Under the new Collective Bargaining Agreement, teams can make a qualifying offer -- the average of the previous year's top 125 salaries -- to any impending free agent. This year's number is $13.3 million. If the player declines the one-year deal, he can still re-sign with the team at a different price.
Should the player sign elsewhere, the team that lost the free agent receives a compensation Draft pick made between the first and second rounds. The compensation pick is determined by reverse order of winning percentage, and the signing team loses its first-round pick. The top 10 picks of the Draft are protected, however, so any team holding a top 10 pick forfeits its second-round selection if it signs a player who received a qualifying offer. The Pirates' No. 9 pick is also safe, as it is compensation for failing to sign their first-round pick this year.
Players have until 5 p.m. ET on Nov. 9 to accept or decline the qualifying offer.
While the Rangers made a qualifying offer to Hamilton, they declined to make one to catcher Mike Napoli. Napoli had a breakout season in 2011 -- hitting .320 with a career-high 30 home runs -- but hit .227 this past season.
Also in the American League West, the Angels did not make a qualifying offer to outfielder Torii Hunter. The 37-year-old Hunter hit a career-high .313 this season for the Angels.
The Yankees extended qualifying offers to three players: starting pitcher Hiroki Kuroda, reliever Rafael Soriano, and outfielder Nick Swisher.
Other impending free agents receiving qualifying offers were outfielder Michael Bourn from the Braves, first baseman Adam LaRoche from the Nationals, right-hander Kyle Lohse from the Cardinals, DH David Ortiz from the Red Sox, and outfielder B.J. Upton from the Rays.