No, this is not possible. There is no "expected damage" or "expected healing" or, idk, "expected threat/positioning/cd usage".
Ex: A dps might have been spending 90% of their time dealing with mechanics (like, say, doing the belt on siegemaster and cc'ing the bombs fixating on people). What is this person's expected damage? Is it different from someone tunneling on boss? If it isn't, then everyone will ignore mechanics and tunnel. If it is, how different should it be?
In general, what kind of a formula would be used to determine someone's "expected damage"? Should it be lower if you used cc? No, probably not, since then people would put cc abilities in their castsequence macro and always get loot. So should it be cc abilities used on specific mobs? Uh oh, this formula would be different for every fight. What if they screwed a formula up and didn't give loot to people who still did decently?
Don't even get me started with healing. That disc priest who is overgeared doing 70% of healing would ensure all the non-absorb healer would get no loot.
The idea seems simple at first, because when you look at the dps doing way less than half the rest of the raid, you can't help say the word "carried" and "unfair" when they get loot. You want a way to motivate them to try. And they might be trying, they are just new (or suck really bad...bad keybinds...clicking...poor UI and bad target switching...w/e). Since there's no way to create a definitive line - "Must do 40k dps" - and no way to create a fair formula, this can never be.