How is it calculated per game? Does it depends on your role (kills for carry, assists for supports)
And is there a faster way to gain it?
League-of-legends – Questions about champion mastery points
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Best Answer
The exact method of calculating the grade etc is unknown, however according to the Champion Mastery FAQ it compares your performance to the average of the other players.
During the calculation your position is also taken into account. If you play Champions with multiple viable positions (such as Annie/Morgana), the system will automatically detect whether you play as a Midlaner or a Supporter for example and compare your performance to the respective role.
Most likely this will happen through analyzing the various stats in-game (KDA, Wards placed/destroyed, Creeps killed) but again the exact method isn't known.
You can speed up the process by playing in a group. Playing with premade friends will give you a small boost in terms of Champion experience. Apart from that the only way to gain more points is being an exceptional player on the champion.