The armies are arranged as follows: the Greeks field general issue hoplites as heavy infantry, and only a few chariots constitute what apparently passes for their cavalry. Admittedly, heavy cavalry would be useless in this attack. The Trojan heavy infantry seem to be a chimera of hoplite and Roman legionnaire: they use spears rather than swords, but have tower shields. Some of them, referred to by that guy from Braveheart as the "Apollonians," preliminarily bombard the Greeks with pila and follow with swords like Romans. No manipular arrangement is in evidence, but they apparently don't plan to charge. The Trojans also have a small contingent of correctly stirrupless heavy cavalry and a number of light infantry (archers) manning the wall. The Greek heavy infantry appear to greatly outnumber their Trojan counterparts (we're told the Greeks have 60,000 men, I think), but the Trojans cannot be enveloped or flanked due to protection from the city's concave wall. Merely to defeat the Trojan heavy infantry, then, the Greeks must punch a hole into the Trojan line, which seems unlikely given the Trojans' far superior shields. Further, Trojan morale should be bolstered by the knowledge that they can't retreat, and perhaps, as we shall see, by the knowledge that under no realistic circumstances will they want to retreat.
Agamemnon's objective, however, is not to defeat the Trojan heavy infantry; he wants to capture Troy. As such, one observes with confusion that he has neglected to bring with him a single siege weapon. And he didn't just forget them for the battle; a quick review of the beach camp reveals that he seems not to have brought any from Greece. He can only hope to starve Troy into submission, then, but no port is in evidence at the beach, meaning the Trojans receive their supplies (assuming they need any) from the other side of the city. In that case, Agamemnon should be attempting to encircle Troy; we don't know whether he has the manpower to do this given the city's size, but he doesn't try. As it is, it's not really clear what Agamemnon expects his army to do should they reach the wall. No one even has a ladder.
One might also wonder why Hector (Eric Bana) has chosen to position the Trojan army outside the city and the protection of its wall. There are a number of possible reasons, presented here in ascending order of merit:
Courtesy: Hector can see the obvious fact that his archers will be killing a shitload of Greeks, and his honor as a soldier compels him to let the Greeks get a few kills too so they can feel they've accomplished something.
Ceremony: Hector's brother Paris (Orlando Bloom) was supposed to fight Menelaus (Brendan Gleeson) to the death for stealing his woman. Hector wanted to provide a properly martial atmosphere.
Enticement: Hector knows that the sight of a bare fifty-foot-high wall might cause a seed of doubt to enter even Agamemnon's tiny brain; because he wants Agamemnon to attack, he gives him a tempting target, as if dangling a shiny object in front of an infant.
Pursuit: Especially in antiquity, it is axiomatic that the losing army suffers the vast majority of its casualties as its fleeing, disordered soldiers are chased by the victorious army. Since Hector knows that there's absolutely no way he can lose any battle that occurs, he wants a lot of troops on hand to slaughter the Greeks during the rout.
It should be a combination of the last two. In any case, it's the right decision, although it could have been the wrong one had Agamemnon just brought some archers with him. Anyway, the battle begins with a hilarious bellow from Agamemnon (pictured above) after witnessing Hector's killing of his brother Menelaus. The Greeks charge the Trojans, but they don't really interlock shields upon impact. Some of them suicidally jump over the first line of Trojans.
The Trojan archers prepare to fire. Oddly, both of the Greeks' leading military thinkers, Achilles (Brad Pitt) and the Odysseus (the great Sean Bean), only now realize that the Greek infantry, by sprinting toward the wall, are going to end up "too close to the walls," "too close" meaning that they are within archery range. Within archery range, there isn't much for the Greek infantry to do but get shot; even if they defeat the Trojan infantry they'll be left to beat ineffectually on an impenetrable wall until they're all killed. Outside archery range, there isn't anything for them to do but stand around dehydrating. They should therefore leave. This is all completely foreseeable. Neither Achilles or Odysseus suggests withdrawal.
Instead of simply overwhelming him, the Trojans are kind enough to give Ajax (some guy) room to use his enormous war hammer; Hector engages him in some Iliad-like single combat and kills him. This is a serious blow to morale! Greeks continue to get slaughtered by the Trojan archers and heavy infantry.
The scene again erroneously presents Achilles and Odysseus as voices of reason: both now insist that the situation would somehow be improved if their army were formed "back into lines." The conscientiously-objecting Achilles says so from his perch on top of a nearby ridge, while Odysseus attempts to reorder his formation from inside the battle, apparently oblivious to the fact that it is impossible to be heard by any substantial number of men over the noise of a battle, and impossible to be obeyed by an engaged mass of men even if somehow heard. It does not actually appear, however, that the Greeks are particularly out of line. Even if they were, that is perhaps their fourth or fifth most serious problem.
The Trojans are a lot better at this. They even have a pretty sophisticated phalangite drill worked out whereby they progressively advance their shield wall in unison. Agamemnon claims that his army "has never lost a battle yet," leaving us to wonder whether he's been honing his skills in the Gauis Terentius Varro Division of the Greek War Games League. Odysseus makes his first helpful contribution of the day, pointing out that Agamemnon "won't have an army left" if he doesn't fall back. The unavoidable retreat commences. The exultant surprise that Helen (Diane Krueger), Andromache (Saffron Burrows), and supposed veteran of "many wars" King Priam (Peter O'Toole) display from the Trojan gallery demonstrates that all of them have also failed to understand their military situation.
In fact, Agamemnon's army should be destroyed despite its retreat. We next see the beginnings of a great pursuit scene, accurate in its portrayal of the unformed Greeks' helplessness and resultant susceptibility to slaughter, inaccurate only in the respect that the Greeks fail to discard their heavy equipment in panic. But now it's Hector's turn to serve narrative convenience by acting like a moron. Despite his potentially fortuitous accompaniment by the smartest man on the battlefield, a random Trojan soldier who reminds Hector that they "have [the Greeks] on the run," Hector orders an end to the pursuit upon encountering a thin screen of Greek archers mounting a ridge between Troy and the beach. Again, without any communications technology or signaling system it should be impossible for Hector to give this order mid-battle. Also, Agamemnon's decision to hold back his archers is, to put it charitably, mysterious.
Hector halts the pursuit because the Trojan army has come "in range of [the Greek] archers," as if that ends the argument. But while it would certainly kill and wound some Trojan soldiers as they traversed the area within archery range, the Greek archer screen, uncovered by any troops suitable for shock action, could not possibly halt the Trojan heavy infantry; the archers would immediately join their fellow Greeks in rout upon the arrival of the first Trojan troops. The Trojans would then have in front of them the entire disordered and demoralized Greek army. Because victorious heavy infantry is still weighed down by their weapons and armor, a pursuit of routed heavy infantry will usually be outrun unless it employs a substantial cavalry force, which the Trojans don't seem to have. This presents no problem here, however, because the Greeks have their backs to the Aegean Sea. After noting that the superhuman Achilles and his Myrmidons are probably still standing on the ridge overlooking Troy, one can say with certainty that nothing prevents the burning of the Greeks' ships, the appropriation of their supplies, and the death or capture of every person in the Greek force who isn't an accomplished swimmer.
Hector declines this opportunity. This leaves "Enticement" as the only reasonable motivation for his decision to post his men outside the Trojan wall. The script contains no indication that he actually intended to tempt Agamemnon in this way, however; the best decision by any commander in this battle thus appears to have been made by accident. Maybe he flipped a coin? The real reason, of course, is that Hector posted his army outside the wall so that Troy could include a big battle scene.
To summarize: Agamemnon chooses a battle he cannot possibly win, none of his colleagues tell him that, and Hector, having achieved a tactical victory, declines the gift of a strategic one.
