Listen up everyone, I am about to end this guy’s career.
First off, I will go by your numbers. Currently there are 338 Protoss players, 175 Zerg players, 273 Terran players in GM ladder. This means n = 786 and x = 338. Let me explain. The rankedftw stats he is using accounts for 4 different regions that use GM (SEA doesn’t count because dead server). These are China, Korea, America, EU. 200 players are in GM, 4 regions, 800 players in GM total. The reason why n = 786 is not 800 is because there are 14 random players in GM. For the sake of argument, we will leave those numbers out. On to the calculation.
In the image he put, he clearly sets n = 600 WHICH IS A MAJOR MISTAKE THAT THROWS THE ENTIRE CALCULATION OFF BY AT LEAST 10^20. When you fix this error and put n = 786, THE CORRECT N VALUE, you get an upper cumulative Q of 1.0467*10^-8. Mind you, this value is still pretty crazy in itself (but not as crazy as OP is), but let’s look at some assumptions of using the binomial distribution.
- The number of observations is NOT fixed. N = 800 is how it is supposed to be, or N - random players, BUT – that is clearly not the case. Players are constantly moving in and out of GM due to the contender pool. MMRs are always changing. Even as we speak there are currently 788 players on GM globally (not 800).
- Each observation is independent. This is a complex question. Is each data point really independent? When the result of being GM is based on matches you play against people of the same and different races? It really isn’t. In the Minecraft example, they use blaze rods and enderpearls. Each of those observations ARE independent from one another. The result of a player of a particular race being in GM is NOT independent of the other - especially when players hit other players in GM. Also, mind you, people move in and out of GM all the time. There’s plenty of reasons to believe these observations are NOT independent. Also as a bonus, the GM ladder constantly interacts with people in the master league too. I could go on, but you get my point.
- Each observation represents one of two outcomes. So p = 1/3 is Protoss, not P is 2/3, we can go along with that.
- The probability of success p is the same for each outcome. I think this is a perfect world assumption of balance where each race is perfectly represented on the GM ladder.
So out of the 4 necessary assumptions, the first one is kind of broken, and the second one is DEFINITELY broken. Do you know what this means? It means you can’t use the binomial distribution. By the way, the Minecraft example passes all 4 assumptions with flying colors, especially because it’s coded into the game, meaning some things are ABSOLUTE.
But let’s just say the 4 assumptions hold, and let’s try to list possible factors as to why the number is still high as is (1.0467*10^-8). Let’s look at the population. The lowest MMR to get into GM is ~5k MMR (I’ve heard various low numbers about KR and AMerica). There is no upper limit, but according to ranked ftw, there are multiple people ABOVE 7k MMR. Let’s put that into perspective. A low diamond player is closer to the lowest GM player than the lowest GM player is to the highest one. That is an INSANE SKILL GAP DIFFERENCE. There is ABSOLUTELY no way the lower half of the GM ladder represents skill at the top level when there is a good number of players above 6k MMR in GM AND MASTER LEAGUE. Also, the games needed to stay in GM are ALL OVER THE PLACE. Also again, the winrates are ALL OVER THE PLACE. There’s too many factors that could easily influence the observation we are seeing!
The conclusion I must draw here is that OP has absolutely no idea what he is talking about, and if you ever see him ramble on about statistics and whatnot, make him remember this post. You can even quantify how delusional he is (about 10^20 crazy).
Sincerely, someone who ACTUALLY studies math/statistics 
(the man in the youtube video studies statistics, OP clearly does not).
Quoting in case you edit