67th Tigers
Banned
I'm sorry but I think your wrong.
First and foremost is the reason that the Confederate records are unreliable at best and the were largely conflicting ideas of the strength of the Army of Tennessee within the Confederacy the time and thereafter.
Joe Johnston claimed 40,000 effective when he took command at Dalton, 60,000 when Polk join him at Resaca and a zenith of 70,000 near Adairsville and Cassville.
63,812 PFD producing 44,000 effectives. It increased to the region of 90,000 PFD and 65,000 effectives when reinforced.
The other reason is that Sherman himself disagrees with your numbers. Sherman reported his strenght at the beginning of the campaign as:
Army of the Cumberland - commander George Henry Thomas - present and absent: 171,450 - present for duty: 88,883 - effectives: 50,000
Army of the Tennessee - commander James B. McPherson - present and absent: 134,763 - present for duty: 64,957 - effectives: 35,000
Army of the Ohio - commander John M Schofield - present and absent: 46,052 - preent for duty:26,242 - effectives:15,000
And he counted his loses on the Campaign as 31,687.
The figures I have show an estimate of 120,368 PFD, producing 78,000 effectives, although he left a Corps behind and set of with just over 97,000 PFD and 60,000 effective.
Now, while this does indeed mean that Sherman's Army Group could have been down to around 68,000 this does not mean he faced an enemy of equal strength as the Confederate Army of Tennessee also lost over 30,000 men (mostly under Hood's direction) and finished the Campaign with only around 30,000 men in its rank.
If the two sides ever faced each other on equal footing it was at Peechtree Creek but other than that Sherman had a clear numerical advantage.
The real killer for the Confederacy was desertion (worse than even the US, which by this period had over 80% of recruits deserting before they saw regimental service). CS soldiers deserted in droves, and their strength couldn't be maintained. Most seem to have simply gone home.