Maybe it messes with the random number generator.. somehow.

Awesome article, but I suspect that something is wrong. If we see Mewtwo, lvl 70, full hp, frozen solid it says that -on average- we need 6 ultra balls. That is FAR from true. I always freezed all the legendaries to capture them easier, and it took always more than 10 balls to capture them.

We can get a more useful translation than "you need approximately 6 balls on average", here's how:

The process of capturing is a Bernoulli process [0]: each time you throw the ball, there is a P chance of catching it, and it is independent of subsequent throws.

Chance of catching, given 1 ball = P Chance of not-catching, give 1 ball = (1 - P) Chance of not-catching, given 6 balls = (1 - P)^6

For P = 17.5%, the chance that you don't catch your Mewtwo with 6 balls is 31% (which agrees with your observation that it often took more than 6 balls).

Let's try for 10 balls: (1-0.175)^10 = 0.15 (still a 15% chance of not catching it).

It's never certain! Even with 100 balls, there's a very slim chance you won't catch it.

[0] https://en.wikipedia.org/wiki/Bernoulli_process

I always held the down arrow. It worked about 30-70% of the time.

In 60% of the time, it worked every time.

- From http://www.imdb.com/title/tt0357413/quotes

it worked about 10 or 90% of the time for me

I held the arrow down, the moment the poké ball went open and stopped pushing it before the pokéball was closed again (so yeah, just a tiny window)