For a club that most fans understandably perceived as a young upstart team, the 2013 Pirates relied heavily on veterans. Three of the highest-performing ones -- Francisco Liriano, Russell Martin and Jason Grilli -- are already under control for 2014. Several, however, are not, including Burnett, Byrd and Justin Morneau.
Morneau isn't worth worrying about. Pirates fans and the Pittsburgh media hyped the Morneau acquisition like crazy, and so it's surprising that very few people seem to have noticed that he didn't actually play very well for the Bucs, posting a -0.1 WAR. The sample size was small enough that you can probably haggle about whether Morneau was actually below replacement level. But there's nothing in his recent performance record that suggests he can be a long-term answer at first base, particularly given his age, so I would just him leave this offseason.
Burnett and Byrd are different. Burnett's 2013 season was one of the best of his career. He led the National League in K/9, narrowly beating out Jose Fernandez and Matt Harvey, and his xFIP was better than anyone else in the NL except Harvey, Cliff Lee, Adam Wainwright, and Clayton Kershaw. Oh, and his ground ball percentage was better than anyone else in baseball.
In other words, Burnett just posted a superstar-caliber season. And if he wants to come back, he has every right to ask for a big annual salary, particularly if, as expected, he only wants a one-year deal. Extending a qualifying offer, which would pay $14.1 million, seems like an easy decision (which is kind of funny, given how eager the Yankees were to get out from under his $16.5 million annual salary a couple years back), and if the Pirates are very lucky, maybe they can convince him to take it. Hopefully the Pirates' decision to go with Gerrit Cole in Game 5 didn't ruffle Burnett's feathers.
Like Burnett, Byrd performed like a star in 2013, posting 4.1 WAR between the Mets and Pirates. Compared to Burnett, though, I'm less certain what Byrd's 2013 season means going forward. Byrd hit .210/.243/.245 in 2012, then got suspended for PEDs. Even when Burnett was with the Yankees, he never had a season that bad. There's good reason to be skeptical of Byrd, particularly given his age.
Also, Gregory Polanco made it all the way to Triple-A in 2013. He didn't hit all that well even in Double-A, so it's doubtful he'll make much of an impact in the majors in 2014, but he looks like he could be an everyday outfielder by early 2015. If the Pirates were to have Byrd under contract that season, they'd likely have four very good outfielders, and only three spots to play them. A one-year deal for Byrd would be ideal, but it probably isn't realistic -- any number of teams should be ready to sign Byrd to a multi-year contract after the season he just had, and Byrd has only had one significant big-league contract, so one would imagine he's want a multi-year deal.
As far as we know, Burnett still hasn't decided whether to retire. My guess is that he won't, and that he'll sign a one-year deal with the Pirates, perhaps for somewhere near the $16.5 million he made in 2013. The Pirates will likely try to keep Byrd, but my guess is that he'll get more money elsewhere.