Toss hits 43% in GM

General Discussion
16

Alright, time for your dose of reality. SC2pulse reports Stats’ mmr is 6254. Dark’s is 6894. The mmr algorithm is detailed in the AlphaStar paper (page 9):

P[0i = 1] = cdf((r1 - r2) / 568))

We are going to rearrange this to make it easier to work with:

P(Win)=1/(1 + exp(X / 568)) 
where X is the mmr difference.

We can use this to calculate the odds of a 6254 mmr player beating a 6894 mmr player, like so:

P(Win)=1/(1 + exp(640 / 568))`
P(Win) = 0.24

So Stats has a 24% chance to beat Dark in a best of 1. But, they played a best of three. What are the odds of winning that?

P(WinningSeries) = (P(Win) & P(Win)) | (P(Win)  & P(Win) & P(Loss))

Solve for the first term:

P(Win) & P(Win)) = 0.24 * 0.24 = 0.0576

And the second term:

P(Win) & P(Win)) = 0.24 * 0.24 * 0.76 = 0.043776

Combine them together:

P(WinningSeries) = 1.0 - ((1.0 - 0.0576) * (1.0 - 0.043776))
P(WinningSeries) = 0.0988545024.

So, Stats has a 1 in 10 odds of beating Dark, which meets statistical significance. What if Stats’ performance is biased by Protoss by the same amounts as measured on GM trends? Well that just bumps his mmr up by ~300. That makes the previous calculations:

P(Win)=1/(1 + exp(340 / 568))`
P(Win) = 0.35

His win-rates in a best of 1 goes up by ~10%. Let’s do the calculation for a best of three:

P(WinningSeries)  = 1.0 - ((1.0 - 0.126) * (1.0 - 0.082))
P(WinningSeries) = 0.2

His win-rate doubles, but is still a 1 in 5 odds of occurring.

TLDR
The odds of Stats beating Dark is 1 in 10 if you assume Protoss has no advantage, but it’s 1 in 5 if you assume Stats receives a +300 mmr boost in PvZ like what happens in Grandmaster. Even with a balance advantage, it’s still an unlikely event. Thus my point is proven: the balance issues of carriers affects the highest levels of SC2 pro play. The “balance counsel” is wrong in their assertion that only low level zergs struggle to beat carriers, and we can say that with a 90% confidence. Carriers need nerfs. It’s just a fact of this thing called R E A L I T Y.

Not only am I right, I proved it. You were provided with the mmr numbers, which were sufficient to prove my point, you just didn’t know what they meant. Please don’t think that an argument is wrong merely because you can’t understand it. If you wanted me to explain it to you, I’d have been glad to do so, but, instead you are all “your argument is nonsense and pointless” and “you’ve provided no proof” aka literal untruths so detached from reality they are bordering on a lie. How am I supposed to respond to that.

This is why I don’t engage with the SC2 community very much, and why I avoided streaming for so long. The “neckbeard syndrome” is intense inside the sc2 community. All you had to do was ask, but, no, we couldn’t be friends because I had opinion about sc2 that you didn’t like. Lmao. Unreal. Oh well. It is what it is. Not everyone thinks scientifically and I am just going to have to accept that.

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