Q:

Is there a single word to describe the belief that one's actions can affect unrelated outcomes

Is there a single word to describe the belief that one's actions can affect unrelated outcomes, especially relating to luck. 
e.g. Every time I bet against Team A, they win. 
Or
If I wear my blue socks, it'll rain. 

A:

Superstition. 

a pejorative term for belief in supernatural causality: that one event leads to the cause of another without any physical process linking the two events

A:

J.R. actually found this answer but posted it as a comment
It turned out the phrase I was after was: non sequitur or the fallacy of false cause and particularly the special case of post hoc ergo propter hoc
As it happens, I was wrong about it being a "single word", and the answer is barely English, more of a Latin loan-phrase! 
Fallacy of false cause or non sequitur: incorrectly assumes one thing is the cause of another.  Non Sequitur is Latin for "It does not follow." 
[Source]
post hoc ergo propter hoc - "after this, therefore because of this".  e.g. After I parked my car, it was because of parking my car the sun came out.