Brewers officials spent part of Thanksgiving week debating whether to offer arbitration to their compensation-eligible free agents, a sometimes complicated decision with immediate and long-term implications.

Four of the team’s free agents are up for debate, and all are pitchers: Eric Gagne, CC Sabathia, Ben Sheets and Brian Shouse. The Brewers have until 10:59 p.m. CT on Monday to decide whether to offer arbitration, a move which could net compensatory Draft picks if any of those players sign elsewhere but also could lock the team into high-priced, one-year contracts.

“Monday is a big day,” Brewers general manager Doug Melvin said. “A lot of teams are waiting until that day passes to make other decisions.”

Here’s how it works. Teams receive Draft-pick compensation for certain high-profile players who depart via free agency — two picks for so-called Type A players and one for Type B players. Sabathia and Sheets are Type A and Gagne and Shouse are Type B, according to a formula set by the Elias Sports Bureau and based on players’ statistics over the past two seasons.

In order to qualify for those compensatory picks, a departing player must first be offered arbitration by the end of the day Monday. Players then have until Dec. 7 to decide whether to accept.

If a Type A player declines, he remains free to sign with any team and his former team is compensated based on his new ballclub’s record in the previous season. If his new team was in the top half of Major League Baseball’s 30 teams, the former team receives the new team’s first-round Draft pick plus a “sandwich” pick between the first and second rounds. If the new team fell in the bottom half, the former team receives the sandwich pick plus the new team’s second-round selection.

Type B players who are offered arbitration and then sign elsewhere net their former teams one compensatory Draft pick instead of two.

The Brewers are certain to offer arbitration to Sabathia, the most prized pitcher in this winter’s free-agent market and who is sure to cash in with a multiyear mega-deal, and Shouse, whom Milwaukee would like to have back on a one-year contract but who instead is seeking two years on the open market.

But Melvin would not offer any clues about longtime Brewers ace Sheets, a four-time All-Star whose value on the free-agent market is complicated by his injury history, including a torn flexor muscle near his right elbow that forced Sheets to miss the Brewers’ postseason series against the Phillies. Sheets earned about $12 million in 2008 and would get a hefty raise in arbitration after going 13-9 with a 3.09 ERA in 31 starts, including five complete games.

The Brewers almost certainly will not offer arbitration to Gagne because he earned $10 million in 2008, a figure that would factor into his 2009 salary. He went 4-3 with a 5.44 ERA in 50 games, and Salomon Torres took over the closer’s role in May after Gagne injured his right shoulder.

The Brewers’ other free agents who did not qualify for Draft compensation include reliever Guillermo Mota, infielders Russell Branyan, Craig Counsell, Ray Durham and Mike Lamb and outfielder Gabe Kapler. Melvin was particularly disappointed that Durham did not qualify as a Type A or Type B free agent, likely the result of Durham’s below-average 2007 season in San Francisco.

The Brewers may have some interest in bringing back Counsell, even after declining his $3.4 million option on Halloween, and Kapler, who was excellent as a reserve outfielder before suffering a season-ending upper back or shoulder injury. Melvin said he would not make a decision on Mota, who posted a 1.57 ERA in his final 25 appearances, until later this winter because there are so many relievers on the market.

It rarely makes sense for teams to extend an offer of arbitration to a player not eligible for compensation. The Brewers are not expected to do so.

Hookscenter.com wire report (McCalvy).