Source
r/bravefrontier•
MasterDelta

Probability Analysis of Summoning Featured Unit

Fluff

Given the newly released (and rather abysmal) summoning rates for Gumi’s new Limited Edition Global Exclusive units, I have decided to calculate the various probability of summoning a featured unit in various given numbers of summons. Although this is a rather useless exercise, I thought people might be interested to know the actual probability of pulling a unit on a given summon.

Calculations are done using the property of indepedence for the first seven summons, then using the Geometric distribution for summons past summon eight. I did not calculate the probability directly; I instead calculated the probability of not summoning the unit in that number of summons, then took the complement.

For the sake of my curiousity, I have calculated the probability of summoning the unit by the time you hit the max summon rate (i.e. summoning the unit before summon 8), and in five summon increments after that.

p(summon before 8) ≈ 0.163

p(summon by 10) ≈ 0.282

p(summon by 15) ≈ 0.445

p(summon by 20) ≈ 0.570

p(summon by 25) ≈ 0.667

p(summon by 30) ≈ 0.743

p(summon by 35) ≈ 0.801

p(summon by 40) ≈ 0.846

p(summon by 45) ≈ 0.881

p(summon by 50) ≈ 0.908

So, if my math is correct (feel free to check and disprove me. I make mistakes all the time), you would have to do 50 summons to have over a 90% chance of obtaining the featured unit. In addition, a 5% summon rate seems like a 1 in 20 chance to get the unit, but the math shows you only have a 57% chance of obtaining the unit by the 20th summon. Apparently $34.99 only being a 50/50 shot is a wise marketing strategy for Gumi?

I mostly did this because I was curious; I don’t expect anyone’s summoning habits to change based on this. Use this information however you like.

Posted Feb 8, 2018, 4:08 PM UTC

5427
FNMokou•

Smart man

15
MasterDeltaOP•

#MathterDelta

19
Navi_King•

Easiest way (in my opinion) to calculate is

1.0 - (1.0-[Chance of summoning])^^[Number ^^of ^^summons]

10
MasterDeltaOP•

Yep, that is the method I used for every probability past the eighth summon (since before then the probability changes with each summon.)

Ye olde cdf of a Geometric rv.

5
acpyPhwoar (Pui) - 8284147640 | Global•

Binomial <3

1
agent_87•

Upvote for quality use of probability

7
rocharox•

I thank the Gods that people like you exist, if humanity depended on me for Math we would still be banging rocks together

3
Anchen•

Calculated the actual probabilities and your numbers seem close enough and is about what I'd expect.

Chance to not roll featured unit: 99/100 * 98.5/100 * 98/100 * 97.5/100 * 97/100 * 96.5/100 * 96/100 * (95/100) ^ n

Where n is the number of spins after the max rate is achieved. Chance to get at least 1 would be (1 - (chance to not roll)).

Technically it is a 57% chance to roll at least 1 by the 20th summon. There's some amount of >1 in there too.

2
Valfodr-•

I made 64 pulls but I still can not get the unit

1
MasterDeltaOP•

The odds were not ever in your favor.

I am sorry for you loss.

7
WhaThaFuc•

Expected number of summons does not mean that you’ll definitely get it by that summon.

1
RealDesho•

Nay 30 summons = dupes

At least in my story. My friend got miku under 10

1
LemGambino•

I appreciate you doing this. Now that I look at your numbers, a 16% chance at pulling the featured unit is quite high to me, and it's somewhat consistent with the luck I've been having.

Miku took me 9 pulls, which is reasonable. I got absurdly lucky with Blaze with the first pull on the resummon, then about 2-3 pulls later I get a second one. And Yan+Yuan took...Exactly 30 pulls. I was about to run out of tickets. >3>

I sometimes wonder if my account is pre-seeded for good luck...Wintia wasn't a GLEX, but I asked a friend to pull for her while he was leveling up my account, and he got her in six pulls, which is far from bad.

Now I'm curious if the gate's rates change for each unit, or if they're the same regardless of which unit is featured, that might have something to do with it.

1
acpyPhwoar (Pui) - 8284147640 | Global•

Theoretically it's actually a bit higher because you excluded the 7 failed summons prior.

1
MasterDeltaOP•

Nope, it's exact. Those summons were included in all calculations. The only approximation is rounding to 3 decimal places.

1
acpyPhwoar (Pui) - 8284147640 | Global•

Ey I stand corrected!

1
FA_Creed•

Just to throw this out there, it took me 47 summons to get 1 snow miku...

1
DSLevantine•

good analysis. Up vote

1
gol4corea•

thank you for this informative post. I feel less inclined to get tilted when I summon now. got my Snow Miku after 80 gems and 13 ST. that's 29 summons.

1
lloydsmith28•

Not really accurate since the chance is so random, yeah mathematically it makes sense but unless you know the algorithm they use it's only a guess. I got the new unit CG sakura on my 2-3 free summon, I didn't even do a single normal summon. Someone else got the same thing as well, so yeah. 🤷

0
MasterDeltaOP•

If their algorithm actually abides by their posted rates, then these probabilities are accurate. If it doesn't, players can sue for false advertising.

1
lloydsmith28•

When did they post the rates?

0
TraneBF03•

if you read the in game news, in every banner of a unit rate up they put the % of rate. for example snow miku have a 5% of rate

2
lloydsmith28•

Oh, i totally thought this was another game lol

1
[deleted]•

[deleted]

-11
MasterDeltaOP•

I mostly did this because I was curious; I don’t expect anyone’s summoning habits to change based on this. Use this information however you like.

Clearly not screeching about the rates, just amusing myself.

Also, 20 summons is doable for a F2P? We are talking about Brave Frontier, right? Maybe if they don't summon for half a year.

6
brokendwarf•

20? Ha. I'm lucky to even get 2 as F2P

6
Navi_King•

It definitely depends on how often you summon. Brave Frontier's issue so to speak isn't that the rates are bad, but that new gates come out so often. It's very difficult to save to get EVERYTHING you want, generally you'll have to pick and choose.

2