fall behind vs go one better

fall behind

verb
  • Used other than figuratively or idiomatically: see fall, behind. 

  • To be late (for a regular event) 

  • To be progressively below average in performance. 

  • to fail to keep up (with) 

go one better

verb
  • To take a bet and add another to it. 

  • To outdo somebody; to do something that surpasses what came before. 

How often have the words fall behind and go one better occurred in a corpus of books? (source: Google Ngram Viewer )