Wuthering Waves Probability Deep Dive

Version: v3.10.0

Soft pity has to exist

Kuro publishes 0.800% for a five star and 1.800% comprehensive, and never says a word about soft pity. But those two numbers together should give it away.

If we interpret the published stats literally: flat 0.800% every convene, and a guaranteed five star at 80. Does that give us the 1.800% Kuro publishes? It gives us 1.6875%, so no.

Next theory is whether Kuro is simply rounding their published figure. Kuro quotes one decimal, so the true figure is somewhere in 1.75% to 1.85%, and 1.6875% is below that whole interval. Something raises the per-convene rate before 80. That's soft pity, deduced from Kuro's own two numbers, and it's exactly the argument that gets us Genshin's curve on that game's page.

Solving the ramp

We use the same shape we use everywhere: flat at the base rate, then a straight line up to certainty at hard pity. One number to find, which is where the line starts.

Where the ramp starts, and what it produces

Convene 70 is the closest and it's what we're shipping, which gets us +0.34% against the published figure and that's pretty good. 71 is also inside our band and it errs pessimistic (arguably the better direction for a planning tool), so this was a real choice and not an obvious one.

How confident are we?

Not super confident. Kuro didn't publish this number, we worked it out, so here's how much to trust it.

Kuro publishes 1.8% to one decimal. Every ramp start that comes out anywhere in 1.75% to 1.85% is consistent with what they actually said, and that admits a first elevated convene anywhere from 68 to 74. Seven possibilities, and nothing published narrows it down further. Our 70 is just the one that gets closest to the published figure under our own rule. It isn't a measurement and the calculators shouldn't be read as if it were.

What the other models get

GGanalysis is the best public gacha probability library there is (MIT licensed, and we've cited it on the other pages). Its Wuthering Waves table gives 1.8483% against the published 1.800%, which is 2.685% out, or about five and a half times the tolerance we hold ourselves to. The rate everyone else on the internet seems to have settled on comes out at 1.8530%, which is worse.

To be fair to them, GGanalysis says up front in its own source that its table is inferred from the game's test phase and can't be guaranteed accurate. It's an honest note and we'll take them at their word.

The four star line does not fit

This is the second game where Kuro's or HoYoverse's own published numbers can't all be true at once, and this time it's worse than Zenless.

Model it exactly as the game describes: flat 6.000%, with a four star guaranteed inside 10 convenes. That gives 12.9873% when Kuro publishes 12.000% which is way too high. And it stays too high no matter how you shuffle the curve around, because a flat base with the guarantee at 10 is already the lowest it can possibly go. So something has to be taking four star progress away from you somewhere.

Kuro's wording is that you get a Resonator or Weapon of four star "or higher" every 10 convenes, and we read the "or higher" literally: a five star counts, and it clears your four star counter. That's the same reading we take in Zenless and for the same reason. It gets us from 12.9873% down to 12.2285%.

Which is still above the published 12.000%.

The four star comprehensive rate under each reading

Why we didn't fit it

That last row is real, by the way. A 73% step on the 10th convene and the guarantee sliding to the 11th gets us to Kuro's 12.000% almost exactly. We didn't do it.

Three of Kuro's numbers can't all be true at once: the 6.000% base, the guarantee inside 10 convenes, and the 12.000% average. One of them has to give. We kept the guarantee, since anybody can check that one in ten convenes this afternoon, and fitting the average instead would leave 13.9% of ten-convene blocks with nothing in them against text that promises something. The average is the one we felt least bad about breaking.

So we ship 12.2285% against a published 12.000% and widen the test band on that row. It's the widest on the site and no, we're not thrilled about it.

The same two inputs, opposite corrections

Genshin's weapon banner and every Wuthering Waves convene publish the same four star base rate and the same guarantee, and then publish different comprehensive rates, which we noticed late and still can't fully explain.

Same inputs, different outputs

Genshin's sits above what those two inputs imply on their own, so Genshin needs something adding probability, and it has it: a soft pity step on the 8th wish. Wuthering Waves' sits below, so it needs something removing progress. Same two published numbers, corrections in opposite directions. So at least one of the two operators isn't really reporting a long-run frequency of the thing they're describing.

The novice convene publishes a rate that cannot be true

Utterance of Marvels is the beginner convene. It guarantees a five star within 50 convenes and then closes. And it publishes the same 1.800% five star rate as everything else.

It can't. A guarantee at 50 instead of 80 means five stars arrive sooner, so the comprehensive rate has to be higher, and the flat-rate floor for that channel is 2.4187%. That's 34% above the published figure, and it's a floor, so no curve consistent with what Kuro published for that channel can get down to 1.8%.

The straightforward explanation, we think, is that the rate block is just copy-pasted. Which is the main reason we're wary of treating the 12.000% four star figure as a measurement, since we can prove at least one of these numbers was printed rather than computed.

What is not settled

Published, and we don't argue with it: the base rates, the comprehensive rates, the 10-convene guarantee, the 50% on the Resonator convene, and the 100% featured rate on the Weapon convene.

Ours, and you should treat it as ours: that soft pity exists at all, that it starts on convene 70, that the ramp is a straight line, that a five star clears the four star counter, and the even split of the four star tier between Resonators and Weapons.

Open: whether two convenes of the same type running at once share a guarantee count. Kuro publishes that some types share with each other, and this game essentially always runs several at once, so this is the normal case rather than an edge one.

Throughout we're saying we model something rather than that the game does it. Where we've guessed we've tried to say so next to the guess.

Sources

[1] Wuthering Waves Wiki, Category:Convenes (CC BY-SA)

[2] GGanalysis, a gacha probability library (MIT)

Where these numbers are used

• Wuthering Waves Inferred Probabilities: the published rates, and the convene with no 50/50
• Zenless Probability Deep Dive: the other game whose four star line does not fit
• Resonator Convene Calculator: False Promise for Tomorrow or Wind of Transcendence
• Weapon Convene Calculator: Absolute Pulsation: Forged Dwarf Star or Absolute Pulsation: Glint of Clouds