Following up on this comment. A proportion sampling distribution is the distribution of a series of samples. That’s not what we are doing here. Blizzard’s tournament stats are adjusted for Elo, which is an aggregate of every game played. That’s not a sparse sampling of games, it’s literally every game. The Aligulac win-rates are also a complete list of every competitive pro game played. It’s not a sample, it’s a population, so the use of a sampling distribution is wrong.
A sampling distribution is the distribution of a series of averages, which because they are, in and of themselves, averages of a sample, will result in lower variance than the parent population. It’s very simple from the math:
s2 = P(1.0 - P) / n = 0.025
where
P=0.5, n=10
Compared to what it should actually be:
s2 = P(1.0 - P) * n = 62,500
where
P=0.5, n=250,000
You are basing your confidence calculations on a completely bogus variance. The maximum variance of a binomial distribution is N / 4 which in this case is 62,500 games. The acceptable tolerance Blizzard has set is +/- 5% which in this case is +/- 12,500 games which is a fifth of the maximum variance (0.25 / 0.05 = 5).