4, 42, 78, then 4th in the following rounds with pick 110 being their next pick. They have no compensation or competitive balance picks. "The 10 smallest-market teams and 10 lowest-revenue teams will have the chance to win one of six extra selections in the 2013 First-Year Player Draft. The odds of winning a Draft pick will be based on each team's winning percentage in the previous season." - Jon Mayo MLB.com I don't have the exact numbers (don't want to look them up) but the Twins seem to be just outside that list now. The D-backs, Orioles, Indians, Royals, A's, Pirates, Padres, Rays, Reds, Rockies, Marlins, Brewers and Cardinals are teams which qualified this season. I would say no way the Twins ever get there, but the Brewers, Cardinals and Orioles inclusion makes me believe ti might be possible.