GM is very homogeneous in age according to research done by a computational biologist on github. The same is true for practice level. The way it bypasses alts is that win-rates don’t count duplicate accounts. Whether a GM protoss wins on this account or that account doesn’t matter – it’s all counted the same. 100 games on 1 account with a 60% win-rate is the same as 50 games on 1 account, 30 games on another, and 20 games on another. It makes no difference. GM level ZvP is within 2 points of Masters 2 PvZ. Flipping wild. By contrast, GM level PvZ is 64%. There are two types of people on Earth: those who know protoss is busted, and those who need to take an intro class on statistics.
The only caveat to gm winrates is that the ladder demotes/promotes to equalize the win-rates. What that means is that, if P is advantaged over Z, Z gms will face easier T/Z opponents as a result of having reduced mmr, and that creates a counter-pressure that fights against the insane PvZ win-rates. The same is true for Protoss who are pushed upward by PvZ (they face tougher P/T opponents). Basically you have two matchups pushing zergs up and one pushing them down, two matchups pushing Protoss down and one pushing protoss up, and PvZ is still so busted to that the 1 matchup is putting almost 2 protoss into GM for every 1 zerg.
Due to how the ladder behaves, the PvZ win-rates equalize as a balance between the advantage of Protoss and the counter-pressure that other matchups create. Ergo Zerg performance is ZvZ + TvZ + PvZ = 1 which if rearranged creates -(ZvZ + TvZ) + 1 = PvZ.
It’s a little more complicated than even this because you have to account for how common each race is on the ladder. The previous equation becomes:
ZvZ*iZ + TvZ*iT + PvZ*iP = 1
ZvZ*iZ + TvZ*iT= 1 - PvZ*iP
-(ZvZ*iZ + TvZ*iT) + 1 = PvZ*iP
(-(ZvZ*iZ + TvZ*iT) + 1)/iP = PvZThe incidence of each race in GM is 0.25/0.32/0.4, and TvZ is balanced and so is ZvZ, which makes it:
(-(0.5*0.25 + 0.5*0.33) + 1)/0.4 = 0.42
(-(0.125 + 0.165) + 1)/0.4 = PvZ
1.775 = PvZDouble checking:
ZvZ*iZ + TvZ*iT + PvZ*iP = 1
0.25*0.5 + 0.5*0.33+ 1.775*0.4 = 1So PvZ win-rates are under-estimated by a factor of ~1.8x. That means PvZ in GM, which has a difference of (63-56=7) is a 14% win-rate difference after demotion is accounted for. That’s a 69/31% win-rate split. This is an approximation, because to have the exact number you’d have to build a full probabilistic model and make sure it fits the ladder data etc. But this will be pretty close. We can do a sanity check on this figure using the Elo algorithm:
r0 - r1 = -ln(1.0 / Wr - 1) * 400
r0 - r1 = -ln(1.0 / 0.69 - 1) * 400
r0 - r1 = 320
We’re talking about ~300 mmr advantage for Protoss. That seems reasonable.