I'm reading Livermore's Numbers and Losses in the Civil War, 1900, and he states some interesting facts. On the issue of field reports of battles, officers on both sides did not count cavalry, artillery and non-combatants in their total losses or strengths, due to the period military doctrine of assertaining firepower. An armies firepower was considered wholely with its weight in infantry units, thus the focus of strength vs loss was with the line infantry and all other units ignored in finally tallies.

"METHOD OF ASCERTAINING THE NUMBERS ENGAGED.

The Records, apparently following the reports and returns of the commanders, give the numbers in the different campaigns and battles variously as "present for duty," "present for duty equipped," or "effective." Sometimes the last-named class excludes on both sides the non-combatants, and on the Confederate side the officers and even artillery and cavalry; and, in the effort to number only the men bearing muskets in the firing-line, the stragglers, even those who have left the ranks on the field of battle, are sometimes excluded in reports of battles.

This practice of counting as effective in the infantry only the men bearing muskets in the firing-line is of great value for informing commanders what weight of fire they can deliver, and the state of discipline in the ranks; but it cannot be followed in ascertaining numbers for comparison between the two sides in the civil war, or between the numbers in battles of that war and other wars, because the published accounts of the Union army, and of armies in other wars, do not usually state numbers on this basis. Officers, artillery, and cavalry are assuredly essential parts of the effective force of an army, and the efficiency of an army is certainly to be gauged quite as well by the number of combatants who fail to join in battle as by the valor of those who come into the firing-line. On the other hand, it is reasonable to exclude non-combatants from those counted as effective for battle. In both the Union and Confederate armies, the members of the regimental, medical, and quartermaster's departments, and the musicians, were non-combatants, and few of them were ever present in the firing-line, for even the drummers and fifers were usually employed in caring for the wounded; and these non-combatants, although essential to successful campaigns, cannot be said to have had any influence in the decision of battles in the civil war."

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David Upton