If someone says "the Yankees are going to lose", and everyone starts believing it, including the players, and it actually happens — what is the word for that?
Self-fulfilling prophecy. (I am not aware of a single-word equivalent in English.)
I remember my cousin, who is a psychologist, mentioned about the term "Pygmalion effect". Here is a definition from Wikipedia:
The Pygmalion effect, or Rosenthal effect, refers to the phenomenon in which the greater the expectation placed upon people, often children or students and employees, the better they perform. The effect is named after Pygmalion, a Cypriot sculptor in a narrative by Ovid in Greek mythology, who fell in love with a female statue he had carved out of ivory.
The Pygmalion effect is a form of self-fulfilling prophecy, and, in this respect, people with poor expectations internalize their negative label, and those with positive labels succeed accordingly. Within sociology, the effect is often cited with regards to education and social class.
If someone says "...", and everyone starts believing it, ... and it actually happens — what is the word for that?
early 17th century: from Latin praedict- ‘made known beforehand, declared,’ from the verb praedicere, from prae- ‘beforehand’ + dicere ‘say.’
- He predicted the Yankees were going to lose (and everyone believed it), and they did lose.
Synonym: foretell (past tense, foretold)
However, logically there is no way to prove that any prediction or foretelling has anything at all to do with any outcome. You might argue that predictions have psychological effects which may influence an outcome, but that's very difficult if not impossible to prove.
But to answer the question more specifically, the noun forms for them would be: