Many historical texts, especially ancient documents gave inaccurate number. For example, Hedorotus inflated the Persian army to more than 1 million. So how do historians make estimation of the real number of combatant in a battle?
I would like to ask the same question for the death count in some events of the 20th century which statistic is unavailable or not credible. For example, if a historian doubt the Great Leap Forward's casualties reported by Chinese official statistic, how can he/she estimate the real number?
I am aware that different historians may give different estimations on the same subject, I am just interested in the methods at their disposal.
If we have administrative records, the estimates are (probably) at least in the ballpark. In medieval England, for example, the Pipe Rolls contain a lot of good information. If we have a list of how much was spent on soldier salaries, food, supplies, travel, and other expenses, those costs can be used to extrapolate a rough estimate of troop numbers. If we have histories, chronicles, or local administrative records that match these results (within a reasonable margin of error), scholars can reach a defendable conclusion on troop numbers.
I'd recommend a couple of things for medieval troops...
(1) John France. Mercenaries and paid men : the mercenary identity in the Middle Ages : proceedings of a conference held at University of Wales, Swansea, 7th-9th July 2005
(2) Adrian Bell, et al. The Soldier in Later Medieval England (Oxford, 2013), especially chapter 6, "Where did soldiers come from?"
(3) David Bacharach, "The organisation of military religion in the armies of King Edward I of England (1272-1307)," Journal of Medieval History 29 #4 (2003): 265-286.
Hope this helps a little. Happy Reading!