internals:gacha-performance-chances

Gacha Performance Chances

Spotlight Flips

At the start of a scout, the game receives which cards were pulled, plus “lot types” for each spotlight. 1 means it can flip, 2 means it should always show the real rarity right away.

If the lot type is 1 and the card is a UR, flips are decided by these chances:

Outcome Weight Chance
No flip, show UR right away 9700 69.29%
Spotlight flip, R to UR 2000 14.29%
Spotlight flip, SR to UR 2000 14.29%
Feather flip, R to UR 200 1.42%
Feather flip, SR to UR 100 0.71%

Rs and SRs will always show as their true rarity - R to SR flips are not possible. (Downwards flips also aren't, obviously.)

Stage

The stage at the beginning of the scout is decided through a “performance level” system. Each element of the screen is decided one by one, each setting a performance level (abbreviates as PL below) as it is chosen, which influences the chances of the options available for the later elements.

1. "Start" Text

Scout Result Weight Chance Outcome Next PL
Only Rs/SRs 10000 100% show normal text 101
Single UR 9700 97% show normal text 101
300 3% show rainbow text 102
2 or more URs 10000 100% show rainbow text 102

2. Stage

Scout Result Min PL Weight Chance at PL Outcome Next PL
101 102
Only Rs 101 10000 100% - show R stage 201
Only Rs and SRs 101 3000 30% - show R stage 201
101 7000 70% - show SR stage 202
At least 1 UR 101 500 5% 2.5% show R stage 201
101 1500 15% 7.5% show SR stage 202
101 8000 80% 40% show UR stage 203
102 10000 - 50% show UR stage 204

3. Penlights

Scout Result Min PL Weight Chance at PL Outcome Next PL
201 202 203 204
Only Rs 201 10000 100% - - - show white penlights 301
Only Rs and SRs 201 3000 30% 15% - - show white penlights 301
201 7000 70% 35% - - show yellow penlights 302
202 10000 - 50% - - show yellow penlights 302
At least 1 UR 201 500 5% 2.9% 2.5% 1.7% show white penlights 301
201 1500 15% 8.8% 7.5% 5.0% show yellow penlights 302
202 7000 - 41.2% 35.0% 23.3% show yellow penlights 302
201 8000 80% 47.1% 40.0% 26.7% show rainbow penlights 303
203 3000 - - 15.0% 10.0% show rainbow penlights 303
204 10000 - - - 33.3% show rainbow penlights 304

4. Screen Animation

Scout Result Min PL Weight Chance at PL Outcome Next PL
301 302 303 304
Only Rs 301 10000 100% - - - single white star, white screen 401
Only Rs and SRs 301 3000 30% 15% - - single white star, white screen 401
301 7000 70% 35% - - single yellow star, yellow screen with yellow stars 402
302 10000 - 50% - - single yellow star, yellow screen with yellow stars 402
At least 1 UR 301 500 5% 2.5% 1.7% 1.25% single white star, white screen 401
301 1500 15% 7.5% 5.0% 3.75% single yellow star, yellow screen with yellow stars 402
302 7000 - 35% 23.3% 17.5% single yellow star, yellow screen with yellow stars 402
301 8000 80% 40% 26.7% 20% three yellow stars, yellow screen with rainbow stars 403
302 3000 - 15% 10% 7.5% three yellow stars, yellow screen with rainbow stars 403
303 7000 - - 23.3% 17.5% three yellow stars, yellow screen with rainbow stars 403
303 2000 - - 6.7% 5.0% five rainbow stars, rainbow screen 403
303 1000 - - 3.3% 2.5% five rainbow stars, rainbow screen 404
304 10000 - - - 25.0% five rainbow stars, rainbow screen + fireworks 404

The final PL outcome does not do anything as far as I can tell.

TL;DR: what does that mean for me as a player

Basically nothing lol, this just tells the game how fancy your gacha result is but doesn't influence what cards you get. But there's some fun insights and maths we can do.

  • Most importantly: Fireworks don't mean anything. It just means you reached the maximum performance level in every step, but that's not a result of the gacha pull or something the player did - just some extra additional luck on top of getting an UR. (4.166% chance with multiple URs, 0.125% chance with just one UR)
  • There is also nothing special for pulling a new or limited UR, the conditions just count UR rarity cards.
  • The most telling element is the “Start” text: The chance to get rainbow text on a single UR pull is quite low, so if you see that colourful button, you've probably got something good coming.
    • Pulling a single UR in a 10-pull multi is a chance of 31.5%, the chance to pull at least 2 URs is 8.6%. You'll get a rainbow “Start” in 3% of single UR pulls, but 100% of multiple UR pulls.
    • The likelihood to get 2 or more URs when seeing rainbow text is $\frac{8.6\%\cdot100\%}{31.5\%\cdot3\%+8.6\%\cdot100\%} = 90.1\%$.
    • Also, if the text is white, but any other element is rainbow, you are guaranteed to have single UR pull (because you can only get rainbow elements on a UR pull, but rainbow text would be guaranteed on more than one UR).
    • A scout where fireworks are shown but you only get 1 UR has been commonly dubbed as “Fake Fireworks”. The chance to see those is related to the chance of a 1-UR-rainbow-text scout, since the chances for all other performance elements stay the same between both a single and a multiple UR pull. The chance to see fake fireworks is simply the inverse of the chance above: The likelihood to get only 1 UR even though you see fireworks is $9.9\%$.
  • If you get a SR-only multi pull, there's obviously no way an UR rarity element can appear - if you see at least one UR rarity element from the four above, you're going to get a UR (it might flip). The reverse can happen though: on a single UR pull, it is possible to get only R/SR rarity elements. So, if you only see white and yellow, what are the chances you shouldn't skip because you might still get a UR?
    • The chance to pull no URs in a 10-pull multi is 59.9%, the chance for a single UR is 31.5%.
    • We need to calculate the chance to get only R/SR rarity elements in a single UR result - let's only look at the intro screen for now. For just the text, the chance is simply $97\%$. If we add the stage, we need to multiply the sum of all chances to get white/yellow at PL 101 with that: $97\% \cdot (5\% + 10\%) = 19.4\%$. Now let's add the chances of white/yellow penlights at PLs 201 and 202: $97\% \cdot (5\% \cdot (5\% + 15\%) + 10\% \cdot (2.9\% + 8.8\% + 41.2\%)) = 6.1\%$.
    • With that, we can get the likelihood to have a single UR pull despite the intro screen - before tapping - being only white and yellow: $\frac{31.5\%\cdot6.1\%}{59.9\%\cdot100\%+31.5\%\cdot6.1\%} = 3.1\%$.
      • That number sounds small, but it's still quite possible: If you go for a spark and do 25 10-pulls, there's a $1-((1-0.031)^{25}) = 54.5\%$ chance to run into a fakeout like this.
    • Once you tap, you first see the screen animation. If we add the chance for that one to just be a single star from PL 301 or 302, we get to: $97\% \cdot (5\% \cdot (5\% \cdot 20\% + 15\% \cdot 45\%) + 10\% \cdot (2.9\% \cdot 20\% + 50\% \cdot 45\%)) = 2.6\%$ So if the screen is still only white or yellow, you're left with a UR likelihood of $\frac{31.5\%\cdot2.6\%}{59.9\%\cdot100\%+31.5\%\cdot2.6\%} = 1.4\%$.
      • That's an even smaller number, but still, using the same calculation as above, a player doing 25 multis has a $1-((1-0.014)^{25}) = 29.7\%$ chance of seeing this outcome.
    • Once all spotlights are revealed and flipped, your only hope left is a feather flip. Any UR lot can become a feather flip with a chance of $300/14000=2.1\%$ (see above). So, at this point we have to consider the chance of getting only R and SR rarity elements on the performance, plus the single UR lot becoming a feather flip: $2.6\% \cdot 2.1\% = 0.06\%$. So at this point, the likelihood is $\frac{31.5\%\cdot0.06\%}{59.9\%\cdot100\%+31.5\%\cdot0.06\%} = 0.0003\%$.
      • Now that number is tiny enough to be pretty much irrelevant: You will only have a $1-((1-0.000003)^{25}) = 0.007\%$ chance of seeing this going for a spark. So yes, you can pretty much skip if there's no spotlight flips after all that… but if you don't, and you do hit that 0.0003%, that's a hype moment.
Chances for all outcomes with 1 UR Chances for all outcomes with 2 or more URs

Special Performances

The above information is for Performance ID 1 - a regular pull. There are other Performance IDs for certain scouts:

  • Performance ID 2 is used for SR-only tickets (no chance for a UR). This performance can not generate any white elements, and no flips are possible. (However, technically, it can still generate rainbow elements, if there was a UR pulled - even though you can only pull SRs in these scouts…)
  • Performance ID 3 is used for UR-only tickets. This performance will always generate rainbow elements only, plus fireworks, and all spotlights will be SR to UR flips. There is no randomness.
  • There is also Performance ID 4 - I don't know what it's used for, but it uses the same performance generation as Performance ID 1 described above.

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internals/gacha-performance-chances.txt · Last modified: 2022/09/17 21:31 by Suyooo