This misconception can apply to any ancient or even medieval army really - the idea that the armies fought one-on-one, single combat to win battles - a-la the intro to the movie Gladiator (the fights in Braveheart, though not Roman, also spring to mind). In reality, battles were a formation-affair. Generally, the only reason one would break formation is if they were turning to run, which is also when the vast majority of casualties would occur - it seems to me that movies like to portray the two armies hopelessly mixed in a wide plain with everyone swinging at each other furiously, with no formation, no order at all.

Forgive me if I am paraphrasing inaccurately (and I should be clear that I have no particular Roman qualifications). One thing that I found striking in terms of how different the Romans were from how we tend to think of them in the present is that they had a very different spatial perception of the world and, specifically, the world they "controlled". That is, we tend to think of them as people with a big Risk-style map and tokens that represent armies, when in practice they built their world around the one dimensional axis that they had most effectively quantified, which was the road. It's obvious, I guess, when you think about it, but when you consider the effort it would take to adapt our modern summaries of how battles were run and empires/republics were managed, that "one dimensional view of the world" potentially means a great deal in terms of how different they were from what has been projected on them. It doesn't mean they didn't have maps, just that the visual component was differently important than it would be to a geographer today, which this news article does a good job of summarizing.

I strongly recommend Mattern's Rome and the Enemy as it moves away from details that we tend to obsess over as a modern audience and really tries to dig into what you might call an intellectual/conceptual history of Roman strategy, from the education of their leaders to the execution of campaigns. That's my source, anyway; I found it an enjoyable read even with my limited background in Roman history.

I've actually met many veterans with a real passion for Roman military studies. It is a somewhat thrilling experience for me, seeing these sorts of cross historical connections being formed, imbued with a sort of meaning I could never understand. And admittedly, until the seventeenth or eighteenth century there aren't really any militaries in the Western world that are as comparable, and perhaps as resonate to a modern veteran, as the Roman one. But this can often lead to a very simplified sense that the Roman military was a professional one comparable to a modern army, when the reality is far from that. The Roman army was a messy institution,.frequently politicized, and bound to the state through personal ties. I personally despise the cliche that the Roman army was loyal to their generals rather than the state and feel it is classist nonsense, but the emperors were forced to create personal ties to the soldiers. I have no doubt that the soldiers had a sincere patriotism, and this is well supported by the literary record, but in function it was controlled as almost a personal army of the emperor. How well they were able to assert control and win the loyalty of the army was often a good measure of how successful an emperor would be.

Also, we don't know as much as we would like to about standardization. We have conflicting sources and limited battlefield archaeology. We do know that individual units maintained intensely local identities, not unlike, say, state regiments in the US civil war.

I would venture that it's probably not commonly understood that the composition of a Republican army was much different from that of an Imperial (Legionary) army. The image of columns of legionaries with lorica segmentata armor is only valid after the Marian reforms - prior to that, in the Republic, battle lines were composed of different units (hastati, principes, triarii) that used much different equipment (Republican soldiers supplied their own weapons, so they would have been of variegated make and condition; hastati carried short swords and javelins, while triarii carried spears).

Romans tried to avoid building onagers (primitive torsion catapults) if possible simply because from a mechanical standpoint they're not as efficient as ballistae, their more favored siege weapon. Movies are always showing onagers as their biggest and coolest siege weapon, whereas using them would be a sign that the siege was rushed or poorly funded because there wasn't the money or expertise to build the more efficient ballistae.