Honkai: Star Rail Probability Deep Dive
Version: v3.15.1
Honkai: Star Rail's Soft Pity Mechanic
See it in action
- Honkai: Star Rail warp simulator - Pearl, Evanescia, from warp 73
Switch to Pull, then press Warp x10.
- How many warps for Pearl or Evanescia? Pity and 50/50 odds, from warp 73
Detailed breakdown below
What is published and what is not
miHoYo only publishes the consolidated rates and does not publish the per-warp distributions or curve directly for any of the three HoYoverse games. We once again know that flat rate is not how the underlying mechanics work (you can see our probability deep dive for Genshin at /genshin_probabilities_deep_dive) and it works the same here too. So we're basically choosing pity cutoffs and linear probability increases (soft pity) to try to arrive at the consolidated rates that are officially published. We believe Honkai Star Rail uses a very similar mechanism to the one we investigated and used for our Genshin calculator. There are potentially errors in this model and we're monitoring community sources to see what is latest.
The answer
The character warp we're shipping is 0.600% flat, rising linearly from warp 74 and hitting 100% at 90 (Genshin's curve, reused without a single change). The four star line is 5.100% flat with 52% on the 9th and a guarantee on the 10th. It looks like 1.6041% and 13.0101% against a published 1.600% and 13.000%, which is pretty good. The Light Cone warp is 0.800% flat rising from warp 66 to 100% at 80, with a four star line of 6.600% flat, 39.7% on the 8th and a guarantee on the 9th. That one looks like 1.8696% and 14.8001%.
The curves we ship, against the published consolidated rates
| Warp | Base rate | Soft pity from | Hard pity | Ours | Published |
|---|---|---|---|---|---|
| Character, five star | 0.600% | warp 74 | 90 | 1.6041% | 1.600% |
| Character, four star | 5.100% | 9th, at 52% | 10th | 13.0101% | 13.000% |
| Light Cone, five star | 0.800% | warp 66 | 80 | 1.8696% | 1.870% |
| Light Cone, four star | 6.600% | 8th, at 39.7% | 9th | 14.8001% | 14.800% |
The control
None of that would mean much on its own (anyone can fit a curve to a number they already have), so before the solver was pointed at Star Rail it was pointed at Genshin, where we already knew the answer, and it recovered both of the shipped Genshin curves to within 0.03%. That is why we think we're okay. The method treats the roll as a Markov chain over the two pity counters and inverts it, which is the same thing we did by hand in the Genshin deep dive.
Worst error across all six banner lines in all three games is 0.292%, against a test band of 0.5%.
What this is not
The soft pity start is an integer we fit rather than something anyone observed. For the Light Cone warp both 65 and 66 are reasonable and 66 is the one the published 1.870% picks. And we assume the ramp is linear because Genshin's appears to be and why would HSR be different?
The published rule
Star Rail publishes a flat 50% for the featured character on the event warp and a 75% on the Light Cone warp, and in both cases losing means the next five star is guaranteed to be the featured one. Capturing Radiance doesn't exist here, so nothing converts a lost 50/50 after the fact and nothing caps how many you can lose in a row (four in a row is impossible in Genshin and totally possible here).
The measurement that disagrees
The complication is that a big community analysis of roughly 15 million warps puts the real featured share above the published 50%. [1]
The explanation that fits
There's a fairly tidy explanation for that gap, and the endpoint hands it to us. The five star list on an event warp holds eight entries, the seven standard characters plus the featured one, so if a lost 50/50 draws uniformly from all eight then the true featured share works out to 0.5 + 0.5 x (1/8) = 56.25%, which is about as good a match for "about 56%" as you could ask for. On that reading the two numbers aren't even in conflict, since 50% would be the coin flip and 56.25% the consolidated outcome, in the same way 0.6% and 1.6% are both true in Genshin.
What the list shape does not settle
Genshin's list is shaped the same way though, nine entries, eight standard characters plus the featured one, and the same reasoning there predicts 0.5 + 0.5 x (1/9) = 55.6%. Genshin does measure around 55%, so it very nearly works (which is exactly why the reading is so tempting), except HoYoverse publishes 55.000% and attributes it to Capturing Radiance, which is a documented mechanic with a documented streak cap. That's not great for our theory because in the one game where the answer is actually known, the list shape isn't what's producing it.
The list-shape reading, in all three games
| Game | Published rate-up | Five star list | What the list shape would predict | What is measured | What explains it |
|---|---|---|---|---|---|
| Genshin Impact | 50% | 9 entries | 55.6% | about 55% | Capturing Radiance, published at 55.000% |
| Honkai: Star Rail | 50% | 8 entries | 56.25% | above the published 50% | The panel's own definition of the losing half |
| Zenless Zone Zero | 50% | 7 entries | 57.1% | No measurement we could find | Untested |
The list shape is not what settled it. What settled it is the panel's own wording: the 50% is the boosted half, and the other half is drawn from a set that includes the featured character, so the featured share is 56.25%. That is the only value that reproduces the 1.113% consolidated rate the same panel publishes, and the Light Cone warp agrees independently at 78.125% and 1.534%. We ship 56.25% because modelling the published 50% made us contradict a published number.
How this gets settled
If we had data from Zenless we could use that to settle the debate, we predict a 57.1% since the agent list holds seven entries currently but we didn't find a good community measure in our search. If that number comes out and looks good we can confidently ship the mechanic.
Sources
Banner data
[2] Honkai: Star Rail Wiki, Category:Warps (CC BY-SA)