There's a hot thread in /r/history right now on the Battle of Julu, and one of the comment threads in it discusses the general unreliability of pre-modern battle numbers, saying that taking off a zero off the figures would be more accurate.
I had an impression that the Warring States period was a period of mass mobilization, so I never thought to question the huge numbers that regularly pop up around battles of the period.
How accurate are these numbers in Chinese antiquity? If it's too broad a question, how reliable are they for the Warring States period?
It's not an accurate statement to say that one should simply "lop off a zero" of Sima Qian's statements to make them approach accuracy... it's a fun statement, it gets the point across, and I've done it myself in the past... but it's not really accurate... probably.*
See, there's a couple things anyone looking at that period needs to know about 1) Chinese historiography and 2) Chinese literary conventions o really understand Sima Qian and his numerations...
That means there's A) a 3-400 year gap in historiography, and B) we're forced to rely on a single source. The problems with that single source are several... First, it's written (as with almost every official Chinese history) with a strong narrative bias against the dynastic order that preceded it. In Sima's case, that meant he was writing for the early Han, which had directly ousted the Qin a half-century or so prior. It's unlikely his account was terribly favorable to the Qin wars, or their wartime conduct... better to paint them as monsters... Sima's career and indeed life may well have hinged on an "acceptable" rendition being delivered. But more than that, there's nothing else in the historical records to either corroborate or disprove his particular telling. That's is not to say nothing else was written... quite to the contrary, later Chinese histories are smattered with references to other works of Sima Qian's time and before... but they either haven't survived the rigors of time, or perhaps (fingers crossed) just haven't been excavated yet... that's not as impossible as it might sound... a medical text long thought lost was recovered in 2013, and major, systemic excavations of historical sites in China have really only being going on in an organized (read: not-tomb-robbing) sense since the late 70's... it's definitely possible that more will eventually turn up. But the other thing is...
The numbers don't even have to be particularly big. But if it looks/sounds nicer, that's what writers have tended to go with... the examples are too numerous to really count (which is itself soft of... ironic? Poetic??)... but everything from the prayer that a dynasty will endure for 10,000 years (meaning: forever), to era names (the 16 Kingdoms was more like 20, the 5 Dynasties & 10 Kingdoms was more like 6.5 and 25 or so...), to the List of "100 Family Surnames" (actually a list of 504 surnames)... numbers are used for their emotional punch much more than their mathematical accuracy in such literary devices. This isn't unique to China, by the way... the "300 Spartans at Thermopylae"? (Yeah, maybe 300-ish, but alongside and among some 7k combined Greeks... Herodotus/Zach Snyder lied, I know it's shocking) The "million-man Persian army of Xerxes? What, did someone sit there and count? Numbers that we've been societally forced to actually come to terms within the modern age... simply meant less in ancient eras, where the maximum one might be reasonably expected to estimate was in the hundreds, or thousands. Above that, we still have terminology analogous to what many of the ancient authors used "hundreds of thousands" or "millions" for... unspecified, hyperbolic words like "zillion", "jillion", and Brazilian "bazillion". That's more akin to what numbers like Sima Qian likes to throw around represent: "there were a crap-ton of soldiers in that fight, no way to count 'em all!"
A good rule of thumb when dealing with Chinese military numbers is to be careful of anything over 100,000 and to take with a huge boatload of salt anything over 200,000, with a few exceptions of course.
Like I said in the other thread, with a highly centralized bureaucracy that practiced universal conscription, states such as the Qin and Han had the potential to field upwards of one million troops. But it would have been highly impractical for them to do so and so they didn't.
When looking at Warring State records, a lot of times politicians during that period will mention how the Qin has one million soldiers and a hundred thousand cavalry, but as the authors of the Cambridge History of Ancient China stated, that's more of a rhetorical device, the same way we say, "I have a ton of homework." It's not meant to be taken literally, but rather to show that the Qin state had a lot of troops.