Given how you need 15% in the first round in order to move to the second round, Sanders supporters are going to play a key role here.
Buttigieg, too. Getting 16% statewide would still mean falling below 15% in many individual caucus-sites (and getting 13% statewide would still mean being above 15% in many individual caucus-sites). What the 15% threshold mostly does is amplify the victories of the leading candidates at the expense of the other candidates. Someone polling at 5% or less statewide right before caucus day will end up with near-zero support showing up in the result because they will miss the 15% cutoff almost everywhere (e.g., right before the 2008 Iowa caucuses, Richardson was polling around 6%, Biden around 4% and Dodd around 2% in Iowa, but Richardson ended up with 2%, Biden with less than 1% and Dodd with only a single delegate (out of 2,500) to the state convention).