The monte-carlo simulation I mentioned on Sunday has been running simulations all week. An MLE (maximum likelihood estimator) is finding what sets of parameters produce the closest match to the EU ladder. These are the parameters for the current best fit. Warning: Not safe for protoss!
Score: 0.872458
Relative Score: 0.011245
Skill mean:
Terran: 68.954508
Protoss: -31.519673
Zerg: 54.204914
Random: 60.438368
Skill deviation:
Terran: 68.954508
Protoss: 31.519673
Zerg: 54.204914
Random: 60.438368
Chance of new player selecting:
Terran: 0.257013
Protoss: 0.367683
Zerg: 0.183231
Random: 0.210366
Matchup biases:
Terran:
vs Terran: -2.937276.
vs Protoss: -91.564336.
vs Zerg: 58.725712.
vs Random: 0.812737.
Protoss:
vs Terran: 20.953692.
vs Protoss: -78.906773.
vs Zerg: -42.065304.
vs Random: 9.192017.
Zerg:
vs Terran: -15.321327.
vs Protoss: -41.713479.
vs Zerg: 46.257139.
vs Random: 64.492764.
Random:
vs Terran: 36.614956.
vs Protoss: -12.590818.
vs Zerg: -77.164219.
vs Random: -67.489791.
Quit ratio: 0.811254
Switch ratio: 0.775829
The score for this solution is 0.872458, meaning it differed an average of 3% per-league per-race from the actual ladder data. These are measured in Elo, which means Terran having 68.954508 average skill and Protoss -31.519673 would produce a TvP win-rate of 64% for Terran if we ignored the matchup biases (aka balance).
According to this, TvP is Protoss favored. TvZ is Terran favored. PvZ is balanced.
This result is remarkably similar to the average rankings of players from the SC2 pro scene:
What do you expect from someone who uses the Moctezuma calculus to point out imbalances instead of pointing out replays/VODS of specific games which is probably easier,faster and more reliable to start a discussion about balance?
I guess it makes sense. The advantage/disadvantage comes from both at the same time. It’s like protoss gets +21 AND +92 vs terran so +113 and terran gets net minus -113.
So in terms of net race balance of this setup:
TvP:
113 in favor of toss
PvZ:
balanced
TvZ:
70 in favor of Terran
Terrans avg ELO get skewed upward even though they have technically the biggest disadvantage in a matchup. Protoss ELO gets skewed downward even though they only have advantage. And zerg is inbetween, even though zerg is strictly at disadvantage–fitting what the previous post had for zerg population getting ‘squeezed’.
There is a matchup bias for each race. So it can change vs T for Protoss or vs P for Terran to affect the matchup.
It means one race was at a disadvantage and the program equalized by moving the other race closer rather than moving both towards 0. It’s easier (probabilistically speaking) to change 1 variable than it is to change 2.
The relationship outlined here is pretty clear from watching replays/vods. GM has literally never been more imbalanced. That means whatever imbalances exist, they are huge and super obvious to spot. Protoss for example has a much faster third / bigger eco in TvP on top of having a more cost efficient army.
PvZ games you’ll see top Protoss players fail allins, transition off it, take repeated probe line losses, and still macro a 200 supply army where 1 disruptor shot can hit and the zerg is out (the recent Dark vs creator).
When a theory can make a multitude of accurate predictions, it’s no longer a theory nor a matter of “trust” nor “opinion”. It’s more in the realm of fact at this point. If you can show that it makes inaccurate predictions, that would move it back into the realm of theory and opinion. As of right now, I am not aware of any such inaccuracies, and it’s made well over a dozen predictions at this point. It’s pretty much fact.