hands down vs willingly

hands down

adv
  • without much effort; easily 

  • without question; undoubtedly 

  • by a large margin (in a game or contest) 

  • Used other than figuratively or idiomatically: see hands, down. 

willingly

adv
  • Of one’s own free will; freely and spontaneously. 

How often have the words hands down and willingly occurred in a corpus of books? (source: Google Ngram Viewer )