The majority of the good ones were drafted high in the 1st round.
Winston, Mariota, Ryan, Newton, Smith, Cutler, Stafford, Bradford, Luck, Eli, Rivers, Big Ben, Palmer and last year Manning.
Pick 15-20 ain't gonna get you any of those guys. Sure, you may get lucky with Brees, Wilson, Carr, Bridgewater or Rodgers but other than that, your best chance is a high 1st.