SR's biggest problem: A Mathematical Proof

  1. Empirically, there is no significant inflation or deflation of SR, so your model must be wrong. For season 3, the rank distribution was Bronze: 6%, Silver: 22%, Gold: 34%, Platinum: 23%, Diamond: 10%, Master: 3%, Grandmaster: 1% (Overwatch Forums). For season 8, the rank distribution was Bronze: 8%, Silver: 21%, Gold: 32%, Platinum: 25%, Diamond: 10%, Master: 3%, Grandmaster: 1% (Competitive Mode Tier Distribution).

  2. You’re making a lot of mistakes on how the system works. See How Competitive Skill Rating Works (Season 13) for a more complete understanding.

Specifically:

The real rating is MMR, not SR. Decay does not affect MMR. It is quite likely MMR is always symmetric (one person gains what another person loses), like it is with Elo in Chess, but this has not been confirmed.

When recovering from decay, winners gain more SR than the losers lose. Leaving may behave similarly to decay (I don’t have data here).

Initial placements add MMR to the system, but that is not the relevant quantity. MMR per person is. MMR per person does not appear to be changing, so it is likely that new players are put in in such a way to prevent inflation/deflation. At least to first order, new players are put in at the median rating (Initial Competitive Skill Rating, Decrypted), but it is possible that Blizzard messes with this number to deal with people quitting the game and throwing the MMR per person off.

Blizzard could also readjust the MMR economy at placements each season, but I’ve seen no statistically significant evidence of this (Season 9 Placements Analysis, High Variance Explained).

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