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The Game Rating is a new concept introduced in FHM2. It provides a numerical 1-100 score that measures how effectively the player performed his assigned role in a game.
Take careful note of that last sentence. Game Rating is not intended as a raw measure of the player's performance in a game relative to the other players. It's an evaluation of how well he met the expectations his team's coaches and management have for him.
GR is therefore tied very closely to the Player Roles system. A player's role will determine how much a particular action will affect his GR. Scoring a goal, for example, is not the primary objective of a Defensive Defenceman. It's nice, and will improve his score, but not as much as it would for a player with the Goalscorer role. Conversely, blocking a shot will get more of a GR improvement for the Defensive Defenceman than the Goalscorer.
As a technical note, GR is calculated on the fly during games, not at the end of them. It'll always be accurate up-to-the-second when you're watching a game. This lets us consider a bunch of statistical events in the GR calculation that would be very expensive in memory and performance to keep separate track of.