placing vs runner-up

placing

noun
  • The position of a competitor at the end of a race. 

  • The action by which something is placed; placement; positioning. 

  • The condition of being placed. 

runner-up

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

  • Second favourite. 

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