The basics of the drop rates are published on the official site, but there’s one significant outlier – the Heirloom box. This special set type, currently only available for Wraith, includes three items, and has a less than 1% chance of dropping every time you open an Apex Pack. There’s also a sort of mercy rule which guarantees you an Heirloom set after 500 Apex Packs.
You’re going to get very close to that pity cut-off before you get the Heirloom drop, as a feature from Polygon breaks down. Across YouTube videos and other community reports, every Heirloom drop seems to be on the immediate cusp of 500 packs, if not the result of the actual pity rule. Nobody’s seen enough reports to render a definitive verdict on the precise drop rate, but there’s enough anecdotal evidence to suggest it’s very bad.