Quote (coLstory @ Jan 25 2014 01:42am)
Last season there was 5 protoss, it's fluctuation renders these types of statistics useless.
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.