What the Pinkerton estimates were of, an answer.

Although he missed the point, the information needed to work out what the parameter Pinkerton was reporting (and McClellan using) is in Fishel's Secret War for the Union.

Pinkerton obtained the roster strengths, that is the "aggregtate present and absent" and applied a correction factor to take out the sick. He meant to use 15%, but apparently his computer used 1/15th instead, thus overstating the enemy strength by about 10%.

Thus is explained why, by inspection, Pinkerton's numbers usually seem in good aggreement with the aggregate present and absent, they were the basis of his reports, and he is not doing his maths properly. It does not explain some of the figures his interogators were producing.