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Mastery doesn’t work that way, it works just the same as the old system.
Level 8 is actually 5.88% stronger than level 7, not 10%. Each mastery level is a fixed multiplier applied to the birds base level (level 1).
Following your example, if an old master caused 840 damage, a level 7 bird causes 840 damage. The same bird at level 8 will cause 892, not 932. Level 10 will be 997, not 1127.
This is the math.
the level multiplier is obtained by multiplying the leve-1 to 10. So level 7 has a multiplier of 160% (1,6). (just like before)
If we divide level 7 attack to the factor we get the base level attack
840/1.6 = 525
Now we want to know what the attack level is for level 10, so we multiply the base health to class 10 factor (1,9)
So 525 * 1,9 = 997,5
I think Rovio explanation is a little confusing, because one could think each mastery level is 10% stronger than the other.