Career in the postseason: 2-7, 5.12 ERA; 0-7, 5.27 ERA as starter
Required Draft compensation: None. As a player who got traded in midseason, Price was not eligible to receive a qualifying offer.
Of the big four on the market, Price is the one most familiar to the Red Sox. Having spent most of his career with the Tampa Bay Rays, Price is battle-tested in the AL East. In fact, the lefty has pitched his entire career in the AL, which, by all accounts, is the tougher league to pitch in. In 11 regular-season starts lifetime at Fenway, Price is 6-1 with a 1.95 ERA.
General manager Dave Dombrowski has history with Price after acquiring him in July 2014 when he was with the Tigers. Of course, Price also has history with David Ortiz, and it's not particularly pleasant. Price took exception to Ortiz enjoying his home runs too much against him in the 2013 AL Division Series, and he promptly plunked him in their first encounter of '14. However, Ortiz wants to win a fourth ring in what will be his final Major League season, and Price is looking to be a champion for the first time. Both veterans would probably put their personal differences aside with the knowledge they are better off with each other than without each other.
The one red flag with Price is the fact he's never won a game as a starter in the postseason. However, Price has produced some good performances in October without getting a win to show for it, such as when he allowed the Orioles just two runs over eight innings in the '14 ALDS.
Required Draft compensation: Red Sox would lose their first pick (12th overall) if they sign Greinke, and the Dodgers would get a pick later in the Draft.
Of the available free agents, Greinke is the most unhittable when he is at his best. The righty is also the oldest of the four. Perhaps the Red Sox could get Greinke on a shorter contract than the other premier starters, but the average annual value will probably be higher.
In terms of statistics, Greinke's 2015 season was the best of his career. Can he duplicate that performance?
Though Greinke's dominant season came in the National League while pitching half of his games in a top pitcher's park (Dodger Stadium), he more than proved he could succeed in the American League, winning the Cy Young Award with the Royals in 2009. Also, there wasn't a big dropoff for Greinke last season between home (1.46 ERA) and road (1.88).
It's fair to question if Boston -- one of baseball's most intense markets -- is the best destination for Greinke. He does have two confidants from his Royals years who currently work in the Red Sox organization in Allard Baird (vice president of player personnel) and Brian Bannister (director of pitching analysis and development). Greinke has started just once at Fenway in his career, but he has the type of stuff that shouldn't be impacted much by venue.
Required Draft compensation: None. As a player who got traded in midseason, Cueto was not eligible to receive a qualifying offer.
When Cueto was dealt to the Royals just before the July 31 non-waiver Trade Deadline, it set him up for a golden opportunity to drive up his market in free agency. But the righty instead sputtered, going 4-7 with a 4.76 ERA. Cueto was a similar mixed bag in the postseason, going 2-1 with a 5.40 ERA in four starts. He certainly finished strong, firing a complete-game victory against the Mets in Game 2 of the World Series.
The good news for the Red Sox is that Cueto's inconsistent performance after the trade could bring his market down to a more manageable cost. Keep in mind that in 2014, Cueto was electric for the Reds, going 20-9 with a 2.25 ERA and leading the NL with 243 2/3 innings. Cueto spoke favorably about Boston during his visit to Fenway last summer, and he is a big fan of fellow Dominican Ortiz.
For those who think Cueto can't handle pitching in the AL, it should be noted that he was exceptional in Interleague Play before last summer's trade to the Royals, going 12-5 with a 2.48 ERA in 23 starts. Cueto did get shelled in his only career Fenway start last August, giving up 13 hits and six earned runs over six innings. Cueto might simply be the classic case of a pitcher who was pressing too much in a free-agent year, and then had the additional challenge of being traded in midseason. He could become a nice option for the Red Sox if Price and Greinke slip away.
Required Draft compensation: If the Red Sox sign Zimmermann, they would lose their first pick in the Draft (12th overall), and the Nationals would get a pick later in the Draft.
Zimmermann's ERA went up a full run in 2015, but the righty still put up respectable numbers and has superb control. In taking a closer look at Zimmermann's season, two subpar months (May and September) made the overall performance look worse than it was. Zimmermann is known for being a top competitor, a trait that would serve him well in Boston.
Zimmermann's last experience at Fenway Park was not a positive one, as the Red Sox tagged him for nine hits and eight runs (seven earned) over 2 1/3 innings on April 13 this season. In 15 career starts against AL East foes, Zimmermann is 5-5 with a 3.79 ERA.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.