Under baseball's old rules, free agents were either Type A, Type B, or no type. If your team offered arbitration to a Type A or Type B player, they declined, and signed elsewhere, your team was awarded a compensatory draft pick or two.
Baseball's new rules are a bit more hardcore. Essentially the qualifying offer works a little bit like the Franchise Tag in the NFL; a player is offered a one-year contract at the average salary of the top-paid 125 players that season, which will be approximately $14.1 million for 2014. Teams have until five days after the World Series to make a qualifying offer and, at that point, players have seven days to accept or decline. Accepting means taking the one-year contract and salary, declining means becoming a free agent.
Teams who sign a player who has declined a qualifying offer lose a first-round draft pick, which is what makes the qualifying offer such a big deal. A team like the Yankees, for example, would lose their first-round draft pick and, instead of that pick going to the player's former team, the first round would condense to 29 picks instead of 30.
One of the caveats of the system is that the first ten picks in the draft are protected. That means if the Twins signed a player who declined a qualifying offer, they wouldn't lose their first round pick but their next-highest pick.
In return for losing a player who declined a qualifying offer, the team will receive a compensatory pick between the first and second rounds. Additionally, compensation can only be granted for players who have been with their team for the entire season. As an example, Matt Garza will not be able to receive a qualifying offer because he was traded from the Cubs to the Rangers - but Ervin Santana will be eligible.
Kyle Lohse declined a qualifying offer last winter, and it made in almost impossible for him to find a job. He did finally sign with the Brewers on March 25, to a three-year, $33 million dollar contract. Lohse missed all of spring training and his situation illustrates the danger of a player turning down a qualifying offer, particularly if that player is not considered a top-end free agent. As a result Milwaukee did not have a draft pick until #55 overall. Signing clubs also have to determine whether losing their draft pick will figure into the contract details.
The Twins will have no free agents worth a qualifying offer this season, and aren't likely to have one until, at the earliest, next winter if Josh Willingham has a great season and isn't traded.
Minnesota is, however, in a position to sign one of these players without losing their first-round pick. Are there any free agents who you'd be willing to surrender an early second-round pick to sign?