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Cobb, 30, spent his first six Major League seasons with the Rays. The right-hander made 29 starts and went 12-10 with a 3.66 ERA and 128 strikeouts in 179 1/3 innings in 2017, his second year removed from 2015 Tommy John surgery.
A qualifying offer is a one-year deal worth $17.4 million for 2018, the average salary of MLB's 125 highest-paid players. If a player is extended a qualifying offer, turns it down and signs elsewhere, the team that loses him receives a Draft pick next year as compensation.
"I really appreciate the offer the Rays have extended to me," said Cobb. "I look forward to speaking with my agent and deciding what the best route would be for my family and I."
In Cobb's case specifically, because the Rays are a revenue-sharing recipient, according to MLB.com's Jon Paul Morosi, they could receive one of two different Draft picks based on the rules of the new Collective Bargaining Agreement. If Cobb signs with another team for at least $50 million, the Rays would receive a 2018 Draft pick between the first round and Competitive Balance Round A. If he signs for less than $50 million, the Rays would receive a pick following Competitive Balance Round B, which comes after the second round.
Players like Cobb, who have been extended such an offer, now have 10 days to accept or reject their offers.
That gives Cobb until Nov. 16 to decide whether to take the qualifying offer, stay with the Rays for one more season and become a free agent following 2018, or decline it and test the free-agent market now.
After the 2012 season, the Rays were faced with a similar choice when considering center fielder Melvin Upton Jr.'s case. They opted to make him a qualifying offer of $13.3 million (the qualifying offer amount at the time), but Upton turned down the offer and signed a five-year, $75 million contract with the Braves.
Bill Chastain has covered the Rays for MLB.com since 2005. This story was not subject to the approval of Major League Baseball or its clubs.