PokéBase - Pokémon Q&A
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With full health, no status:

HP * PokeBall bonus / 3*HP

So, I won't give them to you for ALL Pokeballs... but take an Ultra Ball. Catch rate of 2. Catching... a max HP Mew. 404 HP.

404 * 2 / 1212

Basically 2/3.

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i catch giratina......with a HEAL BALL!!!
So throwing a ultraball right when you encounter mew would give you 66% of catching? Seems legit