Gacha Rates
Official disclosures state a 2% overall skin rate. But often, when rolling on a banner, you're looking to get specific skins. Many banners include one or two live2D skins, which tend to be the most sought after. So what are your chances?
It's easy enough to find someone with a story on how many rolls they did without getting a live2D. You'll also see plenty who got the live2D in their first 500, 1000, 2000, or similar tokens. But without hard data, there's no proper reason to reject the default assumption - that rate does not vary with skin type. To be a little more systematic, and accommodating of my non-infinite funds: allow me to present the results of the renowned, eternally-infallible, online poll. Link over here if you'd like to contribute.
If you're just looking for general info on costumes/what sets there are in the future/anything else like that, I recommend this excellent spreadsheet by /u/ConductorBichir and /u/UnironicWeeaboo.
Sanity Check#
Okay, so maybe online polls aren't always perfect. To gain at least some confidence in the data submitted, let's ask a much more boring question first: is the total skin rate actually 2%?
In short: responders pulled 488 skins from 24709 rolls - a 1.975% skin rate. Extremely close, and easily within the range of random variation.
This gives us a 95% confidence interval of 1.81-2.16% - that is, we have no evidence to suggest the skin rate is not 2%. (And that's all we can ever get - more data can thin our confidence interval, but we can't definitively prove the rate is some exact value. But from what we've seen, 2% fits.)
Expectations#
Given a 0.4% live2D rate and 5460 tokens to get the hard pity, you'd expect to get on average 12 total skins, including 2.4 live2D skins. However, the low rates and limited number of tries make variance huge - it's plausible to get as few as 6 or as many as 21 total skins from those rolls, and 0 live2Ds would hardly be extraordinary.
This makes individual reports unhelpful on their own. But if we can compile a whole bunch of them, we might get somewhere.
Data#
To make things slightly tricker, banners typically have 1 L2D + 4 other skins or 2 L2Ds + 4 other skins. We'll consider those separately.
Single L2D gachas
If the skin rates are all equal, we'd expect l2ds to be rolled 2%/5=0.4% of the time.
On record, we have 24 l2ds out of 12901 rolls - a 0.19% rate. The 95% confidence interval extends up to 0.28%, meaning we have significant evidence suggesting the live2D rate is below 0.4% (p<0.001).
Looking at the numbers from a different perspective, from the sample, ~10% of the costumes rolled (24/259) were live2Ds. If they were equally likely, 20% (1/5, or 52 costumes) should be. So in 1 L2D + 4 skin sets, live2Ds appear to be about half as common as you might expect.
Double L2D gachas
If the skin rates are all equal, we'd expect l2ds to be rolled 2*2%/6=0.67% of the time.
On record, we have 34 l2ds out of 11489 rolls - a 0.30% rate. The 95% CI goes up to 0.42%, so we once again have evidence live2Ds are relatively rare (p<0.001).
Live2Ds made up 15.1% of the costumes rolled (34/225), rather than the expected 33% (75 costumes) - once again, about half.
Conclusion#
The sample estimates above are technically the "best" guesses we currently have, but I'll round them off a little for my guesses here. Live2Ds appear to be 2x less common than you'd expect, with a 0.2% rate in 5-skin gachas and 0.33% rate in 6-skin gachas (half that, 0.17%, per skin). Bring lots of tokens, especially for those double l2d sets.
Notes#
- As a broad principle, keep in mind: if someone claims rates are "different" for some thing or another but doesn't have a specific rate estimate or any data supporting the claim, it's probably made up.
- I will still periodically check the survey for new responses, and update the numbers here as appropriate. It's always better to have more data to draw from.
- I've updated the charts on my general gacha page with these rate estimations.
- This survey was typically distributed alongside the idea of investigating live2D rates. It is possible for that to have introduced some bias in the respondents either for people with better or worse than average luck.
- Given the skin rate lining up, this doesn't seem likely, but it's possible for some respondents to have misunderstood the questions and included skins exchanged for, or simply misremembering how many tokens were spent.
- The data so far represents ~$16,000 of tokens by shop prices, or ~50 years of regular f2p gameplay.
- It's always possible for the game to change rates on the fly, by set, or do any other sort of weird thing to the results. It is next to impossible to detect this, so we'll just have to cross our fingers. There's also no point to such speculation without hard data to reference.
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