Zenless Zone Zero Probability Deep Dive

Version: v3.15.1

Zenless Zone Zero soft pity chart: the five star chance per signal search stays at 0.600% through signal search 73, then climbs in a straight line to 100% at signal search 90. — The flat line is your chance on a single signal search. The dashed line is your chance of having hit one already, which reaches 35.6% by signal search 73, before soft pity starts at all.

See it in action

Zenless Zone Zero Signal Search simulator - Roxy, Promeia, from signal search 73
Switch to Pull, then press Signal Search x10.
How many Signal Searches for Roxy or Promeia? Pity and 50/50 odds, from signal search 73

Detailed breakdown below

The four star line does not fit

Zenless is the one game where taking the published numbers at face value doesn't work, but we think we know the reason behind it.

Model it exactly like the game describes it, a flat 9.400% with an A-Rank guaranteed inside 10 searches, and you get 14.9693% when they publish 14.400%. Too high. And it stays too high no matter how you shuffle the curve around, because that setup is already the lowest it can possibly go.

So something has to be taking A-Rank pity away from you somewhere (you're making progress toward the guarantee and then losing some of it), otherwise these three published numbers can't all be true at the same time.

Genshin's problem ran the other direction (the naive curve came out too low there, so something had to be adding probability), which is how we ended up believing in soft pity in the first place.

Taking the rule literally

The game promises an A-Rank "or above" within 10 searches, so we take it literally: an S-Rank counts, and it clears your A-Rank counter. No fitting at all and that gets us 14.3916% against a published 14.400%.

So this is what we're going with. An S-Rank clears the A-Rank counter in Zenless and it doesn't in Genshin or Star Rail, which isn't one game having it both ways so much as three games just behaving differently. GGanalysis landed on the same split on their own, which is why we think we're okay here.

The four star consolidated rate under each reading

Four star line	Published	Nothing clears the counter	An S-Rank clears the counter
Zenless agent channel	14.400%	14.9693%	14.3916%
Zenless W-Engine channel	18.000%	18.6619%	18.1348%
Genshin character banner	13.000%	13.0101% (fitted)	12.3049%

The W-Engine channel

Oh and the W-Engine channel is the part we're not happy about, since nothing gets us to its published 18.000% and the floor under this reading is 18.1348%. A floor sitting above the published figure isn't something that can be tuned away. Our guess is that HoYoverse rounds the five and three star lines and lets the four star absorb the difference, given that 100 - 2.000 - 80.000 lands exactly on 18.000, though since the rates sum to 100 that may just be the same fact restated in a way that flatters us. We widened the test band for that one row rather than pretend otherwise.

How this gets settled

Anyone with pull history could settle this by histogramming the gap from each S-Rank to the next A-Rank, gaps of 11 or more are impossible if the counter clears and common if it doesn't. If you have that data we'd love to see it.

What is not settled

Some of what's on these pages is HoYoverse's word and some of it is ours, and the split is worth being explicit about.

The base rates, consolidated rates, guarantee rules and rate-up percentages are all published, so we didn't derive them and we don't argue with them.

The per-pull curves aren't published for any of the three games. Ours are solved to reproduce the published consolidated rates, and the linear shape is something we carried over from Genshin because it fits rather than because anyone has shown that's what the game is doing.

HSR's real rate-up share is above the published 50%, and we model 56.25% there for reasons set out on the Star Rail page. Zenless is different: its own panel says the losing half excludes the featured agent, so 50% is the whole answer here.

Zenless's W-Engine channel doesn't reconcile, since we land on 18.13% against a published 18.0% and can't close the gap.

Throughout these pages we're saying we model something rather than that the game does it, and where we've guessed we've tried to say so right next to the guess. Seems like the least we can do?

Banner data

[1] Zenless Zone Zero Wiki, Category:Signal Searches (CC BY-SA)