A common problem with trying to sort out the history of the Greco-Roman era is trying to make sense of the numbers given in the different accounts of, for example, the size of armies.
In this essay reference as already has been made to the problem of wildly exaggerated numbers given by the Greek historians. This is a very wide ranging topic so the author will stick to Ktesias , Herodotus and Diodorus .
Regarding Herodotus the main question is where to begin. So a start will be his numbers for the invasion of Greece. We get the following:
1,207 Triremes, with 241,000 men & 36,210 Marines
3,000 other ships with 240,000 men
1,700,000 infantry & 80,000 cavalry
A camel and chariot corps for another 20,000
Total 2,317,610 men
Add 120 ships, with 24,000 men
300,000 more men
men + Servants equal to above total
Grand total 5,283,320 men; Total ships 1,327 Triremes
This does not include camp women, wives, cooks, etc., of course.1
800,000 men excluding servants
400,000 men in one army
80 Triremes in one fleet
500,000 men in another army
300 Triremes in another fleet3
1210 "Warships", probably Triremes
For the Egyptian Expedition the numbers are:
300,000 men in one army
300,000 in another army
Herodotus for example in his careful listing of his figures for men, and in how he calculates them gives the appearance of being both exact and careful. The problem is it makes his figures look if anything even more absurd. For example Herodotus says:
Meanwhile Xerxes at Doriscus was occupied in numbering his troops. As nobody has left a record, I cannot state the precise number of men provided by each separate nation, but the grand total, excluding the naval contingent, turned out to be 1,700.000. The counting was done by first packing ten thousand men as close together as they could stand and drawing a circle round them on the ground; they were then dismissed, and a fence, about navel-high, was constructed round the circle; finally other troops were marched into the area thus enclosed and dismissed in their turn, until the whole army had been counted.6This truly weak attempt by Herodotus to make his figures look plausible only succeeds in enmeshing Herodotus further in the absurdity of his figures. It appears Herodotus realized that at least some people hearing or reading his numbers would not believe them so this explanation was put in. It is hardly surprising that later writers criticized Herodotus for either gullibility or out-right lying. However it seems that:
Although it should be pointed out ancient writers, to the best of our knowledge, did not criticize Herodotus for including absurdly high figures for Persian armies and fleets.
He (Herodotus–Author) does seem to have believed in the traditional figures, if his arithmetical labours are any indication. That these numbers are a sheer physical impossibility does not seem to have occurred to him.7
No attempt to sort out, analyze etc., such figures can save them, certainly not Herodotus ' absurd explanations. For example dividing by 10, or a hundred. Herodotus’ figures for the number of men cannot be saved by such procedures. The bottom line is that they are pure invention is more likely than that they are not. In fact this is just one more example of Herodotus’ lack of understanding of military affairs.8
Regarding the number of ships here the figures are not quite as absurd. The 80 and three hundred ships recorded for the Egyptian Expedition certainly are plausible. But here we run into problems. The three hundred figure reads like a stereotype, not a real figure and the 80 could be nothing but a doubling of the Athenian 40.9
As for Herodotus' figure of 1,327 triremes this implies a total force of 301,610 men. Accepting Herodotus' figure of 200 men per ship.10 This figure is implausible, especially if we add in the supporting vessels.
Herodotus' figures for ships are not implausible if we accept that the figure he gives for triremes is for total ships. This is so because it was easier to supply and move men by ship than over land and on the sea the very expensive, both financially and logistically, cavalry was not a factor. Further food supplies could be moved much cheaper by sea than overland. Still there were limits so Herodotus' total figures are still implausible for the full fleet. Although it is probable that there were more men in the fleet than in the land army. As for the navy feeding the army it would have had enough problems feeding its self with trying to feed the army as well.11
If Herodotus' figures are, despite his efforts to justify and explain them, impossible, then neither the figures of Diodorus or Ktesias are in the least reliable. Both Diodorus and Ktesias seemed to have selected impressive large figures, quite literally, out of thin air and made no attempt or justify or explain them.
The best way to approach this is in terms of logistics, not crunching numbers taken from dubious sources. Since if the literary sources cannot be taken seriously than what we have left is probability.
Before we leave the "Oriental" hordes behind a good check on these numbers is the forces lead by Napoleon in his invasion of Russia, which totalled, along with reinforcements, about 612,000 men.12 Despite considerable logistic support and trying to live off the land, Napoleon's army was mainly destroyed by logistical and supply problems. Spread out over a vastly larger area than Ancient Greece and one that was more productive, Napoleon's army could not properly feed itself and was destroyed.13 If Napoleon could not feed and supply his army in Russia in 1812, with vastly superior logistic and supply resources it is hard to believe that the huge hordes of Persians mentioned by the Greek historians could have been supplied successfully.14
Logistically the problem, until very recently, has been that the size of an army depended not just on the resources of the nation, empire creating the army but on the local resources of the area where the army would be operating. It is clear that:
In the ancient world, where logistics placed severe constraints on the size and mobility of armies, even a small force, when disciplined and determined, could pose a threat.15What this means, for example, is that despite the huge size of the Persian empire in relation to Greece, the main limit on the size of the Persian Army invading Greece was not the size of the empire but the size of the resources in Greece that could support an army. Since the army would have to be supplied locally it was Greece's ability to support the army that counted not the size of the Persian Empire. The relative strength of states counted in these circumstances not in terms of being able to mobilize vast armies on a battlefield, because logistics set limits on that, but the ability of states to finance and sustain and replace losses in war. Thus if the Persian Empire could only send an army of 50,000 men against a enemy because that was all the area could supply, it could still do so again and again, both financially and in manpower. Whereas its enemy may not be able to sustain such an effort or replace its losses to the same extent.
In one of Thucydides speeches, he puts in the mouth Hermocrates, a politician, during the debate at Syracuse about whether to resist the Athenians, the following:
There have certainly not been many great expeditions, either Hellenic or foreign, which have been successful when sent far from home. They cannot come in greater numbers than the inhabitants of the country and their neighbours, all of whom will unite through fear.16It appears, given the likely-hood, that this represented Thucydides’ views that this also represents his general opinion about Persian numbers against Greek numbers. Further this shows that the general principal of a limit on the size of invasion / expeditionary forces was recognized by some thinkers in antiquity.
How large were the armies that invaded Greece and Egypt ?17 Two conclusions can be drawn. First the numbers given by the Greek Historians cannot be taken seriously has figures for the size of the Persian armies, except has evidence of what the Greeks believed. Second Thucydides decision not to give figures at all of the size of the Persian armies is probably the best course, because we do not know and baring some "find" can not know, the actual size of the Persian armies.
1. Herodotus, Herodotus: The Histories, Penguin Books, London, 1954, Book 7, s. 184-186.