About rolling the same effect in a bracelet
In the latest days, we saw on this sub a lot of posts about bracelets rolling with the same effect.
I wanted to do a (very base level) statistical analysis on this phenomenon.
Method :
I expect each roll to be independant and don't assume this is rigged. I then calculate the probability to roll the same effect twice.
I'm focusing on a single stat (vitality) to aleviate the work needed.
For the roll statistics, I use what SG provides us.
For the distribution of said statistic, I looked at the t4 bracelet of more than a 100 1680+ characters on uwuowo.
I found out that the distribution is not continuous and I found 39 unique values.
If we consider the lowest roll the baseline and the highest the ceiling, we can extrapolate the following : there is a stat each 1% between bottom and top. I would love more data to confirm this but without scapping uwuowo (which is forbiden !! they don't have the infra to handle it) this is just to much to do by hand.
Now we can calculate the probability of rolling the exact same number. SG is not making the task easy because the probability of rolling a 4280 and a 5860 is not the same :
Of course it's harder to roll a legendary....
Probability of rolling vitality is
0.35*0.5 = 0.175 = 17.5%
Now to find the exact probability, we must divide using the same brackets as SG and we get this wonderful table
| Value bracket | Odds to roll same |
|---|---|
| 4000 - 4200 | (0.175*0.1 =) 1.75% |
| 4201 - 4800 | 2.80% |
| 4801 - 5400 | 1.75% |
| 5401 - 6000 | 0.70% |
But this is not over. This table only tells us the odds of rolling inside the same bracket.
To find the exact value, we have to look at the number of possible rolls in a bracket.
Which gives us this table
| Value bracket | Odds to roll same | 1 roll in .... |
|---|---|---|
| 4000 - 4200 | 0.175% | 571 |
| 4201 - 4800 | 0.093% | 1071 |
| 4801 - 5400 | 0.058% | 1714 |
| 5401 - 6000 | 0.023% | 4428 |
We're finally reaching the end of this. Remember that there are assumptions in this thread and this number is not 100% correct. This gives us an estimation only.
Now since we don't have the statistics of same rolling we can only assume from now.
My opinion is that it's very likely to be random and that there is no bug. Lots of people reroll a lot of bracelets (x3 !) everyday. You just never notice when it's a "normal" roll but it jumps to your eye when it's the same one.
If the odds were way lower (say 1 in 10.000 - 50.000) I wouldn't be so sure but this kind of numbers don't look out of place.
Finally, I'll be happy if anyone showed me clear mistakes in my reasoning. I'm not a mathematician or anything, it can happen and I'll be glad to correct any error sliping in.
Ty for taking the time to read !
TLDR : look for last table for the answer → imo very unlikely to be a bug considering the sheer number of bracelet that get rolled every day.
EDIT : to prove my point I'll take an exemple. Let's say you rolled 10 bracelets on each of your 6 alts since the patch came out. It's 60 bracelets. You roll them 3 times which makes it 180. If I use a probaility of 0.1% of rolling the same we found that you have a 16% chance to have rolled a duplicate at least once.