Two rates with the same name
When you open the details of a Genshin character banner, HoYoverse publishes two different numbers for the same event: the base probability of a 5★ is 0.600%, and the "consolidated probability" (including the pity guarantee) is 1.600%. This is not a bug or deceptive fine print: they are two distinct quantities. The base is the chance of each isolated pull before any help from the system. The consolidated is the average per-pull rate across the whole pity cycle, the one that describes your real experience. Confusing one for the other is the source of nearly every "this game is robbing me" complaint.
- Base rate
- The probability of a 5★ on an isolated pull, far from pity. 0.600% in Genshin, HSR and ZZZ; 0.800% in Wuthering Waves.
- Soft pity
- The band of pulls where the rate stops being flat and climbs on every attempt. Estimated by the community, not officially published.
- Hard pity
- The pull at which the 5★ is 100% guaranteed. Officially 90 in most games, 80 in Wuthering Waves.
- Consolidated rate
- The average per-pull rate including pity: 1.600% (Genshin, HSR, ZZZ) and 1.800% (WuWa). It is the rate you feel.
- 50/50
- When a 5★ drops, a 50% chance it is the featured character; if you lose, the next 5★ is guaranteed featured.
Soft pity: where the rate spikes
From pull 1 to 73, the rate is locked at 0.600%. Starting around pull 74 it stops being flat and climbs sharply on every attempt, reaching 100% at hard pity on pull 90. That climb is soft pity, and it is why 5★ almost always arrive between pulls 75 and 80. HoYoverse does not publish the curve: it was reconstructed by projects that pool the pull histories of millions of players. Doing that reverse engineering is the same statistical work found in correlation, regression and R², fitting a model to observed data and measuring how much it explains.
View the data
| x | Value |
|---|---|
| 1 | 0.6% |
| 73 | 0.6% |
| 74 | 6.6% |
| 76 | 18.6% |
| 78 | 30.6% |
| 80 | 42.6% |
| 82 | 54.6% |
| 84 | 66.6% |
| 86 | 78.6% |
| 88 | 90.6% |
| 90 | 100% |
The shape matters more than the exact values: a low, flat line for 73 pulls and then a wall. That is why "I will do just a few more pulls" is a trap before soft pity and a reasonable bet after it. Note that the ramp points (74 onward) are the community reconstruction, with the same slope the Genshin pity calculator uses; the 0.6% base and the 100% at pull 90 are the only official points.
The consolidated rate and expected value
The 1.600% consolidated rate is not a per-pull rate you see at any specific moment, it is the long-run average. Across thousands of pulls, the number of 5★ divided by the number of pulls converges to 1.600%. And when an average rate is the ratio of events to attempts, its inverse is the average number of attempts per event. In other words: on average you spend 1 ÷ 0.016 = 62.5 pulls per 5★. Large community samples land very close to this, which is the empirical proof that 1.6% really does describe the real experience.
P(pelo menos um 5* em N pulls) = 1 - Pi (1 - p_i)- p_i
- chance of a 5★ on the i-th pull (0.6% before soft pity, rising along the ramp)
- N
- number of pulls made from the current pity
- Pi
- product of all factors from i = 1 to N
This formula settles for good why 0.6% misleads. Suppose you do 73 pulls from zero, all still at the base rate. The chance of NOT hitting any 5★ is 0.994 raised to 73 ≈ 0.6446. So the chance of hitting at least one is only 1 − 0.6446 ≈ 35.5%. After 73 pulls, you have just about a 35% chance of a 5★. That is exactly why soft pity exists: without the ramp, nearly two thirds of players would reach pull 73 empty-handed. The ramp packs the remaining ~65% of the mass into a handful of pulls right after, hence the feeling that "it always comes around 76".
The 50/50, the guarantee and the real cost
Pulling a 5★ is not the same as pulling the character you want. On the featured banner, the first 5★ has a 50% chance of being the promoted one, that is the 50/50. If you lose (a character from the permanent pool comes out instead), the system stores a guarantee: the next 5★ must be the featured one. So, worst case, guaranteeing the character costs two 5★. The expected value sits between one and two: with half the time needing 1 and the other half needing 2, the average number of 5★ needed is 1×½ + 2×½ = 1.5.
E[pulls ate o destaque] = (2 - p) x (1 / r_c)- r_c
- consolidated per-pull rate (0.016 in most; 0.018 in WuWa)
- p
- chance of winning the 50/50 (0.5 nominal; 0.55 in Genshin with Capturing Radiance)
- (2 - p)
- expected number of 5★ until the featured one appears
Putting the pieces together: each 5★ costs 62.5 pulls on average, and you need 1.5 of them on average, so guaranteeing the featured character costs 62.5 × 1.5 = 93.75 pulls, about 94. At 160 premium currency per pull, that is roughly 15,000 units. In the worst possible case (lose the 50/50 at hard pity and take the next one at hard pity too), it is 90 + 90 = 180 pulls, or 28,800 currency. In Wuthering Waves, at 55.6 pulls per 5★, the average drops to 55.6 × 1.5 ≈ 83 pulls, and the worst case is 80 + 80 = 160.
You win the 50/50
- The first 5★ is already the featured character.
- Average cost ≈ 62.5 pulls (a single 5★).
- Happens ~50% of the time (~55% in current Genshin).
You lose the 50/50
- The first 5★ is from the permanent pool; it triggers the guarantee.
- The next 5★ is guaranteed to be the featured one.
- Average cost ≈ 125 pulls; worst case, 180.
The four games, side by side
Genshin, Honkai: Star Rail and Zenless Zone Zero share almost the same math, no coincidence, they are all HoYoverse. Wuthering Waves, from Kuro Games, uses a higher base rate and a lower hard pity, which changes the average cost but keeps the 50/50 logic. Each game has its own calculator: Genshin, Honkai: Star Rail, Zenless Zone Zero and Wuthering Waves.
| Game | Base 5★ rate | Hard pity | Guarantee | Currency per pull |
|---|---|---|---|---|
| Genshin Impact | 0.600% | 90 | 50/50 (55% with Capturing Radiance) | 160 Primogems |
| Honkai: Star Rail | 0.600% | 90 | 50/50 | 160 Stellar Jade |
| Zenless Zone Zero | 0.600% | 90 | 50/50 | 160 Polychrome |
| Wuthering Waves | 0.800% | 80 | 50/50 | 160 Astrite |
The practical read: in the three HoYoverse games, budget around ~94 pulls per guaranteed character (~15,000 currency) and a ceiling of 180. In Wuthering Waves, the higher base and shorter pity drop the average to ~83 pulls and the ceiling to 160. All charge 160 currency per pull, so converting pulls to currency is always multiplying by 160.
The gambler’s fallacy inside pity
Here lies the costliest confusion. Pity is a deterministic counter: it counts your pulls without a 5★ and, at pull 90, delivers the 5★ for certain. But every pull inside soft pity is still an independent draw. At pull 80, with a ~42% chance, the 5★ may simply not come, and that does not "bank luck" for pull 81. Pull 81 has its own rate (higher), computed from scratch. "I have gone many pulls without a 5★, so the next is more likely" is true only because that specific pull’s rate is higher, not because previous bad luck is owed back. It is the gambler’s fallacy, the same one that makes people think a number is "due" in the lottery, taken apart in lottery probability.
The full derivation, step by step
1) Average pulls per 5★. The consolidated rate r_c is, by definition, (number of 5★) ÷ (number of pulls) in the long run. Inverting, the average number of pulls per 5★ is E5 = 1 ÷ r_c. With r_c = 0.016, E5 = 62.5; with r_c = 0.018 (WuWa), E5 ≈ 55.6.
2) How many 5★ for the featured one. Let p be the chance of winning the 50/50. With probability p you hit on the first (1 five-star); with probability (1 − p) you lose and need a second guaranteed 5★ (2 total). The expected number of 5★ is p·1 + (1 − p)·2 = 2 − p.
3) Combining. E[pulls to featured] = (2 − p) × E5. For p = 0.5: 1.5 × 62.5 = 93.75. For p = 0.55 (Genshin with Capturing Radiance): 1.45 × 62.5 = 90.625. For WuWa (p = 0.5): 1.5 × 55.6 ≈ 83.3.
4) Exact cumulative probability. For a given target, do not use the average: use 1 − Π(1 − p_i), multiplying each pull’s failure chance from the current pity to the target. That is how this site’s calculators compute the exact chance, pull by pull, instead of an approximation.
Why "spend to soft pity then stop" almost never pays off
Stopping at pull 73 wastes the accumulated pity: you threw away ~35% of chance without harvesting the ramp that comes right after. If you have pulls to reach soft pity, it is almost always worth going until it resolves, because the value per pull spikes precisely there. The symmetric mistake is starting the ramp without pulls to finish it and getting stuck on a high pity until the next banner.
Frequently asked questions
If the rate is 0.6%, why do I almost always get the 5★ around pull 76?
How many pulls do I need, on average, to guarantee the featured character?
Is pity official or made up by the community?
After losing many pulls, does the next 5★ become more likely?
Does pity carry over between banners?
The advertised 0.6% is the base, not the rate you feel: the official 1.600% consolidated rate (1.800% in WuWa) already includes pity and implies ~62.5 pulls per 5★. With the 50/50, guaranteeing the featured character costs ~94 pulls on average and, worst case, 180. Hard pity and these rates are official; the soft-pity ramp is a community reconstruction. And remember: the counter is deterministic, but each pull inside it is still pure chance.
Sources & references
- Genshin Impact Wiki, Wish (official published rates and community soft-pity estimate)
- HoYoverse, "Capturing Radiance" (official announcement: 55.000% consolidated)
- ONE Esports, Honkai: Star Rail pity system (base rate, consolidated, hard pity, 50/50)
- ONE Esports, Zenless Zone Zero pity system (0.6% base, hard pity 90, 50/50)
- Wuthering Waves, Convene Details (Kuro Games official site: 0.8% base, 1.8% with guarantee, 80 pity)
- Wuthering Waves Wiki, Convene (featured banner rates and guarantee)
- Paimon.moe, Wish Tally (aggregated community data on 5★ distribution)