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It's very difficult to differentiate between the importance of each particular player on this Chicago Bulls team. Every person dedicates a certain flavor to the recipe for winning.
Kurt Thomas carried the load while Carlos Boozer and Joakim Noah struggled with injuries. He is one of the main reasons that the Bulls have made it this far. His minutes may be few in the playoffs because of the current health of the team, but if anybody down low goes down, expect this veteran to be able to step in and play lock down defense.
Omer Asik is a great story, himself. At the beginning of the year, I had mentioned that I have never seen such an awkward basketball player in the NBA. He missed screens, misread offenses, and just didn't seem to know exactly what was happening. I believe the exact quote out of my mouth was, "Who is this awkward, lanky white guy just sitting in the paint? Oh-mur A-sick?" Credit to coach Tom Thibodeau for sticking with him and developing his skills to the point that he can become a factor for the Bulls.
The reason these two are sharing a spot is because Thomas played more towards the beginning of the season, and Asik played more towards the end. The obvious thought is that Asik will play more because obviously Thibodeau trusted him more down the stretch, but he may end up choosing the veteran, Thomas, over the rookie in the rotation.