It’s hard to imagine the White Sox having a more depressing start to the season. They are stuck in last place in the American League Central, and their hitting has been abysmal. When you remove pitchers’ hitting from the equation, the White Sox wRC+ is tied for dead last in baseball with the Marlins, who are not even trying to field a competitive team. And while usually the team has fan favorite Paul Konerko to look to as a bright spot, even he has stumbled badly out of the gate. With the AL Central suddenly seeming rather competitive, the question arises — is it time for the White Sox to blow it up and sell?

First thing’s first — we have to figure out who the White Sox actually have to sell. Because as it turns out, many of their long-term contracts are un-sellable. The player on the books for the most money, John Danks, is essentially stuck in Chicago. He is due $14.25 million during this season and then the three seasons after it. And since he hasn’t pitched in a major league season game in nearly a year thanks to a shoulder injury, his isn’t a contract that teams are going to be excited to acquire.

The next-highest contract belongs to Adam Dunn. Since signing with the White Sox in advance of the 2011 season, Dunn has compiled a -2.4 WAR, and it is now questionable as to whether or not he achieves a positive WAR during his contract at all. That contract doesn’t expire until after next season, and he is due $15 million in 2014. Now, if he was hitting in the manner that we associate with Dunn’s career that might be a contract that someone would take a chance on at the trade deadline. But right now, Dunn is hitting .137/.235/.308. His six homers are nice, I suppose, but it’s also not special — 40 players have hit more homers than has Dunn thus far, and 20 other players have hit the same six that Dunn has.

Next up on the hard-to-trade list is Alexei Ramirez. Now in his age-31 season, he has not been a league average hitter since he was 26, and over the last year-plus, he has been nearly 30 percent worse than league average with the stick. And while sometimes one can look at a player who is underperforming in the early going and point to a miniscule batting average on balls in play as a reason for optimism, Ramirez is not one of those players. His .296 BABIP this season is right in line with his .292 career BABIP, and most of his other peripheral stats are in line with his career norms as well. Simply put, Ramirez just isn’t that good. He plays some nice defense, and his UZR/150 of 9.0 ranks fourth among shortstops since 2010, but no one is going to pick up his contract just for that defensive value. Ramirez is owed $7 million this year, $9.5 million next year and $10 million in 2015, when he’ll be 33. Shortstops are hard to come by, but if you take on that contract you want to make sure you’re not getting a black hole offensively. White Sox shortstops are 18th in WAR overall, and 24th in wRC+. It’s highly likely that only a team that finds itself desperate following an injury would make a deal for Ramirez.

This leaves us with two players that both have substantial contracts that could be traded and are players who would definitively not be part of the future if the team decided to tear down and rebuild — Jake Peavy and Alex Rios. Peavy has an incredibly friendly deal — two years, $29 million — and even though he has been brittle in the past, he is durable and productive right now. Some team will gamble if he is dangled. Rios may not be as easy to move as Peavy, since he can block a deal to six different teams, and Rios has in the past run hot and cold, but he was pretty consistent last year and is owed even less than is Peavy.

The question then becomes, is that enough? Would dealing both Peavy and Rios be enough of an incentive to jumpstart the rebuilding process? On the one hand, unless the team wants to dip its toes back into what will be a very shallow free-agent poll come this upcoming offseason, a rebuild seems inevitable. After the season, Konerko, Gavin Floyd and Jesse Crain all come off the books after the season, and Matt Lindstrom and Matt Thornton likely will as well. And other than Danks, the only player definitively signed past 2015 is starter Chris Sale. Unless the team finds several diamonds in what has consistently been billed as one of the roughest farm systems or without significant free-agent investments, the team will be in a full-scale rebuild by 2015 at the latest. So Rick Hahn and company have a good mind to hasten the rebuilding process as soon as possible. By 2016-17, the Tigers will likely be older and grayer, and the rest of the teams in the division are run either cluelessly or thriftily.

On the other hand, if the team doesn’t get as much as they want for Peavy and Rios, will it have been worth it? After all, they can trade them just as easily in the offseason or at next year’s trade deadline and still get something, without having to bail on Konerko’s last season in black pinstripes. Konerko isn’t a guy who gets much play nationally, but White Sox fans love their “Paulie.” By WAR, he’s the 12th-best position player and 22nd-best player overall in team history, and it really would be 13th and 23rd if not for Shoeless Joe Jackson getting himself banned. But since he arrived in Chicago in 1998, only Mark Buehrle was/has been better in a White Sox uniform. So the idea of sticking it out for one last run with Konerko might have some sentimental value.

It might have some actual value, too. The White Sox enter today’s action with one of the best run prevention units in the game. As we can see from our handy and quite dandy new standings page, we see that only five teams are allowing fewer runs per game than are the White Sox, with only one of those teams (Rangers) counting themselves as an AL team. As you scroll to the right, you can see that it’s not something that is expected to continue, but as the Orioles showed us last year, just because we don’t expect something to continue doesn’t mean it couldn’t happen. Perhaps Sale and Peavy can keep carrying the rotation, and the bullpen has room for improvement too, particularly from Thornton and Nate Jones. If Konerko starts hitting, and if Jeff Keppinger can manage a few more good results, and maybe one or two other guys heat up and who knows, maybe they can find enough offense to support the pitching staff. After all, the team isn’t losing by much. They’ve only lost three games by five or more runs, and they enter play today with the same run differential as the Nationals. Crazier things have happened.

The White Sox are probably not a good team, and don’t have much chance of a postseason run — Cool Standings gives them just a 10.9 percent chance of reaching the postseason today. However, since the team has few tradeable assets (and the ones that they have can be traded at a later date) and the fact that it is the last season under contract for the 37-year-old Konerko, there is reason to think about putting the rebuild on hold for one more summer. Obviously no decision has to be made in mid-May, but if the Sox are hanging around come the trade deadline, don’t be surprised if they stand pat.