OAKLAND -- The A's on Tuesday offered arbitration to free-agent right-hander Justin Duchscherer, a formality that ensures the team will receive a compensatory pick in the 2010 First-Year Player Draft should Duchscherer sign with another team.

Duchscherer, 32, made a reported $3.9 million from the A's in 2009 despite missing the season with shoulder and back injuries and a bout with clinical depression.

Because he is ranked as a Type B free agent -- rankings are based on a player's performance over the previous two seasons -- the A's will receive a sandwich pick between the first and second rounds of the Draft next June if Duchscherer declines the arbitration offer by 11:59 p.m. ET on Monday and ends up signing elsewhere.

It's highly unlikely that Duchscherer, a two-time All-Star who made the American League team as a reliever in 2005 and as a starter in 2008, will accept Oakland's offer because he'd run the risk of taking a pay cut. In arbitration, the A's can propose up to a 20-percent decrease on his 2009 salary.

Duchscherer, whose agent has been contacted by several teams (including the A's), likely will get a raise on the open market, but given his injury history -- his 2007 and 2008 seasons were cut short by hip injuries that required surgery -- he'll probably have to accept a contract that features incentive clauses based on how much he pitches.

None of Oakland's other free agents -- righty Brett Tomko and infielders Nomar Garciaparra, Bobby Crosby and Adam Kennedy -- are ranked, so the A's needn't offer them arbitration. Kennedy is the only one among them in whom Oakland has much interest in bringing back.