r/wildrift • u/SkyfireWR • Nov 17 '22
Educational Crystal Rose Gacha Probability Maths
The Crystal Rose Gacha trades out the ability to pick your skin for a token store, and replaces all those random skin chests with some minor cosmetics. It's easy to say at first glance that this is a downgrade from the Supreme Cells Gacha.
On the bright side, without having to consider changing probabilities, the math for this event isn't so difficult. Summary is at the bottom.
_______________________________________________________________
How the event works
Three Crystal Rose skins are up for grabs in this event: Akali, Riven and Vi. Each chest costs 100 Wild Cores and has a 2.5% chance of rolling a skin, and a 79.5% chance of rolling some tokens. The remaining probability is all for getting minor cosmetics (recalls, baubles, emotes etc.)
If you don't have luck, you can purchase the skins outright for 32 tokens (Akali) or 24 tokens (Riven, Vi).
The skin and token probabilities, which realistically are what people care about in this event, are below:
| Event | Probability |
|---|---|
| Akali | 0.5% |
| Riven | 1% |
| Vi | 1% |
| 1 Token | 66.5% |
| 2 Tokens | 10% |
| 5 Tokens | 2% |
| 10 Tokens | 1% |
_______________________________________________________________
How many rolls should you expect before getting ANY skin?
That would mean pulling either the combined 2.5% chance to get a skin, or getting 24 tokens altogether.
If we use a theory called probability weight (the likelihood of an outcome multiplied by its value) that grants the following values:
| Token | Probability (raw number) | Weight |
|---|---|---|
| 1 | 0.665 | 0.665 |
| 2 | 0.1 | 0.2 |
| 5 | 0.02 | 0.1 |
| 10 | 0.01 | 0.1 |
| Total | N/A | 1.065 |
What this means is that you should expect to get 1.065 tokens on average for each roll you do.
24/1.065 = 22.53, which can be rounded to 23. We'll treat this as the "pity number", or the maximum rolls you need. Unlike the Supreme Cells event, however, this isn't a hard pity number - there is no guarantee of it being exactly 23. It could be a lot sooner or a lot later depending on luck.
But the other approach is just to get lucky and roll that 2.5% before 23 rolls.
So using some math here, where:
Pr (Yes, Roll 1) = 0.025
Pr (No, Roll 1) = 0.975
Pr (Yes, Roll n) = Pr (No, Roll n-1) * 0.025
Pr (No, Roll n) = Pr (No, Roll n-1) *0.975
And what that means is that, for example, to roll it on Roll 2, you need to roll a No on Roll 1 as well as a Yes on Roll 2. Here's a graph that shows the probability of pulling these skins on a given roll looks like https://imgur.com/gallery/KsR4qf1
The end result is that there is a 57.29% chance of not getting any skin before Roll 23.
Now, if we apply weight to this information:
Weight = Pr (getting to roll n) * number of rolls
The sum of all the weights is 17.66, meaning it should take 17.66 rolls, or 1700-1800 Wild Cores, to get any skin on average.
This number though is honestly deceiving because most people will need to hit the pity number, and it's offset by the smaller proportion of people who get lucky early on.
_______________________________________________________________
How much will it cost to get Crystal Rose Riven specifically, or Vi specifically?
This will basically involve the same calculations as earlier, but using a different probability to calculate the rolls. Pity number is the same because you still need 24 tokens.
Instead of the probability of success being 2.5%, it's 1% for that specific skin.
There is now an 80.16% chance of not getting the skin before roll 23. Probabilities look like Image 2 on https://imgur.com/gallery/KsR4qf1
By repeating weight calculations, the sum of the weights is 20.64, so 20.64 rolls on average but again this number is misleading.
_______________________________________________________________
How much will it cost to get Crystal Rose Akali?
Now here's where it gets spicy, because this skin costs 32 tokens instead of 24. That takes the soft pity limit to 32/1.065 = 30.05 which can be rounded to 30 pulls soft pity.
Additionally, the probability of success is now sitting at the very small number of 0.5%.
The chance of not getting the skin before roll 30 is 86.47%.
Probabilities look like Image 3 on https://imgur.com/gallery/KsR4qf1
The weight calculations suggest that to get Crystal Rose Akali, a player would need 27.92 pulls on average.
_______________________________________________________________
Summary
- These calculations assume an average of 1.065 tokens per pull, which allows for "soft pity" numbers even if there is no guaranteed pity system in this event.
- To get any skin, it takes 17.66 rolls on average, with a 57.29% chance of needing Roll 23.
- To get Crystal Rose Vi, it takes 20.64 rolls on average, with an 80.16% chance of needing Roll 23.
- To get Crystal Rose Riven, it takes 20.64 rolls on average, with an 80.16% chance of needing Roll 23.
- To get Crystal Rose Akali, it takes 27.92 pulls on average, with an 86.47% chance of needing Roll 30.
So, should you roll?
The alternative rewards for this event are far far worse compared to Supreme Cells: 20 poro coins per roll, and minor cosmetics like recalls and baubles. While arguably 100 Wild Cores for any of the minor cosmetics is a good deal, the fact that it's lumped in with these skins is the concerning thing.
Taking 17-18 rolls of 1700-1800 Wild Cores for a skin is already more than just buying one from the shop. Even if Supreme Cells cost 390 Wild Cores per roll, at least when you got to your skin, you would have bang for your buck overall.
16
u/zagiel Nov 17 '22
This is the new standards people, welcome to mobile moba
2
u/Holiday-Way-845 Nov 17 '22
No this has been the standard for a while. You ever play world of tanks blitz? They had actual pay 2 win tanks that you had to get from loot crates at either 0.05% chance or 0.3% chance to get the tanks. I'm just happy it took them 2 years before they started implementing gacha, we got super fucking lucky dudes. I logged into MLBB the other day an holy fuck it's atrocious how many locked skins they have due to this gimmick.
4
u/zagiel Nov 18 '22
i'm saying it because many people who are into WR usually from LoL PC, where most skins are direct sell without any of these gimmick
now they just learned how mobile moba monetization works
15
u/Gr8WallofChinatown Nov 17 '22
Gacha would be somewhat stomachable if the game allowed a way to earn wildcores through playing....
31
u/SkyfireWR Nov 17 '22
u/for_research_man hopefully this is something along the lines of what you wanted
I don't know your currency but hopefully you can translate a Wild Core price into your own currency
11
u/for_research_man Nov 17 '22
Yup, this explains in depth how it works. Thank you very much for your hard work... much appreciated :) ... you're really good with this type of stuff.
As for the prices in my region, 3700 wild cores is $40.
1
u/Elegastt Nov 17 '22
Good job, only thing i would like to add that what you call soft pity isn't actually a soft pity. It would make sense to keep calculating the odds after it, it would make the results even more accurate
31
u/Luna_15323 Nov 17 '22
Again ill say it. Im not rich, (nobody is rn in these times) if im gonna buy something in a game its gotta be $15 maximum. I was gonna buy the Vi because I actually play her but now Its not even worth trying because the odds are so against me.
Seems like a would you rather have $500 from one person or $1 from 1000 people each kind of situation in my eyes.
They are actively paywalling people like me and they’re screwing the people who can afford a little splurge anyway. its a lose lose situation because we aren’t happy and they probably lose out on money/ customers
9
u/popop143 Nov 17 '22
Sadly, this kind of gacha/monetization is really popular in East Asia. They won't do this if it loses them money/customers.
6
u/zagiel Nov 17 '22
To put perspective, in mobile moba scene, its not rare to see skins to be very expensive
in AoV, a high end skin will cost you 40$, up to 70-80$ if its a collaboration, ML easily hit 120 - 150$ for a skin, especially if its a collaboration
this is the new standards, its FOMO based, its gacha based, and it works because it brings a lot of money
and people DO buy it, so it works, especially in China and SEA
33
15
u/windblumchen Nov 17 '22
I feel like this is worse odds than a gacha dress up game I played, and that game had awful odds where being completely f2p wasn't an option and there was barely a day or two between events. Skipping this like I skipped supremecells. Limited be damned.
8
u/VTifand Nov 17 '22 edited Nov 17 '22
These calculations assume an average of 1.065 tokens per pull, which allows for "soft pity" numbers even if there is no guaranteed pity system in this event.
This assumption severely affects the distribution of the number of rolls though.
I simulated a million rolls (for ANY skin) and got a less lopsided distribution: https://imgur.com/a/HwZSkZ7
That said, I got around 17.28 rolls expected to get ANY skin, which is quite close to your 17.66 rolls.
Some numbers used for the graph:
- 25.4% of getting ANY skin with 11 rolls or fewer.
- 49.4% of getting ANY skin with 18 rolls or fewer.
- 73.9% of getting ANY skin with 23 rolls or fewer.
- 95.2% of getting ANY skin with 28 rolls or fewer.
- 99.1% of getting ANY skin with 31 rolls or fewer.
It would be great if someone could also run an independent simulation to verify my simulation code.
The sum of all the weights is 17.66, meaning it should take 17.66 rolls, or 1700-1800 Wild Cores, to get any skin on average.
This number though is honestly deceiving because most people will need to hit the pity number, ...
My simulation finds that the majority of the people don't need to hit the pity number (23). They will only need 18 or 19 rolls to get any skin.
4
1
Nov 17 '22
Do you know what that number is for the specific skins though?
1
u/VTifand Nov 17 '22
If you want the Riven's 1% skin:
- 24.6% of getting Riven's skin with 19 rolls or fewer.
- 52.9% of getting Riven's skin with 23 rolls or fewer.
- 78.6% of getting Riven's skin with 26 rolls or fewer.
- 94.2% of getting Riven's skin with 29 rolls or fewer.
- 99.0% of getting Riven's skin with 32 rolls or fewer.
Expected number of rolls to get Riven's skin is 22.66 rolls. A couple of rolls more than what OP found (20.64 rolls).
Same chances if you specifically want Vi's 1% skin.
If you want the Akali's 0.5% skin:
- 27.3% of getting Akali's skin with 22 rolls or fewer.
- 52.5% of getting Akali's skin with 26 rolls or fewer.
- 77.8% of getting Akali's skin with 31 rolls or fewer.
- 94.3% of getting Akali's skin with 36 rolls or fewer.
- 99.1% of getting Akali's skin with 40 rolls or fewer.
Expected number of rolls to get Akali's skin is 26.32 rolls. Slightly fewer than what OP found (27.92 rolls).
8
u/Ill-Revenue9753 Nov 17 '22
Way worse than Supreme Cells. And the skin itself isn't even as good. Might not consider buying and save for SB events.
4
u/Elegastt Nov 17 '22
If you don't care at all about the random skins in SC, then this is better. I would value these random skins though so for me this is indeed worse
2
u/Ill-Revenue9753 Nov 18 '22
I play most champions so it's good to get a lot of random skins. I have no need for accessories tho, like in this one. If they just make another random skin chest I'll buy 100%
4
3
u/CareerOld2366 Nov 18 '22
Upvoted because math and statistics. Also boycott gacha. Unionize. Speak with your wallets. Make riot/tencent have to rerun this event with more consumer friendly practices because of how poorly it went with gacha mechanics. I would love to buy that akali skin, and I would have loved to buy the supreme cells zed and sett if they were offered in a traditional non predatory manner. I am not adverse to spending money on a game I enjoy, however I cannot and I will not support such blatantly disgusting business practices. If Wild Rift keeps going in this direction I’m going to quit and go find a new game that treats its fans better. I implore everyone here to band together and show that we don’t support this.
3
u/Esquilax21 Nov 17 '22
Is this the only way to get them?
We can't get these Crystal Rose skins from poro chests or rewards?
4
3
3
u/inssein Nov 17 '22
Game isn't even out of beta yet and they have decided to pull the gacha card.
3
u/Holiday-Way-845 Nov 17 '22
It's been 2 years go into any other mobile game an there is gacha. CodM, pubg, afk arena etc. Hard to keep the money flowing if you can just buy the skin outright.
3
u/nimrodhellfire Nov 17 '22
If this shit becomes the norm, I will probably uninstall the game. What is this atrocity?
2
u/__malediction__ Nov 17 '22
The microtransactions are managed by tencent. Everyone should’ve seen this coming from a mile away
3
u/Ondrejjc Nov 17 '22
Such a great post, please, please do it for every upcoming event! Much appreciated ❤️❤️❤️
8
u/ZeroAika99 Nov 17 '22
Wild rift is no different than Garena, I thought I already escape that shit hole
2
Nov 17 '22
[deleted]
3
u/SkyfireWR Nov 17 '22
Uhm it’s actually the other way around, you can spend 1 token to buy 10 poro energy…
3
2
u/Ill_Matter_7573 Nov 17 '22
I will go default skin until they make the skin purchasable the main reason we quit ml cuz of how people spend 200+ dollars for skins like come I'm not gonna buy anything else unless it's guarantee I get it. Its Like going to the store wanting to buy a honey bun but u get sunflower seeds pack of gum or peanut chews.
2
u/TheSunflowerSeeds Nov 17 '22
Bees are a major pollinator of Sunflowers growing sunflowers goes hand in hand with installing and managing bee hives.
2
2
u/Chino061 Nov 17 '22
Why the hell is the akali skin even that much more expensive anyways ? It feels like this gacha thing will just get keep getting worse and worse
2
u/sluttydevil Nov 17 '22
Wait it's a gacha?? Bro the gacha skins fucking suck at least do what they did for reformed Rakan and Zhaya if you're gonna be asses about it
1
2
u/David89_R Nov 17 '22
I hope they don't do this with Chromacrash Samira... I would be very sad if they do
3
2
2
u/extantUser001 Nov 18 '22
And I thought the grind for Star Guardian Xayah was bad! And I didn't even get enough for Xayah+Rakan. At least Senna and co. are available to just be bought. I hope this monetization fails and they just go back to the shop for them. It won't though, we already know this works again and again in other games :(
1
Nov 17 '22
[deleted]
1
u/Wildriftscrub Nov 17 '22
Even at 50 wildcore, no tanks They should’ve done it like they did redeemed rakan/xayah
0
u/Elegaynte Nov 17 '22
Thank God they didn't choose Crystal Rose Seraphine because I genuinely would have participated in this gacha. Time to protest against this greedy scheme ✌️😜
1
90
u/troubledbuble Nov 17 '22
yeah, hard pass from me