Medieval historians often did not have exact access to precise numbers. I've heard it argued that a medieval historian saying there were hundreds of thousands of people present was less of an outright lie and more of a saying generally then understood to mean "man, there was a whole fucking lot of dudes at this fight, man, it was epic".

As for modern historians pinning down numbers, they generally do it through any logistic/economic documentation pertaining to the battle, if available.

The things we lack to make precise guesses are 1) primary source historians who were actually present at the battle and part of the command structure and are genuinely interested in a factual presentation rather than a good story, 2) the fact that consistent, precise documentation is not generally something you can always count on finding when it comes to the Middle Ages, due to lack of literacy, the literates generally being the priestly class who were not committed to battlefield use regularly, difficulty of actually creating books pre-printing press, and the propensity of certain enemies (or religion inspired jerks like Louis the Pious) to outright destroy libraries.