These are the infamously rare Pokémon introduced back in Gold and Silver. When you encounter a wild Pokémon or hatch a Pokémon egg, there's an incredibly small chance that the Pokémon will be "shiny". These Pokémon have a different colour palette and they will also sparkle when they're sent out in battle.
You can also identify shiny Pokémon by a star symbol to the right of their name when checking your boxes or to the left of their markings when checking their status screen. Besides the rarity factor and the different colour, shiny Pokémon are no different to normal Pokémon. So they aren't stronger or anything.
Pokémon received as gifts, such as the starter Pokémon cannot be shiny, although you can breed them to be shiny. Certain fixed encounters, like the Legendary Pokémon and the sneak preview Galarian Slowpoke, also cannot be shiny.
The standard rate for finding a shiny Pokémon is 1 in 4096. However, there are multiple ways to increase the rate.
After completing the Galar Pokédex, you can receive the Shiny Charm from a Game Freak employee in an upstairs hotel room in Circhester. This key item will provide 2 additional rolls, boosting the rate to 1 in 1365.3.
If you breed a Pokémon with another Pokémon that has a different language tag (what fans refer to as the "Masuda Method"), you'll get 5 additional rolls, boosting the rate to 1 in 682.7 without the Shiny Charm (or 512 with).
Similar to Brilliant Pokémon, the chance of finding a shiny Pokémon of a particular species will permanently increase as you keep defeating that species of Pokémon. At the time of writing, because of a bug, the increased chance itself has a chance (which is small).
|Number defeated||Chance of increased rate||Increased rate (with Shiny Charm)|
|50~99||1.5%||1 in 2048 (1 in 1024)|
|100~199||2%||1 in 1365.3 (1 in 819.2)|
|200~299||2.5%||1 in 1024 (1 in 682.7)|
|300~499||3%||1 in 819.2 (1 in 585.1)|
|500+||3%||1 in 682.7 (1 in 512)|
Doing the Maths
Say you've defeated 500 of a certain species and you have the Shiny Charm. 97% of the time, the rate will be 1 in 1365.3 (0.07%). Only 3% of the time will it be 1 in 512 (0.195%).
Therefore, your effective shiny rate will be 97% times 0.07% plus 3% times 0.195%, which equals roughly 0.0738%. So the increase is 0.0038%, which is tiny! Game Freak!!!
Stars or Squares?
To further complicate matters, Sword and Shield have introduced a new variety of shiny Pokémon. Normally, shiny Pokémon have star-shaped sparkles when you send them out, but these new ones have square-shaped sparkles instead. People generally call them "Square" or "Prism" shinies. Again, this has zero bearing on the Pokémon's performance.
Now, Square shinies were intended to be rarer than the old ones. In fact, they have a 1/16 chance of appearing if the Pokémon is shiny. This holds true for Pokémon that you breed. However, at the time of writing, there is a whopping 4095 in 4096 chance of a wild shiny Pokémon being a square variant, due to yet another bug.