Marcy, of course, was chief of staff of the AoP and this exchange is private, after the war, and meant for no one's eyes but their own:
I have just read Lee's report of the seven days fighting in which he speaks well of you but makes several misstatements. For instance he says that we had greatly superior numbers on the East side of the Chickahominy at Gaines Mill when one of their own writers admits that they had 67,000 after Jackson came up, while we only had, if I remember right, about 35,000.This is one of those odd instances where memory roughly corresponds with ACW "common knowledge."
Wikipedia gives the number of Federals engaged as 34,214 and Rebels as 57,018: David Eicher's Longest Night is given as the source. If you go to Longest Night, the numbers are unsourced and appear on page 288 of the hardback. You would think, readers would want to know where numbers come from but his notes address other matters than strengths and casualties.
But the deep reader recognizes these as exact matches for Livermore's estimates (Eicher gives them as facts) from the Numbers and Losses. Oddly, Livermore is not mentioned in this work except as the author of the memoir, Days and Events, without reference to Numbers and Losses - and Eicher repeatedly uses Numbers and Losses throughout his work without crediting Livermore. The result is what we have here: some chump posts them to Wiki as if they were Eicher's own calculations, none the wiser. Welcome to Civil War history, a brilliant field of scintillating scholarship!
Without digressing into Eicher's gross misconduct, it seems more interesting to speculate how Marcy's memory could line up so closely with Livermore's figuring.
I think we have to understand that as chief of staff, Marcy's was a muster roll view of data, just as Livermore tweaked that same data to come up with his own totals.
I think the federal number here is high unless absentees and shirkers are accounted for, but that is hard to do on a rule of thumb or estimate basis. For that, anecdotal evidence is needed and anecdotal evidence does not always filter up to HQ.
Well worth a ponder.