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Starting in 6th generation, the Pokéball of the female Pokémon is passed down to its offspring.
Male and genderless Pokémon (including Ditto), instead, have no impact on the type of Pokéball inherited.

Has this mechanic changed in 7th generation?

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According to Bulbapedia:

In 7th generation, if a male and female Pokémon of the same species are bred, the offspring will have an equal chance of inheriting either parent's Poké Ball.

Also, when breeding a male or genderless Pokémon with Ditto, the Poké Ball of the male or genderless Pokémon will now be passed down to its offspring.

Here's a summary: enter image description here (Credits to Saiph-Charon)

For the purposes of inheriting Pokéballs, parents in a Master Ball or Cherish Ball are always treated as being in a standard Pokéball as before.

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  • I just realized this was never clarified (or asked, really). Is "species" meant in the restrictive way here or does it include the evolutionary family? If I breed a female Poke Ball Vulpix with a male Great Ball Ninetales, can the offspring be in a Great Ball or will it always be in the female's Poke Ball? – scenia Feb 22 '17 at 19:36
  • @scenia I'm pretty sure it also works for same evolution family. – pinckerman Feb 22 '17 at 19:58
  • After some testing, I don't think it does. "Species" usually applies only to the specific species and excludes the evolutionary family, and based on my anecdotal evidence, this applies here as well. – scenia Feb 23 '17 at 20:12
  • @scenia Interesting. I'll do some testing, too. – pinckerman Feb 24 '17 at 2:03

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