Ancient army numbers

[Paralus]

First, about Gaza... the casualties reported are "more than 500 men, most of whom were cavalry"... This probably means some 300-350 men. These are the casualties that the defeated side sustained, the side that broke and fled.... Fortunately, the cavalry soon regrouped and covered the retreat, else the casualties would be much more.

The cavalry maintained good order until reaching Gaza where some broke for their baggage. This was a battle of xystophoroi and only the defeated side's dead are listed.

The cavalry that took part in the fight (along with the rest of the wing, elephants, light infantry etc) is adequately described and mainly are lancers. Also, the "pantodapoi" are not cavalry of all sorts, but cavalry of other "places", more like allied cavalry, but this is a small detail.

Yes the pantodapoi are "allies"; they are cavalry of many races or nations. We can assume they are armed in their customary fashion (Asian and so are not Macedonian style xystophoroi).

Now, Demetrius has at least 1,500 lancers in his numbers and hid enemies array against him the strongest 3,000 of their own cavalry. Diodorus clearly says how the first attack was with the xyston lance and then with drawn swords. The battle is described as particularly vigorous and still... the side that breaks into flight only loses the most part of the 500+ casualties...

The pantodapoi are likely armed in their customary fashion (as above). Demetrius is surrounded by 500 xystophoroi and we can assume his "so called" companion cavalry are similar. That would give him 1,300.

Now, about Hephaesteon... the text actually reads :

"Ἡφαιστίων μὲν εἰς τὸν βραχίονα ξυστῷ βληθεὶς ἐτρώθη", which is translated as :

"Hephaestion was wounded by a xyston spear that was hurled on his arm." The text is very clear. It was no hand to hand thrust, it was a xyston that was thrown at him...

Which is really neither here nor there; he was hit by a xyston or a throwing spear (the latter given it was thrown).

Moreover, the somatophylacae are not counted among the hypaspistae. They are a small group of men that are supposed to be closest to Alexander and protect him always. In battle, they were not always beside him. They could even lead other units.

Which is the point re Arrian above. Arrian unarguably terms the agema of the hypaspists "somatophylakes" several times (as well as hetairoi, agema basilikon). At 1.24.1 he describes a Ptolemy son of Selecus as sōmatophulakōn tōn basilikōn but he is clearly not one of the seven. At 3.17.2 Alexander takes the "somatophylakas basilikous" and the hypaspists" (σωματοφύλακας τοὺς βασιλικοὺς καὶ τοὺς ὑπασπιστὰς). At 4.3.2 he does so again (σωματοφύλακας καὶ τοὺς ὑπασπιστὰς). The clincher is 4
30.3 where Alexander took some 700 of the "somatophylakon and the hypaspists" (ἀναλαβὼν τῶν σωματοφυλάκων καὶ τῶν ὑπασπιστῶν ἐς ἑπτακοσίους). Diodorus also refers to the paides basilikoi as "somatophylakes" and so it is clear that the ancient sources could refer to the agema of the hypaspists in this way (somatophylakes). Thus it is surely the "somatophylakes" (agema) that Hephaestion commands the agema of the hypaspists at Gaugamela and is wounded doing do. Whether the spear was thrown at him is not terribly important. Diodorus also describes spears as being hurled at Mantinea (362).