We could use some help at that No. 3 pick, John. (Tony Dejak/AP)

The Wizards have the No. 3 pick, obvious deficiencies in talent and glaring needs on the perimeter. But there is also a formidable pool of talented players who can help address those areas of weakness in Kentucky swingman Michael Kidd-Gilchrist, Florida guard Bradley Beal and North Carolina small forward Harrison Barnes. Big men Thomas Robinson from Kansas and Connecticut’s Andre Drummond are also expected to go high in the June 28 draft.

“We’re going to add another young player, another solid piece to our puzzle in the draft,” Wizards President Ernie Grunfeld said this week. “We don’t know what position that’s going to be right now.”

Grunfeld, Coach Randy Wittman and other members of the basketball operations department are in Chicago through Sunday to evaluate the draft’s top prospects. Not only will they get to see how players respond to exhausting speed, strength and agility drills, but the Wizards will also get 15-minute interviews with the top players to get a better sense of their character and personality.

Successful franchises have proven that fit is just as, if not more, important than talent. And they will need a player who can form a solid union with Wall.

Acquiring Nene was a major move in upgrading the talent base for a franchise that has been stuck below mediocrity for the past four seasons. Nene, Wall and Jan Vesely are the only lottery picks on the roster and superior talent is necessary to compete and contend in the NBA. This draft gives the Wizards a chance to snag the third-best player available. That’s a big deal. Owner Ted Leonsis has already declared that the Wizards aren’t moving the No. 3 pick, which Grunfeld did not dispute.

“We do what our owner says,” Grunfeld said. “You never say never to anything, but in all likelihood, this is a player that will be with us for many years to come. And this could be a really solid piece to what we’re trying to build.”

The last two teams to trade top three picks have had the decisions explode in their faces. Portland gave Utah the No. 3 pick in 2005 and missed out the chance to pick Deron Williams and Chris Paul. The Trail Blazers took Martell Webster instead. Chicago traded the No. 2 pick in 2006 and got Tyrus Thomas in exchange for LaMarcus Aldridge.

Of the teams fortunate enough to get a building block in recent years, Oklahoma City is the best example of a team that got it right in subsequent drafts. After taking Kevin Durant second in 2007, the Thunder drafted Russell Westbrook and Serge Ibaka the next year and James Harden the year after that. That quartet is now the young core of a team that has already reached the NBA Finals.

Cleveland got LeBron James in 2003 but drafted Luke Jackson (over Al Jefferson and Josh Smith) the following year and didn’t have a first-round pick in 2005. James was able to lift the Cavaliers to the NBA Finals and another trip to the conference finals but left because he didn’t believe he had an adequate supporting cast.

Orlando took Dwight Howard in 2004 but selected Fran Vasquez (who will likely never play in the NBA) the next year and drafted a solid role player in J.J. Redick after that. Howard lifted Orlando to the NBA Finals in 2009 but has already expressed a desire to go elsewhere.

Wall certainly has yet to prove himself worthy of being mentioned in the same class as those elite talents, but the Wizards have to provide the best environment for him to succeed and reach his full potential in Washington. The best way is by adding the talent that can make Wall better and vice versa.

The jury is still out on Vesely, who came on in the final month of his rookie season but has yet to establish a position or a consistent shot outside of five feet. While some could argue that the Wizards would’ve been better off taking Klay Thompson last year, the sixth pick historically isn’t considered a slot that can alter the direction of a franchise.

A top three pick, however, carries a different level of expectation and hitting correctly — or misfiring — could go a long way toward determining the course of an organization that repeatedly states that is being “transparent” about building through the draft.

“We’ve got to increase the talent level on this team,” Wittman said this week. “We’re not where we want to be from that standpoint, so we’re going to get that, at the third pick.”