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For example, I am radar-hunting a Bagon. It is written in Bulbapedia that if you catch the Bagon instead of defeating it, the chance of getting the Shiny one is increased by 10%. Will these effects stack? Like, lets say you caught the regular Bagons twice. Will the chance rise to 20%? Or will it stay as 10%?

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“The chance that the patch in a ring contains the same species (to continue the chain) depends on the ring. Starting from the closest ring, the chances are 28%, 48%, 68%, and 88%. Catching a Pokémon rather than defeating it will increase these odds by 10% for the patches automatically generated after the battle.”

I believe you misread. It doesn’t increase the shiny odds, it increases the odds of the generated patches being the same species. Also, it only increases the odds for the generated patches after the battle, so it doesn’t stack.

Source: What else? Bulbapedia

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