why is it that i win more normals than rank

I imagine it's a combination of the type of attitude people have towards playing normal as opposed to playing ranked as well as the general level of serious play in comparison between the two. It could also be that you are over stressing yourself while playing ranked whether consciously or through your subconscious.

More inexperienced players seem to think that ranked is more important than it is. They consider ranked nothing more than a "badge of honor" of sorts, or something to prove, when it's supposed to be a fun way to test yourself. It's unfortunate, but that's how it is. More people who play normals are actually playing for fun or playing seriously than in ranked.

I would argue that people in ranked can take it more seriously than people in normal games who may be trying out new champions

I'm sorry did you really ask that question? I know there is no such thing as a stupid question but the answer is in your question. People care more about ranked therefore you get more try-hards than in normals because people want to win in ranked in normal most people are trying to learn or just having fun.

trolls - RANK (MOST OF THE TIME) pros - Unranked (MOST OF THE TIME)