Gacha maths

Every pity system, in one table

Nineteen games, and no two of them promise the same thing. Here is where each one's odds start climbing, where they stop, and the four that never owe you the unit at any count.

By the GachaData team Updated 4 min read

“Pity” is one word doing at least four different jobs. In one game it is a ramp that quietly raises your odds from pull 74. In another it is a counter that hands you the unit outright at 200 and does nothing whatsoever before then. In a third it guarantees a rarity and then draws at random from twenty-six units, which is not the same promise at all. And in three of the games here it does not exist at all.

Every game explains its own system in its own words, on its own terms, and never next to anyone else’s. Here they are next to each other.

The table

GameSoft pity fromHard pitySparkGuaranteed byWhat the mechanic does
Silver And Blood80neverHard pity at 80 · ~50% featured rate-up
Blue Protocol: Star Resonance658080Soft pity from 65, hard pity 80 · no featured split — the pool's SSR is the advertised reward
Reverse: 199970140Hard pity at 70 · 50/50 featured
Arknights5199neverSoft pity from 51, hard pity 99 · ~50% featured rate-up
Azur Lane200200200200-pull spark guarantee
Wuthering Waves7080160Soft pity from 70, hard pity 80 · 50/50 featured
Hololive Dreams200200200200-pull spark guarantee
Persona5: The Phantom X7080160Soft pity from 70, hard pity 80 · 50/50 featured
Genshin Impact7490180Soft pity from 74, hard pity 90 · 55/45 featured
Duet Night Abyss7490180Soft pity from 74, hard pity 90 · 50/50 featured
Honkai: Star Rail7490180Soft pity from 74, hard pity 90 · 50/50 featured
Zenless Zone Zero7490180Soft pity from 74, hard pity 90 · 50/50 featured
Limbus Company200200200200-pull spark guarantee
Blue Archive200200200200-pull spark guarantee
Fate/Grand Order330330330330-pull spark guarantee
DIGIMON UP200200200200-pull spark guarantee
Umamusume: Pretty Derbynot carriedNo pity on the pull — every summon independent (the game's Scout Exchange Point ceiling is not in our data yet)
Dragon Ball Z Dokkan BattleneverNo pity — every summon independent
CookieRun: CrumbleneverNo pity — every summon independent

Soft pity from is the pull where the per-pull rate starts climbing, listed only where the climb is separate from the cap. Hard pity is the pull that forces the top rarity. Spark is a separate counter that buys the unit outright regardless of what you have pulled. Guaranteed by is the pull at which the game finally owes you the specific unit you are chasing — which, as the column shows, is a much rarer promise than the other three.

Three things the column layout makes obvious

1. Hard pity and a guarantee are different promises

Look at Arknights and Silver and Blood. Both have a hard pity — 99 and 80 — and neither has a value in the Guaranteed by column. That is not an omission. Hitting hard pity in either game gives you a top-rarity unit, chosen from a pool. The unit you were actually pulling for is one member of that pool, and the game never owes it to you.

A game can have pity and still never guarantee you the unit. Two of the nineteen here have a pity mechanic that promises a rarity and nothing more specific — and two more have no pity at all, which lands them in the same column for a completely different reason.

The spark games make the opposite promise and make it plainly: Fate/Grand Order’s 330 and Blue Archive’s 200 are counters that end in the unit itself, whatever the pulls did on the way.

2. The advertised rate tells you almost nothing about the ramp

Six games here advertise 0.6% and they do not behave alike. Genshin Impact, Duet Night Abyss, Honkai: Star Rail and Zenless Zone Zero start climbing at 74 and cap at 90. Persona5: The Phantom X starts at 70 and caps at 80 — the same headline number, ten pulls cheaper at the ceiling. CookieRun: Crumble advertises 0.6% as well and never climbs at all, which is why the identical rate costs it nearly twice as many pulls as the rest. What you experience is set by the ramp, not the rate; soft pity explained walks through what the climb actually does to a pull.

3. “No pity” is a real design, not an oversight

Dragon Ball Z Dokkan Battle, CookieRun: Crumble and Umamusume: Pretty Derby have no pity on the pull. Every summon is independent, which means there is no number of pulls after which anything improves. That is exactly why they sit at the expensive end of what a featured unit costs, and why their unlucky cases run so much further than everyone else’s — see the unlucky tail.

What this table does not tell you

It compares mechanics, not value. A 200-pull spark is only generous relative to what a pull costs and how often the unit you want is on a banner — neither of which is in this table. It also describes the banner type each game leads with; several games run additional pools with their own rules. And a pity counter that carries between banners is worth considerably more than one that resets, a distinction the columns above deliberately do not try to compress into a number.

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