The Toilet Paper

A good centurion is worth their weight in a model

An agent-based model suggests that centurions in the Roman army had a pretty large impact on the outcome of battles.

A centurion sets an example by attacking the enemy like a fencer
Centurions were role models to look up to

The last time I wrote an article about Ancient Rome, it was about poop and didn’t have anything to do with software engineering or computer science. This time I found a research note that is at least somewhat related to our field of work.

Much of what know about the Roman army and its combat system comes from descriptions by classical authors and archaeological evidence.

These sources tell us that played a crucial role in Roman legions throughout the long history of the Roman empire and its countless military reforms – but they don’t tell us exactly why centurions were so important.

We can use a model to learn why centurions were so central to the Roman combat system. But first we need to understand what the Roman combat system is about.

A framework of Roman combat

The authors of the research note propose that Roman combat can be understood as follows:

  • Individual experience: Roman legionaries were people like you and me, and as such more interested in staying alive than being agressive fighters. They also . Fights were therefore a succession of sporadic charges rather than what you usually see in movies. Casualties usually tended to be low until panic broke out and soldiers would try to escape rather than fight, at which point the number of casualties increased exponentially.

  • Ranged combat caused most of the casualties according to written sources; not only in an initial volley, but also throughout battles.

  • The figure of the centurion: Centurions transmitted orders from generals, led their troops, and thus needed to have exemplary leadership qualities.

  • Battle dynamics: Combining all three points above, not much would have happened outside of sporadic charges towards the enemy. Thrown projectiles resulted in casualties and disruptions, but only hand-to-hand combat during charges would be capable of breaking enemy lines and deciding the outcome of the battle. Centurions led such charges by example, and could also keep their own lines intact due to their training and virtus.

Based on the above, there might be three main factors that explain the battle outcomes:

  • The behaviour of centurions in battle: Centurions prevented panic in the ranks, led soldiers in attacks, but also served as examples of proper behaviour. Given the importance of centurions as role models, it is safe to assume that centurions were better at combat than the soldiers under their command.

  • The position of centurions on the battlefield: There is little evidence about which positions centurions adopted during battles. Academics believe that depending on how the legion was organised, centurions may have stood on the front right, front left, or somewhere in the middle.

  • The number of ranks: Roman legions might have been deployed in ranks from as few as three to as much as sixteen. Each century would have been only three or four ranks deep, but multiple centuries could be aligned behind the other to create deeper ranks.

    The ranks in the front are clearly involved in the battle, what about the ranks in the back? Ideally one could use fewer ranks in order to present a greater front to the enemy, but on the other hand such a formation would be less cohesive (and thus more risky).

An agent-based model for Roman combat

Traditionally, historians relied on descriptive models to explain how things worked. While simple, such models are also very inadequate if you want to model warfare. The thing with modelling warfare is that models cannot be deterministic, because in warfare similar situations may have different outcomes. On the other hand, war should not be seen as un-modellable chaos either, as warfare tends to follow certain rules.

A model based on complex-systems theory covers the middle ground between these two extreme perspectives. The idea of such a model is simple: you have a system that consists of many individual parts, which interact with each other. These interactions result in cascading system-level effects that do not exist on the individual level.


Specifically, the researchers use an agent-based model, where agents represent soldiers with similar (but slightly unique) behaviour. Each agent:

  • has a psychological state that is affected by his proximity to the enemy and friendly casualties. Both cause stress, which determines whether he continues to fight or will retreat;

  • can either advance or retreat;

  • may throw a pilum (javelin) if an enemy is within his range;

  • will attack a randomly picked enemy that is nearby, which may or may not result in a kill.

The effect of each of the three possible main factors is then studied by repeatedly ; one with fixed parameters (the control group), and the other with adjusted parameters (the experimental group).


First, two patterns emerged when the experience level of the centurions were modified:

  • The cohesion (willingness to fight) increases linearly with the qualities of the centurions;

  • At the same time, that of the enemy formation decreases following a sigmoidal curve (that decreases more gradually in the beginning).

This means that even “average” centurions can have a significant effect on the formation during combat, but only seasoned centurions would be able to rally their troops to break through enemy lines.

The model also suggests that the position of the centurion within the army has a significant effect. It does not seem to really matter where the centurion is, as long as it is at the first line. The decisiveness of engagements is significantly reduced when the centurion is positioned randomly within the century. Many sources claim that centurions preferred to position themselves on the right; the simulations suggest that there is no practical reason for doing so and that this is primarily a fossilised cultural trait.

Finally, the number of ranks matters a lot when the centurions are inexperienced: such formations need higher number of ranks to compensate for the lack of cohesion. Formations with experienced centurions are able to widen their front, even if the soldiers that they lead are not experienced.

A small number of centurions, evenly distributed among soldiers, can therefore have a critical effect on the performance of the battle formation. Experienced centurions can even outweigh an increase of more than 30% in the number of enemy soldiers.


  1. Agent-based models can be used to explore theories and test their plausibility

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