Toss hits 43% in GM

Biological or not has nothing to do with it. It’s a process which has an element of luck and we want to know what variables control the outcome.

Experiment 1:
Variable 1: True
Variable 2: True
Outcome: True

Experiment 2:
Variable 1: False
Variable 2: True
Outcome: False.

Your conclusion: variable 2 controls the outcome even though the outcome changed when variable 2 stayed constant. Aka, your theory contradicts the data. It’s that simple.

In case you are wondering, variable 1 is “true or false, is this matchup asymmetrical”, and variable 2 is “true or false, is the protoss player stats”. The outcome is, “True or false, did Stats win?”. The player stays constant, but the outcome changes. The outcome changes at the same time as the symmetry of the matchup changes. The symmetry has a correspondence with the outcome, the player does not.

Definitely false. The variability at the pro level can’t explain an effect this large. At the pro level, matchup performance correlates with a player’s skill in the ballpark of 0.97. That means any variability in performance, between matchups, is within the standard mean error. The standard mean error represents the inherent volatility of an experiment. A player’s performance per matchup varies so little it’s indistinguishable from background noise.

If a player is winning at a 6900 mmr level in PvZ and losing at a 6600 mmr level in PvP, it means their true skill level is <= 6600 and the asymmetries of PvZ gives a >=300 mmr advantage. Amazingly, that perfectly corresponds with numbers generated using 3 separate calculation methods on the GM population (here, here).

If it walks like a duck, quacks like a duck, looks like a duck, it’s a duck. This isn’t variability in matchup skill. It’s Protoss being advantaged.