What I Noticed About Heirlooms

@Midnight9746 

I think your "empirical study" is a bit too narrow with too little input data to draw such conclusion =) Sounds more like wishful speculations.

If this was the case, all smurfs would get one  (just create new smurfs when you stop getting packs every free level) --> everyone would switch main from their current main to their smurf with heirloom --> everyone would have heirloom ---> no one would complain they didnt get one.

But sure: I got my first heirloom on a smurf at low level. But not my first smurf and I havent got one after that on any of my smurfs after that. I think a much simpler and therefore more plausible explanation is that a majority of all packs being opened globally happens on accounts below lvl 300, i.e when you get many for free. Therefor it might seem that "low level" accounts have a higher probability of getting one, but in fact its just because most packs are opened at low level accounts.

I have 3 on a level 40 account 😂😂😂 and just got one on a lvl 14 account 

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I think a much simpler and therefore more plausible explanation is that a majority of all packs being opened globally happens on accounts below lvl 300, i.e when you get many for free. Therefor it might seem that "low level" accounts have a higher probability of getting one, but in fact its just because most packs are opened at low level accounts

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This is probably a good estimation. You get 58 pack in the first 100 levels, 50 in 101-200 and 200-300 and only 40 more in the last 200.

Furthermore there's only 14 (7 free) packs in a season with about 10 in the packs (total of 24).

So a level 300 with 2 seasons completed has opened about 200 packs.

Now if getting heirloom shards from a pack has a probability between (we don't actually know the single pack probability, we only know the guaranteed shards after 499 packs without) 1/2000 and 1/500. Then the probability of them getting heirloom shards lies between 9% and 33%.

(For only 100 packs it would be between 5% and 20%).

So probably at minimum 1 out of every 20 new-ish players has an heirloom and at most I'd guess about 1 out of every 3.

Which is much more than you'd expect, couple this with the large influx of newer players and you get a lot of newbies with heirlooms.

For those interested in some mor math:

The average number of packs to get an heirloom lies between 443 and 316.

With between 22% and 63% of the heirlooms opening before the 500th pack.

Note:

For those curious how to get the exact numbers. The probability is given by

P(heirloom) = 1-(1-p)^n

With p the single pack probability and n the number of opened packs (n must be lower then 500).

The average is given by:

<n> = (1 - (1-p)^500)/p

The fraction of early heirlooms by

F = 1 - (1-p)^499

To find these you can use the Geometric sum

S = 1 + q + q² + ... + q^m = (1-q^(m+1))/(1-q)

It is difficult to get an heirloom thats for sure, I made a list of the best heirlooms in case you get that lucky chance and want to know which to buy.

@CatcherLes 
As this thread is a bit old at this point, we are going to lock this down so that we can prevent any necro-posting.

If you run into any further issues please create a new thread so that we can begin tracking accordingly!