How does rarity and find frequency work????

[Persicaria]

The rarity of a card most definitively does correlate with the odds of it being pulled, but it doesn't seem to correlate at all with the frequency that it is found.
For example, Sanctaria was found 695 times (according to the Finds History), and since S3 started 760 days ago, that means it's found by someone nearly once a day. But West Chanchajilla, a completely normal common card, was found 626 times, making it marginally rarer. Many other cards seem to be twice as rare, some extremely more rare, but it all fluctuates and seemingly has no rhyme or reason.

[Riemstagrad]

Rarity doesn't affect the spawn rate.

At the start of a season, all cards are given rarities:
0.1% = legendary and 3% = Ultra rare for example.
All cards are thrown into one pool and have an equal chance to spawn when you open packs.

That's the basics. There are some more mechanics that chance the spawn rate of nations that ceased to exist and there is a chance that you pull a pack with cards from a previous season.

[The Ambis]

So, as already said, all the cards are thrown into a big old pool, and the only reason that commons are more common is that there's more of them.

If I reach into a bag of 100 marbles, and 50 are grey, 30 are green, 10 are blue, 5 are purple, 3 are gold, and 2 are yellow, I'm gonna draw the grey ones more than anything.

However, now assume that each marble has some other unique identifier, like stripes or spots. I'll get the same yellow ones more often than I will the greys, cause there are fewer yellows than greys. Overall, I'll get yellow less than I get red, but I'm theoretically going to get the striped yellow marble since there are only two yellows I could get than I will the speckled grey marble.

Does that make any sense?

[Atlanc]

So, as already said, all the cards are thrown into a big old pool, and the only reason that commons are more common is that there's more of them.

If I reach into a bag of 100 marbles, and 50 are grey, 30 are green, 10 are blue, 5 are purple, 3 are gold, and 2 are yellow, I'm gonna draw the grey ones more than anything.

However, now assume that each marble has some other unique identifier, like stripes or spots. I'll get the same yellow ones more often than I will the greys, cause there are fewer yellows than greys. Overall, I'll get yellow less than I get red, but I'm theoretically going to get the striped yellow marble since there are only two yellows I could get than I will the speckled grey marble.

Does that make any sense?

I think you missed the mark with that last example and conclusion, though.

A better one would be assuming each marble has a unique number (from 1 to 100) on them (still 100 marbles with 50 gray, 30 green, 10 blue, 3 gold and 2 yellow). If you close your eyes and pick a marble from the 100, the chance you get the marble with the number 1 and the chance you get the marble with the number 100 would technically be the same, no matter their colors, since they are all have unique numbers. In other words, if you are aiming for one specific card without caring about its rarity, the chance you can get that card is the same even if it is common or legendary.

So it is technically correct for Sanctaria card to be found almost as often as West Chanchajilla (we are talking about, idk, thousands if not tens of thousands of cards being found every day here, 695 and 626 are very small in comparison that they can be considered approximately the same).

[Riemstagrad]

This difference between Sanctaria (Legendary) and West Chanchajilla (a common) can be explained by the fact that cards with rarity Rare or above have a slightly higher chance to spawn then a common or uncommon.
I didn't mention it because of the rather small effect. It works like this:
If the first 4 cards in a pack are all commons, the 5th card is ALWAYS Rare or above. With about 2/3 of the cards being common, that effect becomes noticable in the long run. The effect fades as the season ages and relative amount of commons goes down.

I have made a spreadsheet that calculates the spawnrates of a given card. It predicts for Sanctaria to spawn once every 1.04 days and for the common to spawn once every 1.11 days.
If we look at how often both cards are actually pulled:
Sanctaria: 696 = once every 1.04 days
West Chanchajilla: 626 = once every 1.15 days

[Persicaria]

So, as already said, all the cards are thrown into a big old pool, and the only reason that commons are more common is that there's more of them.

If I reach into a bag of 100 marbles, and 50 are grey, 30 are green, 10 are blue, 5 are purple, 3 are gold, and 2 are yellow, I'm gonna draw the grey ones more than anything.

However, now assume that each marble has some other unique identifier, like stripes or spots. I'll get the same yellow ones more often than I will the greys, cause there are fewer yellows than greys. Overall, I'll get yellow less than I get red, but I'm theoretically going to get the striped yellow marble since there are only two yellows I could get than I will the speckled grey marble.

Does that make any sense?

I think you missed the mark with that last example and conclusion, though.

A better one would be assuming each marble has a unique number (from 1 to 100) on them (still 100 marbles with 50 gray, 30 green, 10 blue, 3 gold and 2 yellow). If you close your eyes and pick a marble from the 100, the chance you get the marble with the number 1 and the chance you get the marble with the number 100 would technically be the same, no matter their colors, since they are all have unique numbers. In other words, if you are aiming for one specific card without caring about its rarity, the chance you can get that card is the same even if it is common or legendary.

So it is technically correct for Sanctaria card to be found almost as often as West Chanchajilla (we are talking about, idk, thousands if not tens of thousands of cards being found every day here, 695 and 626 are very small in comparison that they can be considered approximately the same).

Ah, i see, that does make a lot more sense. I'm so used to gacha games (which mostly work by picking rarity first and pull from an infinite pool) that it didn't occur to me that rarity correlates with the number of cards. Thanks for the explanation!