Every war, every conflict, every single battle is unique in different ways. No swimming in the same river twice is allowed, to borrow a bit freely from Heraclitus. That said, there is, I think, a general formula that often leads to victory in any conflict.

First, you need a good amount of force if we are talking about an active or possible military conflict. Turks had, and built as they went, enough of it. They converted anything into weaponry. They obtained the weapons Italians left in Anatolia, the same with the French later on; and they received a considerable amount of financial and material support from the USSR. That said, you are right that the Allied forces (even the Greek forces alone) had, on paper, greater resources. Second, and related, they had good strategic leadership. While sheer force is undoubtedly a great advantage, history is full of examples where smaller forces beat a more wayward but stronger-on-paper force: Vietnam versus the US and Afghanistan versus the USSR are two rather recent and classic examples. If you do not have a realistic enough idea about what you can and cannot get out of the conflict, if you do not know where to push and where to stop, you may find out that even a constant wave of resources cannot bring you victory. With strategic leadership, I do not mean just the military aspect. Take the Chanak affair of September 1922. This happened when the Turkish forces threatened the British with prolonging the war and fighting to the last man if need be unless the British evacuate their forces out of the Dardanelles. It sounds like madness, right? Yes, the Turkish army had just beaten the Greek forces and recapture Western Anatolia including its crown jewel, İzmir, but challenging Britain into yet another open conflict? Except, clearly, the Turkish leaders knew perfectly well that this was a risk the British government would simply not take. The government of Lloyd George had at home a nation already tired of years of warfare, and had its opponents. When George overplayed his hand and ordered General Harrington to stop the Turkish advance whatever the cost may be, and when Harrington refused to obey the order, George's government was done for. Very soon, the Tories took his government down and the Chanak affair was gone.

I think the division among the Greek forces also helped. A historian of Greece may provide better information here, but suffice it to say that there were at least two contrasting factions within the Greek Army: one supporting the King and one supporting Venizelos. If this division was strong enough, and I suspect in cases it really was, this might also explain the pace with which the Greek forces lost their discipline and rushed towards the Aegean Sea following 'the Great Offensive' of August 1922.

Another factor was the Greek invasion of Western Anatolia. The generalised version of this rule is familiar from mafioso TV series too: do not push your rival too much when he's already cornered. Allies, especially the British, had good reasons to help create a stronger Greece in the region, doubtlessly. But the Greeks were simply different for Turks. They could barely tolerate the status quo with the British, the French, who were the major powers of the day anyhow. The Greeks, on the other hand, were the bitter rivals and, to quote from an earlier Ziya Gökalp poem (excuse the language, but it's necessary to reflect the then prevalent mentality) 'old slaves of the Empire'. Indeed, the Greek invasion of İzmir provoked a reaction greater than ever among Turks, leading to many incidents from meetings in Istanbul and other cities to organisation of guerilla groups in the Aegean region (to be ultimately coordinated by the Ankara government later).

I suppose you can keep counting many other major and minor factors. That the Turks knew their geography better than the Allies was also important, for instance, as was the fact that fronts against the Armenian, French, and Italian troops were concluded by the time the Ankara government turned its full attention to the British-backed Greek occupation. And I'm sure there were factors from the Allies' side of equal importance. So I'll leave it here, hoping that the account thus far gives an idea!