Everything about Tim Lincecum is unique. The delivery. The dog named Cy. The hair. And now, his arbitration case.

Lincecum is eligible for salary arbitration for the first time this offseason, and he enters the process with a resume like no one before him. Two full seasons. Two National League strikeout titles. Two All-Star Game selections, including a start. And, most impressive, two Cy Young Awards as the best pitcher in the National League.

Lincecum and his agent, Rick Thurman, have indicated he is not interested in a multi-year contract with the San Francisco Giants, preferring instead to go year-by-year, signing one-year contracts until he’s eligible for free agency after the 2013 season. That sets the stage for what could be a record-setting salary award this offseason, a test case for the value of “special accomplishment” by a pitcher.

In most cases, the arbitration panel considers the player’s performance and leadership, the club’s record and attendance, and salaries of comparable players in his service-time class and the class one year ahead of him.

But there’s a catch. The service-time limit for “comps” does not apply if the player can show “special accomplishment,” which may include All-Star Game appearances, awards, or post-season performance. For Lincecum, this exception allows him to slip the surly bonds of the six- and low seven-figure salaries earned by most players with similar time in the majors, comparing himself instead to the highest-paid starting pitchers in the game. For the Giants, the exception threatens to blow a hole in the budget for payroll. For the game’s other 29 owners and the Major League Baseball Players Association, the Lincecum case could set a new benchmark for salaries for players in arbitration.

For both sides, the high stakes place a premium on the process of determining the salary figure to submit to the three-person arbitration panel. If Lincecum shoots too high with his request, the panel could find the more reasonable route is to award him the Giants’ lesser figure. But if the Giants come in with a low offer, they run the risk of making even a request of $10 million or more appear to be the reasonable number. With the two sides exchanging figures next Tuesday, both camps are deep into strategy sessions, deciding how to play their hands. How much does he want? How much will they offer? How do you find a comparable for a player nicknamed “The Freak”?

The record salary for a first-time arbitration-eligible starting pitcher is Dontrelle Willis, who settled with Florida for $4.35 million after leading the NL in victories, shutouts, and complete games in 2005. Willis, the runner-up in the 2005 Cy Young vote, also had two All-Star selections and a Rookie of the Year Award.

His figure was matched last season by Philadelphia’s Cole Hamels, who earned $4.35 million as part of a multi-year contract signed in the wake of his magical 2008 postseason, when he was selected as the MVP of both the National League Championship Series and World Series.

But both pitchers settled in January before submitting salary figures in anticipation of arbitration hearings. Moreover, Lincecum’s numbers and hardware are superior to those of the platform seasons of Willis and Hamels, so they’re hardly ideal for comparison.

Boston’s Jonathan Papelbon got $6.35 million last offseason, avoiding arbitration in his first time eligible. Though he was a three-time All Star and had closed out a World Series victory, Papelbon had never received a vote in the Cy Young balloting. And, like all relievers, his contribution in terms of innings pitched pales in comparison to top-line starters like Lincecum, so he is not a fit.

Two starting pitchers can approach Lincecum in terms of special achievements at such an early point in their careers: Bret Saberhagen and Roger Clemens. But, obviously, baseball’s revenues and salary structure were far different in the 1980s than they are today. And, unlike Lincecum, Clemens was actually not able to file for arbitration as a player with two-plus years of big-league experience.

Saberhagen qualified for arbitration after the 1985 season, with a Cy Young award and a World Series MVP in tow. He filed for $925,000, which would rank 22nd on the list of the highest-paid starting pitchers in the game in 1986. He won his case against the Royals, receiving a raise of 478 percent from $160,000 to $925,000. While that jump sounds impressive, Willis’ raise from $378,500 in 2005 to $4.35 million in 2006 represented an increase of 1,050 percent. A similar pay raise for Lincecum would push him from $650,000 to $7.475 million.

Clemens capped his dominant 1986 season with both the AL Cy Young and MVP award, but he fell 30 days shy of qualifying for arbitration, a victim of the change to baseball’s labor agreement increasing the service time required from two full years to three for the 1987 season. When the Red Sox made Clemens a one-year offer of $460,000, Clemens left spring training and held out, incurring a $1,000 a day fine. Commissioner Peter Ueberroth personally intervened in the negotiations with the two sides, and Clemens ultimately agreed to a two-year contract worth $2 million. The deal made Clemens baseball’s 43rd highest-paid starting pitcher for 1987 and the sixth highest-paid for 1988. Not coincidentally, baseball’s next labor deal instituted the Super Two provision, extending eligibility to the top 17 percent of players with at least two years of experience, beginning in 1991.

Recent Cy Young performances do not offer ideal comparisons, either. Besides Lincecum, the last eight pitchers to win the award (Zack Greinke, Cliff Lee, C.C. Sabathia, Jake Peavy, Brandon Webb, Johan Santana, Chris Carpenter, and Bartolo Colon) did so in the middle of multi-year contracts or, in Carpenter’s case, six months after signing a long-term extension.

Santana, the most recent multiple winner, parlayed his 2004 award into a four-year, $39.75 million deal from the Twins that paid him $9 million in 2006-the year he won his second award-and $12 million for 2007. Santana and Sabathia are now the two highest-paid pitchers in baseball at average annual values of $22.9 million and $23 million, respectively. That suggests a range of anywhere from $9 million to $23 million for Lincecum’s request, depending on how bold he and his agents are feeling.

However, anything less than a eight-figure request might not be enough, if recent filings by the most decorated position players with special achievements are any guide.

Albert Pujols reached arbitration for the first time after the 2003 season with a long list of special accomplishments: two All-Star selections, two Silver Slugger awards, a batting championship, a Hank Aaron Award, and two consecutive second-place finishes in the NL MVP voting. He filed for $10.5 million. The Cardinals offered $7 million, but avoided arbitration by signing their young star to a seven-year, $100 million deal.

Four years later, Ryan Howard came to the arbitration table with an MVP, an All-Star selection, a home run title, and a Rookie of the Year award. The Phillies offered him $7 million for 2008, but he won an award of $10 million, becoming the first player with two-plus years of experience to receive an eight-figure salary.

Though both Pujols and Howard received record-setting contracts, neither player vaulted immediately to the top of the pay scale at his position. If Lincecum’s case evolves along those same lines-a request of, say, $12 million and an offer of, say, $9.5 million-The Freak should be in line to add another unique achievement to his resume: highest-paid third-year player ever.