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.
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.