This is a really messily-phrased question because I'm quite confused and ignorant... so for games like mobile games Candy Crush has things like Ranking, Highest Score. Skyrim has things like Bunnies Killed, Potion Made. Mass Effect has things like ( I recall faintly) Total Head Shots, Enemies Exploded.... you know what I mean. What exactly are those things called?
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well its all about stimulating the reward pathways in the brain, there needs to be some challenge, a point you overcome, than a recognition or reward.
Quest>Boss>killed>level up, achievement, quest gold
or something more simple like guitar hero, where you hit the right key and you get the music playing nice, or some disjointed noise, thats basic positive and negative reinforcement.
but theres tons of material you can find and look up on this aspect of game design, its probably one of the most understood (which doesn't mean people often can't get it wrong)
Metrics for the devs.
Depends what you need it for. If you`re lookin into how to do something, then checking out how to find metrics would be more useful i think.