When breeding, it’s not just the Pokemon that you can make awesome. You can also control what the Pokemon is in! That’s right, breeding somehow magically generates Poke Balls out of thin air. Either that or the Eggshell has the magically ability to become a Poke Ball. Who knows?
For whatever reason, you can control the Poke Ball the offspring will hatch in.
Females will always pass down their Poke Ball over the male if bred with a male or with a Ditto. Males will pass down their Poke Ball if bred with a Ditto. There are two exceptions to this rule.
One is if the female and male are the exact same species. Then the female’s Poke Ball and the male’s Poke Ball each have a 50/50 chance of being passed down.
The second exception is if the Pokemon was caught in a Master Ball or a Cherish Ball . The former is the ultimate Poke Ball, and the latter is for event Pokemon. If the Pokemon within these two ball types are breedable and you breed them, offspring always hatch in a standard Poke Ball.
If you’re the type to always look stylish, make sure you catch the original parent in a stylish Poke Ball to match!
Beast Ball is a particularly popular option. It’s difficult to catch Pokemon in a Beast Ball, and they are exceptionally awesome to look at. Other valuable balls to pass down include the Apricorn Balls. For example, Alolan Vulpix in a Love Ball is utterly adorable.
By the way, not all Pokemon can be in every type of Poke Ball. This mostly applies to Generation 7 Pokemon only given as a gift, such as the starter Pokemon, Type: Null and Cosmog. These Pokemon cannot be caught, so they will only be in a boring old Poke Ball.
The other exceptions are Pokemon not found in Sun and Moon or HeartGold and SoulSilver and thus cannot be in an Apricorn Ball. Porygon is an interesting case, since it was found in earlier games, but is a gift Pokemon in Sun and Moon; therefore it cannot be in a Beast Ball.