Hey everyone. I decided to do a little math and see how many catches it would take to get master angler, since I’ve seen exactly zero since the dark sea update released. There are some fundamental assumptions that I made to make this doable for me that resulted in a couple flaws that I noticed, but I don’t know how to deal with those myself. Also, if you see anything blatantly wrong with my math, please let me know! Here’s what I came up with
Fundamental Assumptions
First of all, the fish catch chances on the wiki are unconfirmed, so take everything with a grain of salt. The estimated values are as follows:
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Assuming we use a bronze rod for this and that the item chance stat is multiplicative, the chance to catch a fish would be 0.8 (item chance for bronze rod) times 88.7% (Chance to catch a fish given items are caught the rest of the time). Subtracting this product plus the chance for junk items (3%) yields a 90.36% chance to catch a fish with each catch.
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Next, I multiplied this percentage by the estimated chance to fish up each rarity of fish, being 87% for common fish, 10% for uncommon fish, and 3% for rare fish. With these probabilities stored. Next, I just found the probabilities for small giant, and golden fish, being 10%, 12.5%, and 3% respectively. This leaves the remaining 74.5% of fish as normal sized. It’s also worth noting that in insanity 1+ ranges of the dark sea, giant fish are replaced by their massive counterparts. I assumed the 12.5% chance for massive fish in the dark sea.
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Here is how I went about finding the average catches it would take to catch every variation of every rarity of fish:
Where n is the total number of fish within a rarity category (I got this from the Coupon Collector’s Problem, pls lmk if this is wrong). I used this for every region of fish, that being warm freshwater, cold freshwater, and ocean. I also excluded the giant eel and colossal squid from the giant and small chances for rare ocean fish. Here’s an example for expected number of catches for common fish in the warm freshwater region, of which there are 12 unique fish.
- I did this for every variant of every rarity of fish in every region. In total, there are 24 calculations for freshwater fish (12 warm, 12 cold) and 15 for ocean fish (3 massive). Here is the scuffed spreadsheet I made.
Ignore this:
Adding all of the expected number of catches calculations yields this number: 182,825. In my opinion, this is ridiculous, and I kinda like fishing. I know the master angler title is supposed to be exclusive, but this number is far larger than the unique title for the first person to reach 100k fish
Edit to the above part: I was silly and dumb and didn’t realize that the standard deviations of all the categories before rare golden are so far from the average of rare golden in each region that you can just add all the golden rare fish in each region and would practically guarantee all more common variant would have been caught by that point. Anyway, this brings the new total to an estimated 76,300 fish for master angler.
There’s some glaring limitations that I noticed. Firstly, this doesn’t include the rarity stat. I chose to leave it out for simplicity’s sake, but also because I heard that the graced enchant is bugged, and if its bugged, do we even know if its supposed to be multiplicative at all? Secondly, I’m not great at stats, so if you see anything wrong with this I’d love to change it.
Anyway, this begs the question, should the numbers be changed to make the master angler title more obtainable? Assuming it takes 30 seconds to catch a fish on average, it would take about 635 hours to obtain master angler by these numbers, and absolutely insane amount of time. Should the title be truly exclusive? Should the whole system be changed to make 635 hours of fishing fun? Feel free to discuss all of the above here 
