Quote (BardOfXiix @ Jan 26 2014 09:33am)
To an extent, yes. And there are a lot of variables to be considered, like player skill. But if you set up a basic statistics approximation, using the standard alpha of .05, you can get a good feel for the numbers.
Let's define a binomial variable, K. K is the probability that a randomly selected player in the GSL is of our target race--we'll do one for the 5 Protoss, and one for the 3 Terran.
Assuming that the number of players of each race is approximately equal, and that all players are approximately equally skilled, the probability that a randomly selected player will be our target race is .33 (3 races, 1 target race = 1/3).
Since there are 32 players in the GSL, this gives us a standard deviation of (pqn)^1/2, or (.33 * .66 * 32) ^ 1/2 = 2.64, and a mean of .33 * 32 = 10.56.
To find the likelihood of having 5 players of the target race in the GSL, we'll use a standard Z test.
Z = (A - M)/SD, actual minus mean divided by standard deviation. For the Protoss example, it's
(5-10.56)/2.64 = -2.11 = Z
Then you go plug your Z score into a handy dandy calculator, or look it up on a chart, and you'll find that the probability of having 5 or fewer Protoss players in our simulation is p = .017. Since p < alpha, we conclude that, if there is an equal player distribution and everyone is equally skilled, Protoss was underpowered.
A similar case can be made for the Terran situation, and since the number is even smaller I can safely say that the odds are even lower. So currently, one could make the claim that Terran is underpowered within the professional scene.
Mfw you can't objectively know that all players are equal skill, hence your "math" fails to be of any relevance.