It seems to be generally taken that when the Confederates say "effective" they are only including enlisted combatants, a position I have previously subscribed too. To wit, US Grant wrote in Century Magazine:
"The effective strength of the Union force on the morning of the 6th was 33,000 at Shiloh. Lew Wallace brought 5000 more after nightfall. Beauregard reported the enemy's strength at 40,955. According to the custom of enumeration in the South, this number probably excluded every man enlisted as musician, or detailed as guard or nurse, and all commissioned officers -- everybody who did not carry a musket or serve a cannon. With us everybody in the field receiving pay from the Government is counted. Excluding the troops who fled, panic-stricken, before they had fired a shot, there was not a time during the 6th when we had more than 25,000 men in line. On the 7th Buell brought 20,000 more: Of his remaining two divisions, Thomas's did not reach the field during the engagement; Wood's arrived before firing had ceased, but not in time to be of much service. Our loss in the two-days' fight was 1754 killed, 8408 wounded, and 2885 missing. Of these, 2103 were in the Army of the Ohio. Beauregard reported a total loss of 10,699, of whom 1728 were killed, 8012 wounded and 957 missing: This estimate must, be incorrect. We buried, by actual count; more of the enemy's dead in front of the divisions of McClernand and Sherman alone than here reported, and 4060 was the estimate of the burial parties for the whole field. Beauregard reports the Confederate force on the 6th at over 40,000, and their total loss during the two days at 10,699; and at the same time declares that he could put only 20,000 men in battle on the morning of the 7th."
In fact, whilst reading the OR's it has become clear to me that their meaning of "effective" is simply the number of not-sick enlisted men, see Rodes' state going into Gettysburg for an example(ref).
By the statements of the two armies commanders Shiloh was 20,000 Confederate combatants wrestling with 25,000 Federals. It's food for thought.