discredit vs drag someone's name through the mire

discredit

noun
  • A degree of dishonour or disesteem; ill repute; reproach. 

  • A person or thing that causes harm to a reputation, as of a person, family, or institution. 

  • The state of being discredited or disbelieved. 

  • Discrediting or disbelieving. 

verb
  • To harm the good reputation of a person; to cause an idea or piece of evidence to seem false or unreliable. 

drag someone's name through the mire

How often have the words discredit and drag someone's name through the mire occurred in a corpus of books? (source: Google Ngram Viewer )