The western theater rewarded maneuver, yet Bragg tied his smaller force to a loose siege around Chattanooga. A force dependent on mobility surrendered its chief advantage when it became fixed around one position. The pause let the Union recover and bring together formations from the Armies of the Cumberland and Tennessee as well as Hooker's eastern reinforcements. The Union eventually had roughly 72,500 troops present for duty and equipped against the Army of Tennessee's claimed 49,000, a concentration Bragg could not match. Grant's arrival turned a local containment effort into a confrontation with a much larger and more capable command team.
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Bragg's siege gives the Union time to concentrate
By fixing his smaller army around Chattanooga, Bragg allowed Thomas, Sherman, Hooker, and Grant to assemble an increasingly dangerous Union concentration.