PokéBase - Pokémon Q&A
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A friend of mine says that the HP of your Pokemon will affect the catch rate (lowering your chances if your Pokemon has low HP). I'm fairly certain this isn't true, but wanted a second opinion.

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Yes. If all the Pokemon in your party have 0 HP, the catch rate of the opposing Pokemon is 0, since you are forced to leave battle.

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The formula also takes into account the following factors:

The health of the Pokémon (relative to its full health)
The type of Poké Ball
Any status condition of the wild Pokémon
Any active Pass Powers (in Generation V), O-Powers (in Generation VI), or Rotom Powers (in Pokémon Ultra Sun and Ultra Moon)
Certain other factors, such as the target Pokémon's level, may also factor in depending on the type of Poké Ball used or the generation.

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A party Pokemon's HP doesn't affect the catch rate of a Pokemon.

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