Usually, it’s pretty difficult to find significant weaknesses on the team that posted the best record in the NBA, but that’s not the case with the 62-win Chicago Bulls. In their case, the weakness is extremely glaring, perhaps more glaring than any other weakness any other team has in the entire league.

Put simply, the Bulls need a shooting guard.

Last season, the Bulls started Keith Bogans at that position and he was among the least effective two-guards in the NBA, averaging a scant 4.4 ppg. Nothing against Bogans, who’s always been a solid pro, but when your starting shooting guard isn’t, you know, shooting, then you’ve got a serious problem.

Backups Kyle Korver and Ronnie Brewer were both better at times in their own right, but Korver’s defensive deficiencies in a defense-heavy system limited his time on the floor, and Brewer’s inability to score the ball with any sort of consistency made it hard to give him extended minutes, either. Going back to when those two guys played together in Utah, it was always said that if combined into one guy, they make one heck of a two guard. On their own, though, they’re too one-dimensional to see big minutes.

Again—problem.

In an ideal world, the Bulls would have the cap space to make a run at one of the free agent scorers set to hit the open market whenever basketball returns. Jason Richardson on a three-year deal would fit this team’s needs perfectly, and he could very well be enough to push the team over the top. Even Denver’s Arron Afflalo, a younger but more promising long-term option, could grow with this young core and keep them fighting for championships for the next half of a decade.

This isn’t an ideal world, however, and the Bulls simply don’t have the money to spend on anything more than a small handful of veteran’s minimum contracts. With 11 players already under contract for the next season, Chicago is pretty much stressed to their financial limit, and that’s with Derrick Rose still on his rookie deal.

Long-term, Chicago simply can’t afford another big signing, no matter how much that signee might help them. Unless they’re able to move Carlos Boozer—and shipping off four years and $60 million worth of injury-prone Alaskan power forward isn’t going to be easy—the Bulls are stuck with what they’ve got.

Truth be told, it wouldn’t be surprising at all if the organization came back with the same lineup again for 2011-2012. Fans would love to see an upgrade at the two guard, but it’s also not a hard sell to come out and say: “We’ve got the reigning MVP, we’re defending the best record in the league, and it was only our first year under Thibodeau with a ton of new players. Let’s give this situation a little time to marinate before we blow it up.”

It’s not ideal, but it is realistic.

Despite that, Chicago might luck into some interesting options at shooting guard this year. If Vince Carter does eventually get bought out by the Phoenix Suns and then decides he’d rather chase a championship for a lower paycheck than take more money to play for a lesser team, Chicago would appear to be the ideal situation for him. He’d get to start, play plenty of minutes, and probably even score the ball at the rate he’s accustomed to. He might resist hunkering down on the defensive end this late in his career, and he’s not necessarily known as a career “winner,” but talent-wise he may be the best and most realistic option the Bulls have when it comes time to look for depth at the two.

There’s also the possibility of Carter’s free agent cousin, Tracy McGrady, who played much better in Detroit last year than anyone expected. T-Mac is clearly on the downswing of his career and the fact Chicago passed on McGrady last season when he clearly wanted to play there doesn’t necessarily bode well for his chances of ending up in the Windy City in 2012. Still, he’s shown there’s a little something left in the tank, and a season with McGrady at his age might still be better than some of the younger guys out there with less talent and less experience.

Who Chicago really should be holding out hope for is Richard Hamilton, however. With two seasons left on his deal, a buyout isn’t anything remotely close to an inevitability, but should it happen and Rip end up a free agent willing to take the minimum to play for a winner, there wouldn’t be a better situation for him or the Bulls. Hamilton, despite being on the downswing of his career, isn’t quite as burned out as McGrady or Carter, and he’s accustomed to working his tail off and playing defense. That suggests he’ll fit well in Thibodeau’s system, and his combination of offense, defense, and work ethic make him a better option than anybody they currently have on their roster.

The options here are mostly older ones, but for the money Chicago has to spend these types of veterans are probably the best they can hope. Of course, they can always bring back the same team they ran with last year (more or less), but an upgrade at the two would really, really help.

To come into another season with the same team that fell so painfully short in the last playoffs would be a huge disappointment. Many have argued that Thibs squeezed 110% out of that roster, and to expect more than 110% this year would be silly. Expecting 62 wins with this batch would also be silly, as would any expectation of a follow-up MVP performance from Derrick Rose.

No, the only way this team gets better in 2012 is if they fix their biggest problem, which is shooting guard. They do that, they’ve got a chance. They don’t, then they’ll be watching Miami play for the championship again next June.