If someone says "...", and everyone starts believing it, ... and it actually happens — what is the word for that?

(verb) predict

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

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.

If someone says "...", and everyone starts believing it, ... and it actually happens — what is the word for that?

(verb) predict

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:

• prediction
• forecast