Thread: Theorycrafting: The likelihood of drawing SR and SSR kamihime in Gatcha

Originally Posted by Lothario

Ok back on topic, I had some free time so I decided to collect some more data for OP.
docs.google.com/spreadsheets/d/1h50CB6M2Z8uo0DuxX9rgWnhhfceIhO2LjzOz_0zh3Ns/edit#gid=698248666

Good job. I used this data to calculate the category rates for SRs. My full calculations are available in the spreadsheet linked in the OP.


Based on this data from 1000 rolls (100 10-rolls), we can conclude with high confidence that category weights differ by rarity tier. While R kamihime are observed at a frequency that resembles what would be expected with no weights at all, SR kamihime are far more likely to be drawn than lone SR weapons, and SR eidolons are also drawn at a higher frequency than their share of total SR possibilities would suggest. This confirms that the Gatcha rates provided in-game are incomplete because they give no information about the relative likelihood of pulling kamihime vs. eidolons vs. weapons.

Given data from 200 more 10-rolls, I can determine the category weights for SSRs, giving us a full picture of Gatcha rates that should remain accurate even as more Gatcha items are added in future updates. This is information that Nutaku should've provided to users to begin with, but has chosen to withhold. These rolls can come from any combination of users over any period of time, so long as you decide to document and report the roll before you see the results.

I'd collect more data once the event is over, also I'd love to find out more regarding the rate up with certain kamihimes as well. At the time the data was collected, it was shown that Amaterasu/Acala/Ifrit had a higher pull rate but out of the 100, I did not get any of them

I've updated the OP with the results of my analysis. Updates include:

1. Incorporation of data from 1000 rolls to empirically determine category rates (kamihime vs. non-kamihime weapon vs. eidolon).
2. Factoring in the guaranteed SR+ in 10-rolls.
3. Added an estimate of the total # of kamihime of a given rarity one could expect from N 10-rolls.

The results should now be robust for R and SR, and approximate for SSR.

Sanahtlig's Kamihime Project R Theorycrafting

Originally Posted by sanahtlig

I've updated the OP with the results of my analysis. Updates include:

I used your data... I think the following summary table, which is easy to calculate, is also much more useful:

Per 300 Jewel:
SSR SR R Total
Kami 1.10% 8.60% 9.70% 19.40%
Eido 1.10% 11.60% 33.30% 46.00%
Wea 0.10% 4.10% 30.40% 34.60%
Total 2.30% 24.30% 73.40% 100.00%

Per 3000 Jewel (chance of 1 or more):
SSR SR
Kami 10.471% 59.312%
Eido 10.471% 70.858%

- - - Updated - - -

By the way, with my results, I'm getting nowhere near 50% chance of SSR Kamihime for $98 (3.3 rolls).
My calculations show it to be 50.184% chance at 6.3 rolls.

- - - Updated - - -

How did you get 19.03% from raw data of 11/1000?
This is probably where our results diverge.
My calculation method is quite simple.
11/1000 = 1.1%
1.1%C10 = 10.471%
1.1%C63 = 50.184%

Originally Posted by Unregistered

By the way, with my results, I'm getting nowhere near 50% chance of SSR Kamihime for $98 (3.3 rolls).
My calculations show it to be 50.184% chance at 6.3 rolls.

You're misreading the table. The category rates are the rate of pulling a given type (kamihime, eidolon, weapon) within a given rarity tier. They're estimated from empirical data and used to generate the subsequent tables. This method is less subject to random biases because the category rates are much higher than the rate of obtaining a SSR, dampening the impact of variance. Also, we know the rarity rates exactly; they don't need to be estimated.

This misunderstanding happens frequently so I've revised the table to try and be clearer.

Also, I have no idea where you're getting the 50% chance of SSR kamihime from 3.3 rolls. My spreadsheet currently shows that a 50% rate is achieved at 4.8 10-rolls.

Originally Posted by sanahtlig

Also, we know the rarity rates exactly; they don't need to be estimated.

This misunderstanding happens frequently so I've revised the table to try and be clearer.

Also, I have no idea where you're getting the 50% chance of SSR kamihime from 3.3 rolls. My spreadsheet currently shows that a 50% rate is achieved at 4.8 10-rolls.

1. Where are the exact rates?
2. The 50% from 3.3 rolls is from your 4th/5th tables in your OP, where it states 3.3 rolls $98 for 50% chance of SSR Kamihime. Using 1.1% SSR Kamihime probability, 50% occurs at the 63rd roll, not 48th roll.
Formula is 1 - (1 - r)^n = p
where:
r = rate per pull
n = number of pulls
p = probability of at-least 1 pull of r rate

- - - Updated - - -

Formula is 1 - (1 - r)^n = p

So if we want to isolate n...
(1 - r)^n = (1 - p)
n * log(1 - r) = log(1 - p)
n = log(1 - p) / log(1 - r)
n = log(50%) / log(98.9%) = -0.30102999566398119521373889472449/-0.00480370840282059472713473451959
n = 62.666167556553876882697804745512

Originally Posted by Unregistered

1. Where are the exact rates?
2. The 50% from 3.3 rolls is from your 4th/5th tables in your OP, where it states 3.3 rolls $98 for 50% chance of SSR Kamihime. Using 1.1% SSR Kamihime probability, 50% occurs at the 63rd roll, not 48th roll.
Formula is 1 - (1 - r)^n = p

1. The game states that the SSR rate is 3%.
2. I multiply that 3% by the category rate for kamihime in the SSR tier (47.83%). That equals a SSR kamihime rate of 1.43%, not 1.1%. That's likely why our end results are different.

Originally Posted by sanahtlig

I've updated the OP with the results of my analysis. Updates include:

1. Incorporation of data from 1000 rolls to empirically determine category rates (kamihime vs. non-kamihime weapon vs. eidolon).
2. Factoring in the guaranteed SR+ in 10-rolls.
3. Added an estimate of the total # of kamihime of a given rarity one could expect from N 10-rolls.

The results should now be robust for R and SR, and approximate for SSR.

Sanahtlig's Kamihime Project R Theorycrafting

Sorry to necropost but I'm curious if this data changed at all with the gacha removing non-hime SSR weapons from the mix? Is it safe to say it's still approximately $200 USD for a SSR kamihime?

Originally Posted by Saberborn

Sorry to necropost but I'm curious if this data changed at all with the gacha removing non-hime SSR weapons from the mix? Is it safe to say it's still approximately $200 USD for a SSR kamihime?

Is it confirmed that non-kamihime SSR weapons have been removed from Premium and Jewel Gatcha?

Originally Posted by sanahtlig

Is it confirmed that non-kamihime SSR weapons have been removed from Premium and Jewel Gatcha?

See 12/10/17 news post. I can't verify its validity beyond that.