This isn't exactly Bears news, or even professional football news. But I think that some of the conclusions drawn here can apply to the professional game. If I were to connect this to the professional game, it would be titled, "Why Mike Martz's Offense Was No Better Than Ron Turner's (at least, for this past season)"
If you're a stats buff, you'll really like this article, BTW.
tl;dr: Canning an Offensive Coordinator does not affect an offense's performance to any significant degree. Canning a Defensive Coordinator generally improves the performance of the defense, though not to any great degree. The biggest indicators of season-to-season offensive and defensive rankings is player retention and previous season rankings.