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The Chicago Bulls moved expediently in free agency, snapping up Mike Dunleavy Jr. with their taxpayer mid-level exception on the first day. That, coupled with their draft day additions, leaves them with one big hole to fill—a second backup center.

Nazr Mohammed has already agreed to return to take up some of the duty of backup center, but the Bulls are still in need of another frontcourt player. Joakim Noah, Carlos Boozer and Taj Gibson combined to miss 36 games last season with an assortment of injuries.

Noah’s plantar fasciitis flared up, possibly as a result of playing excessive minutes.

If you need compelling evidence that Noah needs more help, try this—last season he ran 2.74 miles a game, (roughly 214 miles on the season). That's more than any player in the league.

It’s pretty reasonable to conclude running that kind of distance every other night on a hardwood floor might start to wear on a man, especially his feet.

The way the system works, the center is asked to do a lot, and maybe Noah more than anyone, even more than Asik was asked to do. Noah extends his defense out to the perimeter more than any center in the league. It’s not just the minutes; it’s the system. Not many teams use their centers the way the Bulls do.

According to mysynergysports.com, Noah defended either the spot-up or the isolation 382 times. Compare that with Defensive Player of the Year Marc Gasol who defended those plays just 260 times. That's roughly 50 percent more often that Noah was stepping out to the center, and Noah played fewer games.

Noah defended 89 three-point attempts to Gasol’s 36. And again, Gasol was the Defensive Player of the Year. The point here is not to compare how well they defend; it's how much distance they defend.

The range of Noah’s defense is greater than other player's. As much talk as there has been about time, the greater concern is distance. The Bulls don’t just need a player who can fill up minutes; they need a player who can take up miles.

Ergo, when looking at bargain basement centers, we have to keep these two things in mind. Can they run, and can they defend? Whatever you get at that cost is going to be flawed in more ways than one. When you are looking at players at that price you get them for what they can do, and in spite of what they can’t do.

Nate Robinson, for example, has his flaws, but his ability to score was critical last season.

The Type of Player to Avoid—Greg Oden

One type of player that the Bulls want to avoid is the big-name, low-risk, high-reward scenario like Greg Oden. It would seem like a player with that kind of promise would be a winner but there are issues with it.

Foremost among them is, do you really want to add a player with a multitude of knee issues into the Thibodeau system? It’s only a matter of time before he goes down with yet another micro fracture and whenever that happens it's bad.

If it happens at the beginning of the year, that means that Noah just keeps playing more minutes and running more distance and he’s drained by the time the playoffs come. If Oden goes down late in the season, it means the rotations are thrown out of whack for the playoffs.

The rewards aren’t as great as you might think either, because Oden's strengths contradict what the Bulls do.

He’s a great low-post scorer, but that’s not the Bulls offense. They don’t want a center that can play under the rim and dunk at will. They want one who can step away, who can handle the ball a little bit and who can knock down an occasional jumper.

The Bulls prefer to have Derrick Rose and Jimmy Butler driving the lane and finishing at the rim, or getting to the line. Having bigs who can stretch the court and pull bigs away means fewer blocked shots. Oden isn't known for doing that.

So, there are three players who could make sense. They aren’t going to be All-Stars. They aren’t even going to be substantive rotation players possibly.

Of course all this might be moot anyway, as Oden is probably not going for the minimum. However, Oden-types who have a more "traditional center" resume" might not be the best options.

Tyrus Thomas

Tyrus Thomas is getting amnestied by the Charlotte Bobcats, and would be a nice fit.

The reason Chicago is called the Windy City has temporarily been changed to the gale of laughter that follows the reading of this suggestion.

But think about it. For all of Thomas’s faults, and I’m not going to deny there are many, he would fit like a glove in Thibodeau’s system.

I keep trying to talk myself out of it, but there's a lot potential here.

Thomas brings massive energy. He’s highly athletic. He can jump out of the gym. His problems are between the ears. Everything below the ears is perfect for the Bulls' current defensive scheme. If only he didn't have the basketball IQ of a scarecrow.

But if he follows the yellow-brick road back to Chitown, could Thibodeau be his Wizard of Oz?

Seriously, if he ever did get his head straight, he could be one of the best backup centers in the league off the bench. And playing next to Taj Gibson, they’d make a pretty fearsome tandem.

Of course the downside here is that he could come to Chicago and be exactly what he’s always been, himself.

Plus, there would the whole irony thing if he worked out and we got to keep the Charlotte pick. Michael Jordan is still a Bulls fan at heart. I know it.

Jermaine O’Neal

Granted, with injuries being a concern there’s justifiable cause for reluctance in considering Jermaine O’Neal. But if he’s a backup playing in limited minutes, that’s less of a concern. He did manage to squeeze out 55 games last year, playing 18 minutes a game.

He is an innate shot-blocker who plays intelligently. In fact, his blocks per 36 minutes was a career high last year.

He’s sort of the opposite of Thomas. He has what you want between the ears but is lacking the athleticism and agility which once made him one of the league’s better defenders for years. He knows where to be and what to do when he gets there. His instincts are right. Sometimes his body just doesn't cooperate though.

In limited minutes, in a backup role, he could still be a presence on the court.

Between Thomas and O’Neal, it could come down to whether it’s better to have a defender out of position because he didn’t know where to be, or because he couldn’t quite get there in time. Pick your poison. But you're not getting a perfect center for the minimum.

O'Neal has a higher floor, but Thomas has a higher ceiling.

Byron Mullens

Of course there’s a third option, which is to go with a center who has more of Noah’s offensive ability and none of his defense and hope that Thibodeau can just work his magic on him. Another ex-Bobcat, Byron Mullens, could possibly be had for the minimum as well.

Mullens is a center who you can just barely say has three-point range (he’s made 78 in his career, three more than Rajon Rondo). He has decent but not great passing skill (2.0 assists per 36 minutes) for a big man, and he’s basically an average rebounder (8.5 rebounds).

However, defensively he leaves a lot to be desired, and it’s why he was eventually let go. He does have the mobility to be average—just not the instincts. Thibodeau could probably figure him out eventually. But it would take some time.

Regardless of who the Bulls get, they’ll get someone with flaws. The best scenario is that they don’t get someone with the fewest flaws, but is also equally bland on all fronts. They’re better off having a center that can at least do one thing well, and then having the team compensate for the weaknesses.