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Other players who would seem a possibility to accept the qualifying offer include left-hander Brett Anderson of the Dodgers; shortstop Ian Desmond of the Nationals; catcher Matt Wieters of the Orioles; and right-handers Hisashi Iwakuma of the Mariners, Marco Estrada of the Blue Jays and Ian Kennedy of the Padres.
The qualifying offer's value is based on the average of the top 125 player salaries in 2015.
For Zack Greinke, it is no gamble. Having established himself among the game's elite pitchers, Greinke turned 32 last month, and the right-hander has put together back-to-back seasons in which he is 36-11 with a 2.16 ERA, and the Dodgers won 42 of the 64 games he started.
For the likes of Jason Heyward, Daniel Murphy, Justin Upton and Alex Gordon, the idea of a multiyear guarantee most likely will outweigh a one-year deal, even if the annual average value of the contract is less than $15.8 million. And even if they do reject the qualifying offer, they could still re-sign with their former team.
The fact that all 34 offers were rejected in the first three years of the current free-agent system has seemingly given clubs the confidence to make the offer, giving themselves a chance to receive a high Draft choice in return for losing a player without the risk of a player accepting the deal.
This year, however, seems primed for at least one player, if not more, to call the bluff of the teams.
Enter Rasmus, who will play most of the upcoming season at age 29. By accepting the qualifying offer, he will earn more in 2016 than he did the past two years combined: $7 million with the Blue Jays in 2014 and $8 million with the Astros in '15.
Rasmus did have a career high in home runs (25) this past season, but his .238 batting average was seven points below his career average, his .314 on-base percentage was only one point above his career OBP, and he struck out a career-high 154 times.
Rasmus will have a chance to go back on the open market after next season at the age of 30, and can build off his 2015 season to create a stronger market if he does not eventually sign a multiyear deal with Houston.
Anderson, 27, is coming off a career-best 31 starts for the Dodgers. It was the first time since 2009, his rookie season with Oakland, in which he made as many as 20 starts in a season.
A second season of making regular turns in the Dodgers' rotation -- and their pitcher-friendly home park -- could bring teams into making a more lucrative long-term deal to Anderson next year.
Iwakuma, a native of Japan, has indicated a desire to remain with the Mariners, who in turn have shown interest in retaining him. Even though he will turn 35 in April and was limited to 20 starts this year, Seattle has indicated an interest in signing him to a two-year deal, and accepting the qualifying offer could facilitate that by creating a parameter for negotiations.
Desmond, who has spent his entire career with the Nationals, was a 2012 All-Star and a Silver Slugger recipient in '12, '13 and '14. However, he had career lows in batting average (.233) and on-base percentage (.290) this year, his second-lowest RBI total (62) and hit his fewest home runs (19) in four years while committing 27 errors, the second highest of his career.
Does Desmond gamble that a team will overlook his struggles, blame it on self-created pressures with free agency looming, and consider 2015 a mulligan? Or does he take the $15.8 million -- a $4.8 million raise -- and gamble that he can revive his market value in 2016?
Wieters was limited to 101 games across the past two seasons because of Tommy John surgery, but he did come off the disabled list to play 75 of those games in 2015, showing the Orioles he was recovered. There had been speculation the Georgia Tech product would wind up with the Braves, but they re-signed A.J. Pierzynski to a one-year deal this week, eliminating that possibility.
Estrada and the Blue Jays are believed to be close to finalizing a multiyear deal, and Kennedy, 29-38 across the past three seasons, would receive a $5.95 million raise if he accepted the offer.
Teams have gambled in all four years of the qualifying-offer system. The players have not called their bluff the three previous offseasons.
This year, however, is different.
Rasmus took the first step, and others could follow.