runner-up vs second best

runner-up

noun
  • Second favourite. 

  • The person who finishes second, or in any position after the first. 

second best

adj
  • Characterized by one or more optimality conditions not being satisfiable. 

noun
  • A situation where one or more optimality conditions cannot be satisfied. 

  • Something (or someone) that is inferior to the best. 

How often have the words runner-up and second best occurred in a corpus of books? (source: Google Ngram Viewer )