Hoping the plots are self explanatory. Stats used was 10 million samples.
Building a Single 5* from Latests (Starting at 0/0/0)
Building all Three 5* from Latests (All Starting at 0/0/0)
I will post more plots in this thread as I make them
Since everyone seems to be in an uproar about the specific value of 5:1 cover exchange, I was curious how tuning this knob affected things. Now, in theory the maximum size of the storage and the exchange rate could be different values, but in the new system they are identical. My simulation doesn’t currently allow for these knobs to be tuned independently.
Effect of N:1 on Building Single 5* from Latest
Instead of flooding the above plots with 100s of curves, I extracted the averages and variance of the distributions and plotted them as a function of Exchange Rate, or Storage Max.
Since the exchange rate is linked to a full storage, decreasing the exchange rate creates more waste. The exception being if you decrease it all the way to 1 (the old CS value). Increasing the storage reduces waste, but then the number of pulls approaches the No Swap limit.
So with the new change I’m considering switching back to Classics. Less fear of wasted covers. Anyways, I wanted to get some numbers so I had some idea of what I was up against. Modeling Classics is a bit complicated for 2 reasons
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Dilution outdating my numbers every few weeks
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Classic characters are almost always partially built to some degree so modeling from 0/0/0 isn’t as useful
To deal with Dilution I needed a method to model the effect dilution has on the PDFs. Then I simply ran the code for every possible build permutation to get an idea of how many pulls are needed to finish specific characters on my roster.
Modeling Dilution
With each new character that is added to the token, the PDF shifts to the right and becomes wider (shorter). I then extracted the mean and variance from these curves and plotted them as a function of how many characters are in the token.
At this level of dilution, both the mean and variance have a trend that is approximately linear. The non-linear effects are observed at low dilution, but since dilution is a problem that only gets worse, this should model the change for the foreseeable future.
I was also curious what affect the BH had so I ran the code with and without it, Its pretty substantial.
Averages/Variance for Classic Characters with Dilution Adjustment for each Build Permutation
The character was started with the specific build permutation and 0 covers stored.
Here is a link to my google sheet with tons of numbers. Great reference if you can make sense out of it.
https://docs.google.com/spreadsheets/d/1Jx4p2YF0GeVqzT_OvlMjawp-JlLEfV_FLsvfokhG_Oc/edit#gid=441349777
Same Table as above for 4* Characters
Keep in mind that my code only models finishing the character using token draws. There are many other opportunities in the game to acquire 4* rewards that are not modeled here.
The character was started with the specific build permutation and 0 covers stored.
Due to the much higher dilution, Bonus Heroes has an even larger impact here.
For Classic 5* the BH cuts the average pulls in half approximately, but for 4* it reduces it by 80% or more. If you focus on one 4*, the character is built almost entirely out of BH covers.
Great info but I need a 5 year old explanation of most of this cuz trying to read it my eyes gloss over and brain turned off due to overheating
I was going to ask for a TL;DR myself, yeah.
A TL;DR version, ok
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New exchange system is awesome
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Removal of CS exchanges stinks
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Changing the exchange rate doesnt have that much of an effect, unless you make it to 2:1 or 1:1
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Token Dilution stinks
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Bonus Heroes are awesome
Now I understand, Thanks.
The information you post is awesome.
I have some questions that may or may not be answered within this data.
If I’m a 5/5/0 build with 5 covers already stored in the saved cover system.
How many pulls will I need to hoard to finish this character?
Same question but with different build variations. 5/5/1, 5/5/2, 3/5/3, 3/5/4.
To me this is the data that will be most important because I have no reason to change what I’ve already been doing before until I run into one of the above situations. Then and only then will I consider hoarding in order to safely complete the character without wasting covers or using the 5:1 trade in.
Well its partially answered, but you need to give me more info.
Assuming this 5/5/0 is a 4*
570 ± 270 without BH
134 ± 63 if you BH
Also these stats assumed empty storage. For your character the numbers drop from what is in the table.
so perhaps 5/5/1 is a better reference since you closer to it
396 ± 234 without BH
93 ± 55 with BH
Technically you are somewhere in between these two points, but closer to the 5/5/1. Every time a character is added into the token, the numbers increase. The amount they increase is the slope.
Holy math, Batman! Great job Hadronic, the breakdown really helped clarify the new landscape (once you broke it down to 5yr old lvl for me anyway)
So with the new sistem and pulling latest, if you´re lucky, it takes around 80 pulls more to finish a new 5*. Lovely.
Great analisys Hadronic, i just love me some plots 
2:1 or 1:1 seems fair for 5* covers. I’m a day 1635 player who buys VIP and Logan’s Loonies when on sale. My highest level character is 453. I have used the CS cover swap 3 or 4 times before but never more than once for the same character. I have sold 4 or 5 unusable covers across all of my 5* characters.
A policy that that requires you to accumulate 5 unusable characters in a single 5* character is essentially the same as having no saved cover policy at all for that tier.
So if they turned off cover save for 5’s but left it in place for 2-4 stars that would essentially be the same as what we are actually getting?
Stop exaggerating. True they could have been more generous to the players with this change (like the 2 years of cover swaps they offered to players while not having to). For an in game system this works fairly well to address the issue of 6th cover frustration.
I just hope they don’t listen to people who want to make the exchange rate smaller. I never actually plan to use the bank to exchange covers and instead plan to use it as a storage area while I try to cover characters naturally. The bigger the bank the less waste there. As Hardonic said, 1:3 would be the worst. I say either make it 1:1 for Latests or make the bank bigger if you make any changes at all. I’m scared that people who don’t understand what this actually is are going to ruin it and make it worse.
no one has ever asked for the bank to be smaller though, just the exchange rate. i think people are just over reading that comment.
Yes, but given the current setup, the size of the bank is dependent on the exchange rate, so decreasing the exchange rate will probably decrease the size of the bank too. This is something I hadn’t considered when making my initial comments, and I wouldn’t be surprised if other people hadn’t either.
I, too, wanted a lower exchange rate before I considered this aspect. I think I would rather have 5:1 with a 5 cover bank instead of 3:1 with a 3 cover bank. I can’t see the devs dropping the ratio to 3:1 and still letting us keep a 5 cover bank.
Made a web version of my code. Its much slower than my local version, so i had to remove some features.
https://script.google.com/macros/s/AKfycbxN_tv6BD3fVwM3WrYjqnSmmz2k3Aky1ZV-ZXwVKnfLyR9m1Wps/exec
My Okoye is currently 0/5/0. Without swaps, what are the odds I will be able to champ her without having to use the Saved Cover feature?
(I am opening as much as I can while swaps are still available. Once swaps stop I will probably hoard for a while since Jessica and Cap are already champed…)
Pulls needed to finish Character:
227.438 +/- 88.098
Expected number of wasted covers:
1.353 +/- 2.524
Expected number of bonus covers:
1.715 +/- 1.260
Expected number of exchanges:
0.000 +/- 0.000
Probability of no waste:
62.450%
https://script.google.com/macros/s/AKfycbxN_tv6BD3fVwM3WrYjqnSmmz2k3Aky1ZV-ZXwVKnfLyR9m1Wps/exec