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The most normal you could get would be a gunslinger of some sort, which people have been asking for for quite a while. And which I would play in a heartbeat.
The problem with having a normal human in this game is that you can't have a normal human in this game, it'd be impossible for them to compete. Think about it, over the course of one round, you get shot by arrows, stabbed by spears, blown up by bombs floating right over your head, eaten, pummeled 30 feet through the air, dropped upon from heights of over 9000, eaten, disintegrated by acid, stabbed with your own blood from the inside out, slammed with gigantic swords, bombarded by cannons, smashed by meteors, and dazzled by the fabulousness that is Taric, over and over again. I'm not sure how a normal human could live through that.