PokéBase - Pokémon Q&A
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When I throw a pokeball at a Pokémon sometimes the pokeball makes a whistle sound, it shakes one time before landing, and successfully catches the pokémon in one shake. This specifically happens when I immediately throw the Pokéball without battling, why is this happening?

Thanks, I was just worried about it.

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This is normal. It is a special mechanic added in Generation 5 called a "critical capture", which happens randomly and causes the PokeBall to shake only once instead of three times before the Pokemon is caught, meaning that the chance of capture is increased considerably. It is purely a coincidence that this happens to you mostly when you throw a PokeBall on the first turn.

The chance of landing a critical capture is based on the amount of Pokemon that have been registered as caught in the Pokedex. According to Bulbapedia, the chance ranges from 0% with 30 or fewer species caught to around 41.67% when the Pokedex has over 600 completed entries. The chance can be calculated as follows: (capture rate x multiplier) / 6. The value of the multiplier is determined by the number of Pokemon registered as caught in the Pokedex.

Species caught     Multiplier
Over 600           2.5
451 to 600         2
301 to 450         1.5
151 to 300         1
31 to 150          0.5
<=30               0

Once the formula has been completed, the result is rounded down to the nearest integer. A random number between 0 and 255 is then generated; if this number is less than the number the formula generated, then the critical capture will take place.

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A little confusing but thanks
No problem! I included the formula because I found it interesting, but really all you have to worry about is catching lots of Pokemon if you want to get these more often.
So basically your guy/girl gets better at catching Pokemon somehow?