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Relic Odds & Currency Efficiency

Lililira

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A thread compiling all the relic odds calculations I've done over the years. I'll fancy it up a little later with the full equations and such so folks can double check my math, but for now I'm just gonna copy & paste the raw values from the excel sheet I've been keeping.

Table of contents:​

Elemental Exclusives
Character Release Relics (i.e. Cosmic Premieres and such)
Shiny Odds


Posts will updated periodically as needed, so values shown reflect the values in game. (i.e. Elemental Exclusive odds will change as more Golds are added.)
 
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Lililira

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Elemental Exclusives Calculations​


Since Elemental Exclusive Variants appear both in Elemental Relics and in Holiday Relics, I ran the numbers for both to find the best way to get them.

EE variants + the last time they showed up in Holiday Relics:
Pyrotechnique (Fire) - Fourth of July 2020
Star Crossed (Wind) - St Patrick's Day 2021
Idol Threat (Water) - Halloween 2019 (missing from 2020 holiday relics entirely)
Grim Fan (Light) - Valentine's Day 2021
Megasonic (Dark) - Back to School 2020

Rarity Odds​

Elemental RelicElem +1Holiday RelicHoliday +1
Bronze82.0%0.0%0.0%0.0%
Silver14.0%92.0%90.0%0.0%
Gold3.5%7.0%9.0%98.0%
Diamond0.5%1.0%1.0%2.0%

Essence Shards

2575.0%50.0%
5019.5%39.0%
1005.0%10.0%
10000.5%1.0%

Elemental Relics for 3000 theo​

GoldsEE% per relicEE% per +110+16 500t packs (=18 single relics)
Fire120.29%0.58%3.50%5.25%
Water120.29%0.58%3.50%5.25%
Air110.32%0.64%3.82%5.73%
Light120.29%0.58%3.50%5.25%
Dark130.27%0.54%3.23%4.85%
Essence Shards38.552.0437.0993
EE% per relic = Gold% * Number of Golds
10+1 total = (EE% per regular Elemental Relic * # of regular Elementals) + EE% per "+1" Elemental Relic
18 single relics = EE% per regular Elemental Relic * # of regular Elementals)
Essence Shards = sum of all (Quantity * Percentage) + (# of 500t packs * 50 [aka the amount in each 500t pack] )

Conclusion: The 500t packs from the Store are a far better use of theo; the additional single relics outweigh the boosted odds of the 10+1, and the packs also give bonus essence shards. All further calculations will only use the 500t elemental packs since they are a far better deal than the 10+1 in all possible ways.

Total Relics for 5000 theo​

Elemental 500t store packs: 30 singles
Holiday relics: 10+1

Odds per relic of getting the Elemental Exclusive​

GoldsEE% per relic"+1"Elemental Relics for 5000t
Fire120.29%0.58%8.75%
Water120.29%0.58%8.75%
Air110.32%0.64%9.55%
Light120.29%0.58%8.75%
Dark130.27%0.54%8.08%
Holiday33.00%32.67%62.67%
Avg shards38.552.01655
EE% per relic = Gold% * Number of Golds
Holiday = (EE% per regular Holiday Relic * # of regular Elementals) + EE% per "+1" Holiday Relic
Elemental Relics for 5000t = 30 single Elemental relics = EE% per regular Elemental Relic * 30

Conclusions​

Holiday relics are the best choice by far, as the odds per relic is 10x the odds per Elemental relic, and if you splurge for the Holiday 10+1 you're practically guaranteed to get a gold from the +1, which has a 1 in 3 chance to be the Elemental Exclusive. Probably a good idea to wait until after the PF to buy them though, just in case you get lucky with the relics from the PF rewards.

Coming in second are the 500t daily elemental fighter packs in the store tab! 3 relics for 500t is a much better deal than saving up for a 10+1, since you end up with almost double the number of relics, which more than outweighs the +1's boosted odds. Plus, you end up with way more essence shards that way!


This post will be updated each game update that adds new Golds into the Elemental Relics. Last Updated: ver 4.6
 
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Lililira

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Character Release Relic Calculations​

Calculations done based on the assumption that '2x odds' means that the new character has twice the odds of being pulled as all other characters. (i.e. Annie has a 2/16 chance from Cosmic relics, all other characters have a 1/16 chance.)

Numbers over 100% mean you're likely to get multiple. (i.e. 300% = 3 fighters)

Table 1: Rarity Odds​

Premiere RelicPrem +1Jackpot RelicJackpot +1
Bronze82.0%0.0%0.0%0.0%
Silver14.0%92.0%90.0%0.0%
Gold3.5%7.0%9.0%98.0%
Diamond0.5%1.0%1.0%2.0%

Table 2: New Character Odds​

Premiere RelicPremiere +1Jackpot RelicJackpot +1Character RelicChar +1
Bronze9.65%0.00%0.00%0.00%82.00%0.00%
Silver1.65%10.82%10.59%0.00%14.00%92.00%
Gold0.412%0.824%1.059%11.53%3.50%7.00%
Diamond0.059%0.118%0.118%0.235%0.50%1.00%

Table 3: Currency Calculations​

Premiere RelicPremiere +1Jackpot RelicJackpot +1Character RelicChar +1
For 5000t333101n/an/a
For 10,000t666202101

Table 4: Odds of New Character for the Currency​

5000t​

Premiere RelicJackpot Relic

10,000t​

Premiere RelicJackpot RelicCharacter Relic
Bronze318.35%0.00%Bronze636.50%0.00%820.00%
Silver86.82%105.88%Silver173.65%211.76%232.00%
Gold16.06%22.12%Gold32.12%44.24%42.00%
Diamond2.29%1.41%Diamond4.59%2.82%6.00%

Assumption: 2/17 chance of new character, 1/17 chance of all other existing characters.

Assumption: Relic RNG rolls results using the following sequence: Rarity > Character > Variant. Meaning that every *character* has the same chance at being pulled, but results in the odds of individual *variants* being pulled is slightly different between characters. (i.e. Ms Fortune will have 5 golds in normal Premiere relics after the next update, but Valentine only has 3 since one of hers is an Elemental Exclusive. The Rarity > Character > Variant sequence means that if the RNG rolls a gold, both Ms Fortune and Valentine have a 1/15 chance of being chosen, but after that each Fortune variant has a 1/5 chance while each Valentine variant has a 1/3 chance.)

For the math, the equation is: Character Odds = 1 / total # of Characters
and Variant Odds = (Rarity Odds * Character Odds) / # of Variants of that Character

IMPORTANT NOTE: The above assumption may be untrue. In which case the RNG sequence is Rarity > Variant directly, meaning that every *variant* has an equal chance at being pulled, but the odds of each *character* vary based on the number of variants they have per rarity.

For this sequence, the math would be: Character Odds = Sum of all Rarities [ Variant Odds * # of Variants of that Character of that Rarity ]
and Variant Odds = Rarity Odds * total # of Variants of that Rarity

(aka way messier and more complex, so until I can find some strong proof for either, I'm just sticking to the simpler R>C>V math, as the differences between their final calculations for total Character Odds are pretty small. Also, the R>C>V math can be done now, while the R>V math can't be accurately calculated until the patch notes are released for the the new character's release and we know the total number of variants for each rarity.)



Alright, now that's out of the way, here's the number crunching.

Table 1: Rarity Odds
taken directly from the game

Table 2: New Character Odds
New Character Odds per Rarity per Relic = (2/17) * (Rarity Odds for that relic)

Table 3: Currency Calculations
How many of each relic can you get for notable quantities of theonite, based on prices taken directly from the game

Release Premiere: 150t each, 1500 for 10+1
for 5000t: 3 (10+1 price) + 3 (by the each) = 4950t
for 10,000t: ^^^ x 2 = 9,900t

Release Jackpot: 500t each, 5000 for 10+1
for 10,000t: 2 (10+1 price) = 10,000t

Hyper Pack costs 10,000t and gives one New Character 10+1

Table 4: Odds of New Character for the Currency
= New Character Odds per Rarity per Relic * total # of each Relic you could buy with that amount of currency


Conclusions​

The Hyper pack is the best deal by far if you can afford it, since it gives the most of the desired fighter, plus a 10+1 of all other characters.

The Premieres and Jackpots end up with pretty similar odds for everything except bronzes. I'd personally recommend the Premieres, since the bonus bronzes will make good fodder for skill point grinding and evolution fodder.


Calculations done using the New Characters odds, based on several assumptions based on how the relic randomizer works and that their release will be similar to Annie's; (i.e. Premiere and Jackpot variants with 2x odds of the new character, for the same prices as they were for Annie.) Inaccuracies will be corrected once we get closer to the new character's release date and we have more info.
 
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Lililira

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Shiny Odds​

We were told when shinies first released that each rarity had different odds of being shiny, so each rarity is tracked separately. We were also told that all fighters have a chance of being shiny, regardless of how they were obtained (Premiere relics, Rarity relics, CoC, PF rewards, etc.)

TotalShiniesCalculated Odds
Bronze97340.41%
Silver42061.43%
Gold30930.97%
Diamond4800.00%
Total134710
Note: some close approximate values added in.

Conclusions​

Something funky is happening here, but I don't know what. Based on what we were told, the gold shiny odds should be higher than the silver shiny odds, but they're not.

There must be something more going on here, like maybe the source of the fighter affects its odds of being shiny? Like, sources that guarantee the rarity of the fighter have a lower chance of being shiny (PF rewards and Rarity relics). Another possibility is that shiny odds vary based on how many shinies you currently have in your collection (possibly total, possibly based on natural or current /evolved rarity). Yet another possibility is that there's a tracker in the background that updates your shiny odds dynamically based on how long it's been since you got a shiny of that rarity.



Updated periodically. If you have any data, please feel free to share it! (Last updated: April 25th)

Please note: I need to know the total number of each rarity fighter you got from all the relics you opened in that pull in order to have usable data. Even if you didn't get any shinies from that pull, it's still good data if you tracked the rarities of all the fighters you pulled.

Other useful data: screenshots / list of all shinies in your collection (and their natural and current rarity!). I'm trying to figure out if that effects anything.
 
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Lililira

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...And that should be all the posts I need! Feel free to post while I get all the numbers and tables in place.
 
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Lililira

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Updated post 3 with the preliminary numbers for the Release Relics for the new character, based on the assumption that everything will work the same way it did for Annie.

Added the "Full Calculations" Spoiler to this post with the equations and assumptions I used to find these numbers.
(Note: I had to state some of the assumptions that went unsaid for the Annie calculations, now that we're getting 4th silvers and 5th golds for some characters that will probably be added into the regular relics. It's kind of a mess, and it's sort of going down a statistics-based rabbit hole in the name of 100% accuracy instead of settling for just 99.5% accuracy, but all assumptions still need to be stated for the sake of transparency.)

Maybe I'll run the numbers for the other possible RNG sequence ( R>V ) as stated in the post 3 spoiler at some point, but for now I need a break from number crunching. Math is Complicated and I am Tired.
 
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Lililira

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Y'all, something is really seriously wrong with Shiny odds for Golds and Diamonds, and in order to find out what I'll need some help from as many people as possible.

Thread link
Not sure I agree with a way of earning shinies, but definitely agree that something needs to change about their drop rates, especially since they currently seem to be *broken* for golds and diamonds.



I've been tracking shiny odds for a while now, and here's what we have currently: Thread Link




We were also told these things about shinies in the patch notes for their release: Thread Link


[snipped out sentences not relating to their odds]

However, based on the data, one or more of the statements shown above must be wrong.


At this point, I've gotten enough Gold data to consider what I have to be statistically sound, as even though we only have 1 Gold Shiny on record, the following statement *should* be true if everything is working as intended: "Lastly, the odds of finding a Shiny Fighter are increased the higher the rarity the Fighter is."

But it's not.

The on-record odds for Gold shinies is currently lower than, not just the Silver odds, but the Bronze odds as well.

And these Gold odds are even out of date, as for the last few month have been tracking every single Gold drop I've received via every possible methods (pf rewards, random pulls, gold relics, etc), and haven't taken the time to add them in for quite a while.


Assuming that all statements made in the release post are the way things are intended to be, Shiny odds are currently *broken* for higher rarities, and there's some kind of bug or design flaw that's responsible.

Something is seriously wrong here, and it needs to be looked at.


But, unless we gather some more data, we won't know how exactly. I have my suspicions though, and I *highly* encourage everyone reading to submit a screenshot of their full shiny collection to my tracking thread here: Thread Link


I think it might have something to do with how many fighters you have in your collection, either based on their natural rarity or their current rarity.

Please, submit a screenshot of your current shiny collection, list any shinies that you've received in the past that aren't shown, and screenshots of your full collection sorted by rarity and alphabetically. I'll be doing to shortly, both for data and to show exactly what I'm looking for.


EDIT: Having to break mine in two for all the images.
 
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Lililira

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Shiny collection:
IMG_4654.jpg
Shinies not shown: Frayed Ends dupe

Full collection:
Diamonds:
IMG_4643.jpgIMG_4644.jpgIMG_4645.jpg
Golds:
IMG_4646.jpgIMG_4647.jpgIMG_4648.jpgIMG_4649.jpgIMG_4650.jpgIMG_4651.jpg
 

Lililira

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Silvers:
IMG_4652.jpg
Bronzes:
IMG_4653.jpg


Totals:

Shinies:
Current Rarities:
- Diamond: 7
- Gold: 6
- Silver: 1
- Bronze: 0
Natural Rarities:
- Diamond: 0
- Gold: 2
- Silver: 4
- Bronze: 9 (counting Frayed dupe)

All:
Current Rarities:
- Diamond: 75
- Gold: 198
- Silver: 32
- Bronze: 22

Natural Rarities:
- Diamond: 25
- Gold: 9 + 6 + 9 + 8 + 6 + 9 + 10 + 9 + 11 + 8 + 7 + 11 + 12 + 7 + 8 = 130
- Silver: 7 + 3 + 4 + 4 + 4 + 7 + 4 + 11 + 8 + 7 + 4 + 4 + 4 + 7 + 9 = 87
- Bronze 3 + 6 + 8 + 6 + 5 + 8 + 4 + 5 + 3 + 6 + 3 + 8 + 6 + 7 + 6 = 56


(Note:

Counting is easy in-game using sorting and phone size to break it into chunks. For example, each of my screenshots is 11 columns wide, so I only need to count the number of full screenshots + any extra columns then multiply by 3 to get the fighter total for current rarity counts.

Natural counts are easier when filtering by character + sorting alphabetically, and *probably* only necessary for just the shiny chars, but I'm counting my full collection just to see if that might be affecting things.)



The whole reason for this is I believe that shiny odds are variable based on the total number of fighters of each rarity in your collection (which is part of the reason why they haven't been 'revealed', because they vary per player, with the intention that they're supposed to be weighted to help balance against bad luck ), however I believe it's being erroneously applied based on *current* rarities, rather than *natural* rarities as intended.

i.e. It's supposed to work like so:
You get a Bronze shiny -> The game realizes you have a *natural* Bronze shiny, so the shiny odds get weighted more towards *natural* Silver / Gold / Diamonds for your next shiny.

But it's actually working like so:
You get a Bronze shiny -> You transfer it to your evolved Gold of that fighter -> the game realizes you have a *current* Gold shiny, so the shiny odds get weighted more towards *natural* Bronze / Silver / Diamonds for your next shiny, reducing your odds to get a *natural* Gold shiny.

As a result, the more shinies of each *current* rarity fighter you have, the less likely you are to get a *natural* shiny of that rarity.



( So good luck getting a shiny for a natural Gold variant if you've been transferring the shiny status from your Bronze / Silver pulls to your evolved Gold / Diamond versions of those variants...

...and it'd explain why newbs seem to get more shiny diamonds than veteran players. Newbs have no other current diamonds for the game to weight the odds with. )


Just to finish out the math, here's all my *current* rarity shinies vs my total of that *current* rarity, which shows the kind of data curve that shinies should have based on their *natural* rarity (according to the release notes) to prove my point a little more thoroughly:
- Diamond: 7 / 75 = 9.3%
- Gold: 6 / 198 = 3.0%
- Silver: 1 / 35 = 2.8%
- Bronze: 0 / 22 = 0%
 
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BallotBoxer

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The math and probabilities stuff is hard for me to follow but I can contribute data! Here are my SHINY six:
6shiny.jpg
Two diamonds, two golds, one silver, and one bronze. They all hatched from character relics except for Harlequin Cerebella (Scorched Relic) and Inner Pieces Eliza (gold gift).
 

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( So good luck getting a shiny for a natural Gold variant if you've been transferring the shiny status from your Bronze / Silver pulls to your evolved Gold / Diamond versions of those variants...

...and it'd explain why newbs seem to get more shiny diamonds than veteran players. Newbs have no other current diamonds for the game to weight the odds with. )
Merlin's Beard!
This is unexpectedly sad to read.


I may not post my collection right now, as I have only 3 shinies.
But I have collected some nice amount of relics. I'll open them after the special characters (Beast, GG,etc.) are added to the premier relics.
I'll post here, may be in a table, all the variants I got.

Looking forward to that day!
😁
 
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Disasterrr19

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As a result, the more shinies of each *current* rarity fighter you have, the less likely you are to get a *natural* shiny of that rarity.
As much as I appreciate your efforts to figure out how Shiny roll works, I really doubt that the game counts *current* Shinies in your collection. Because when I got my first two Shinies (ShOps and Dreadlocks), I immediately transfered them to Diamond versions - and then, after that, I've pulled Shiny Shadow Puppet and Summer Salt withing 3 months from each other. I had another Shiny ShOps and pulled a RE. I have a lvl50 Gold Harle and I've just got Wulfsbane. And during all that time I've got only one single Shiny Bronze (Understudy... I WANT MY SPARK-SPRAYING RUSTY!!!).

This is my Shiny collection before recent pull:

D - Summer Salt, Shadow Puppet, Dreadlocks, Shadow Ops, Resonant Evil
G - Harlequin
S - Shadow Ops
B - Understudy

My recent pull (Shiny/Total):

D - 0/1
G - 1/14
S - 0/26
B - 0/71

I'll keep track and submit more data when I collect at least 100 new Fighters.
 

Lililira

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Thanks for your contributions everyone! It's helping a ton with figuring out what's going on behind the scenes here.

It's reassuring to know that my theory is most likely incorrect, but I still feel like there's probably some kind of balancing algorithm that's not working as intended behind the scenes due to how far off the numbers are from what we've been told should be true.

The other thing I was thinking is that drops with guaranteed rarity like Gold relics and PF rewards might have lower shiny rates than the ones of random rarity like Premieres and Jackpots. Would possibly explain why the data is skewed, considering most of the Gold / Diamond data that I've gathered from my own playthrough has been from rarity relics and PF rewards.


But I can confirm that PF rewards can be shiny! I got one today from the Painwheel PF rewards, so I took the time to add in the Gold data I've been collecting since the last time I added in a batch. (I screenshot all Gold / Diamond drops I get and then add them into the spreadsheet in batches, approximately once every 2-3 months.)
IMG_4708.jpg

That pulls the Gold shiny odds up above the Bronze odds again, up to 0.71%, but it's still not even close to the Silver odds, so who knows what might be happening there.
 

Disasterrr19

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But I can confirm that PF rewards can be shiny!
That is true, I've got my Shiny Harle and recent Wulfsbane as PF rewards.

While I did not keep detailed track of my pulls earlier, my own impression tells me that the chances should be along the lines stated initially by HVS: Bronzes < Silvers < Golds < Diamonds. I was opening relics without focusing on specific tiers, mostly Character, Elemental, and Premiere ones, and I have 1 Bronze, 3 Silvers, 3 Golds and 2 Dias. Well, I suppose I can explain having only one Bronze Shiny by the impact of guaranteed Silver and Gold relics.
 

Lililira

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Updated the Elemental Exclusive post.
- Added in which Holiday Relics typically have EE fighters.
- Re-ran the EE calcs for 4.6 and the addition of the new fire Fortune to regular relics.

Also, I plan to run the numbers for Theonite to Essence efficiency at some point when I have the time.
 
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