back up vs go to bat for

back up

verb
  • For the non-striker to take a few steps down the pitch, in preparation to taking a run, just as the bowler bowls the ball. 

  • To move backwards, especially for a vehicle to do so. 

  • To copy (data) so that it can be restored if the main copy is lost. 

  • To undo one's actions. 

  • For a fielder to position himself behind the wicket (relative to a team-mate who is throwing the ball at the wicket) so as to stop the ball, and prevent overthrows. 

  • To fill up because of a backlog. 

  • To halt the flow or movement of something. 

  • To provide support or the promise of support to. 

  • To reconsider one's thoughts. 

  • To move a vehicle backwards. 

  • Coordinate terms: back away, back off, stand back 

go to bat for

How often have the words back up and go to bat for occurred in a corpus of books? (source: Google Ngram Viewer )