving one specific egg changes drastically.

=> This is what I'd ensure as well if I had to come up with the drop-retrieval algorithm as explained above. And those percentage-values posted by Klei (and quoted by @CarlZalph above) are exactely that.

No matter how many 'Common' items would exist in total, you'll always get any with a percentage of 52.7.

So just like @CarlZalph also already mentioned, with the addition of new items merely the likelyhood for one specific item changes.

Equation: PercentageForRetrievingSpecificItemOfAGivenRarityLevel = PercentageForRarityLevel * (1 / AmountOfOverallItemsOfThatRarityLevel)

These 'statistics' are still up to date, as these would refer to retrieving any item of a given rarity level though. Klei never stated anything different apart from that afaik. 

The post itself was never about the rate of obtaining rare items but about the rate of obtaining certain items like the one I mentioned the name. It was not me who started this conversation about obtaining fees at GENERAL. There is no clear problem with these rates, they are reasonably consistent, but it is precisely the difficulty of obtaining specific items that increases, making as I mentioned, certain items increasingly rare given their difficulty in appearing as more packages are added .

For me the drops are quite good, I get a lot of elegant items, but items I already own and sometimes several times the same item. Of course, I don't play especially for the clothes but they are a differential in the game for those who have played for so long.
 

So, for a better understanding, let's put it this way, the statistics related to obtaining a certain item are not updated, because whenever variables are added they are distant from the initial value.

I think it's nice that certain items have their rarity consolidated in this way but at the same time it is frustrating to receive the same items over and over again. I'm in that "Wow, a new gift ... Ok, whatever."