I want a simple objective. The Wiki is too confusing and not updated. All I want are a series of commands to create a scoreboard that will show each player's total damage dealt. Can you reply if you have some commands to help?
I'm not sure there's a criteria that tracks that exactly, totalKillCount counts how many kills a player has if that's useful at all.
If you really need to count how much damage a player deals I'm thinking you could probably use an execute command to get the health of nearby mobs and update the damage dealt scoreboard when a mob's health decreases but I'm not sure of the specifics. You'd probably get more useful answers if you posted this in the redstone or command blocks forum.
At least from my experience, kills is the best way to do this. You could however use a long statement of if an entity has been hit and who hit it and if the player hits something add a value to a dummy scoreboard