This happens in White version, don't have Black or their sequels to know if it does it in those. Sometimes when I throw out the Pokeball to catch the Pokemon, it wobbles once then succeeds in catching it. First time this happened I thought I just wasn't paying attention and it did it's 3x wobble, but I have had it happen more times. Anyone else have this happen?
In Generation V, there is a chance of a critical capture, where the Poké Ball will only shake on the ground once before capture. When a critical capture occurs, the Poké Ball will make a high-pitched whistling sound as it is thrown, then pause in mid-air, and shudder before it drops down to the ground.
The probability of a critical capture depends of the number of Pokémon that have previously been caught in the Pokédex. First, compute the value of a (the modified catch rate), as above. Then, whether or not this value is less than 255 (above which the Pokémon is caught regardless of whether or not it is a critical capture)
Something similar happened to me when I played pokemon yellow a few years ago.
I threw a pokeball at a mewtwo by accident while it had full health and it just caught it on that one try.
I really didn't know what to make of my masterball though afterwards since it kinda lost it's use.
This has always been part of the game as long as I can remember. Might be superstition but it seems to be more successful if the pokemon I have out is much higher leveled than the one I'm trying to catch. Also more successful if I have caught it before.