counterfactual vs on the wrong track

counterfactual

noun
  • A conditional statement in which the conditional clause is false. 

  • A claim, hypothesis, or other belief that is contrary to the facts. 

  • A hypothetical state of the world, used to assess the impact of an action. 

adj
  • Contrary to known or agreed facts; untrue. 

  • Of or in comparison to a hypothetical state of the world. 

on the wrong track

prep
  • using the wrong general approach to a particular task or problem; pursuing something in an unpromising way 

How often have the words counterfactual and on the wrong track occurred in a corpus of books? (source: Google Ngram Viewer )