In a short series of posts I will deal with the strength figures in the books of the author Stephen Sears, starting with his book on Antietam "The Landscape Turned Red", principly because it is the easiest.
The first strength figure is on page 102 and deals with the total strength of the Army of the Potomac on 7th September. It lists 85,000 "under arms" (i.e. effectives) in McClellan's Army and 72,500 left to defend Washington. Sears states that because of serious straggling ans sickness en route to Frederick McClellan was setting forth with nearly a 2:1 advantage, 3:1 if he could call in reserves from Washington.
The figures are from (a) Palfrey's the Antietam and Fredericksburg pg 7 and (b) OR19(2) 264-5. Although the latter carries the caveat in the original (not reproduced in Sears) "There is the old exaggeration in these figures, due to failing to distingish between for duty and extra or daily duty.". The former 85,000 was obtained by Palfrey taking the 20th September return of 89,452 (this figure being the aggregate present), deducting the strength on that date of Porters Corps (19,477) and adding the casualties sustained of 14,794 yielding, in round figures 85,000. Although represented by Sears as an effective strength, this appears to be an aggregate present strength (or at least PFD). Lee on this date had around 75,000 "for duty" and a larger number "aggregate present". Thus rather than 2:1 or even 3:1 superiority, McClellan's army had rough numerical equality.
On page 117 Sears adopts the value in McClellan's report of 87,000, noting that this is "almost exactly double". It is roughly parity.
On page 163 Sears states that "60,000 fighting men" (i.e. effectives, in fact this figure would fit the PFD of the force present on the field on dawn of the 17th) were with McClellan at Antietam on dawn of the 16th September, giving him a 4:1 superiority in numbers (then quips about McClellan's "phantom calculation). In fact McClellan had 48,000 effectives strung out, still on line of march (Harsh, Taken at the Flood, p330). Only 2 of McClellan's Divisions were on the field, Richardson's (lead division of Sumner's wing) and Sykes' (lead division of Burnside's wing), with maybe 6,000 effectives between them. Rather than outnumbering Lee by 4:1 as Sears suggests, McClellan's forces on the field at dawn were outnumbered 3:1, although this quickly changed during the day as the columns came off their roads and ployed into position. There was no massive superiority in numbers that McClellan missed (and in fact McClellan endeavoured to attack as soon as he had 3 Corps up but the movements of his subordinates were too slow).
On pages 173-4 Sears has his last words on strength, giving a statement of the balance of strength. He states that "by roster counts" McClellan had 75,000 of "all arms and services", plus another 19,000 in the Loudon Valley under Franklin. He also gives the whole armies effective strength at 71,500 (although not explicit, running through the attached footnote and repeating his maths shows that he has included both the force in the Loudon valley and Humphrey's division in this figure, which is based on Carman's figures with an attempt to add the forces Carman didn't count in them. There is no attempt to fix, i.e. downrate to "effectives", those figures given by Carman as PFD or even aggregate present). Lee has "fewer than 26,500" including his artillery and cavalry after Jackson and Walker arrive (i.e. McLaws, Anderson and AP Hill aren't up yet, as the text makes explicit, but no numbers are given for them in the book, in a footnote Sears quotes "less than 40,000" and "not 35,000" excluding cavalry).
It is clear Sears understands the difference between effectives and present (since it is explicit in his main source, Carman), but seems to adopt the maximum possible value by including forces not on the field on the 17th (covering this as forces under McClellan's command), whilst adopting the lowest possible effective value for the Confederates (for example, following Carman only half of AP Hill's division is counted). McClellan certainly did have superior numbers during the battle, but a careful examination of Carman places this figure between 5:4 and 3:2, rather than 2:1 used here.
Overall, although the figures chosen are those that make Sears' case look best, by using Carman Sears has not majorly run off track (although his figures for the morning of the 16th are very wrong, they're not referenced and so were probably taken from the known strengths at the end of that day rather than the begining). The most serious mistake is including forces that didn't arrive in time to participate in the battle.
Next we shall look at his Richmond Campaign, and see his figures without the crutch of Carman. Then I'll read his Chancellorsville and Gettysburg books.