Game ratings are a fairly new feature and, as you have figured out, are based on the person's rating plus or minus several hundred points for how they played in the opening, middle and endgame.
They were really designed to give people a quick and dirty assessment of how they had done in a game.
Hey everyone. I've lately been training a bit against bots in custom mode with the engine activated trying to guess best moves before looking and playing them. It's been interesting. Something I notice is that the Game Rating for both players after the game is very dependent upon the opponent's Elo. Here are two examples of me as the engine playing against the Magnus Carlsen Bot rated at 2882 and against Wendy Bot rated at 1500.
Me as Engine vs Magnus Bot
Accuracy
Me as engine: 98.3
Magnus Bot: 84.3
Game Rating
Me as engine: 2750
Magnus Bot: 2250
Me as Engine vs Wendy Bot
Accuracy
Me as engine: 98.6
Wendy Bot: 82
Game Rating
Me as engine: 2050
Wendy Bot: 1650
I'm currently rated 1079, and I play a lot of rapid games against closely-rated players and often check the post-game game analyses. I recently had a 37-move game against an 1106-rated opponent that ended with accuracy ratings of 95 and 87.2, yet our game ratings were only 1900 and 1800 respectively.
What are your thoughts on this Game Rating feature? I assume that the accuracy ratings are actually pretty accurate, but the Game Rating?