The data you posted strengthens my argument, so I am not sure what you are getting at here. The cumulative binomial function defines the probabilities for these events occurring under a balanced game assumption:
- EU: 0.00004
- KR: 0.00066
- NA: 0.19026
We can combine these with Fischer’s method:
X2(v) = (ln(0.00004) + ln(0.00066) + ln(0.19026)) * -2
X2(v) = (-10.13 + -7.32 + -1.66) * -2 = 38.22
P(X >= x) <= 0.00001
So the Protoss performance (on a global scale) has such a low probability of occurring that it’s effectively 0. We can definitely say the null hypothesis is false (protoss is definitely overpowered). In statistics, the null hypothesis is the assumption that there is no correlation between Protoss and performance, so if that assumption has a <10% chance of concurring then the assumption is rejected and we conclude there is a correlation between Protoss and performance. These odds are far more extreme than what is required – there is less than a 1 in 100,000 chance that Protoss is balanced.
To demonstrate how absurd Protoss imba really is, here is a Chi-squared chart:
https://i.imgur.com/hTSOcP8.png