Poisson distribution... I do get it as what you said but it is as a matter of fact really complicated. If possible, should I try to roll on the same server time which other players rolled and got legendary heroes.. ? Is it possible.. ? Please reply. Thanks.
You will have to make a study with around 500+ observations on different times in order to get some data to work on. Just because some youtubers got them at certain hours doesn't mean anything, statistically speaken. There are so many myths when it comes to predict randomness that it is insane, you can only rely on numbers here.
The problem here is that we lack of data. If i had the exact % of legendary roll, a graphic of legendary rolls according to the time server, I would be able to tell you something more exactly, but I am afraid I can't.
Also, keep in mind that I assummed the Poisson distribution, but this is generated by a computer algorythm, and I have studied statistics in real life problems, focused on business issues, so I don't know if Poisson would fit here.
But what i can tell you is how many rolls would give you a reasonable success rate.
If you roll 30 times, you will have a 71,12 % to get between 1 and 3 legendaries, according to the data available.
PD: it doesn't matter if you roll 30 at once, or if you roll once a day, the numbers will be the same. People tend to believe that you have to roll everything at once, but that is not how it works. I have a PD, Cupid & Aries by rolling once per two days (F2P)