What I Noticed About Heirlooms
One of the rarest thing to get in Apex Legends, is an Heirloom, unless you dropped 300 or so for the event ones. It takes 500 packs to get a guaranteed heirloom. Well, here's what I've noticed... ...
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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 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
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)
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