Saturday 31 March 2018

Unit scale - Large vs Huge: an experimental analysis

Changing the unit scale is one of the subtlest ways to influence gameplay in EB.

Campaign-wise, the main difference between Large and Huge lies in the strategic concern of avoiding the depletion of city population when recruiting units; but the effects of an increased unit dimension can be noticed in the tactical map as well, even if this aspect is often totally overlooked.

My purpose in this report is to provide evidence of the main differences related to the tactical part of the game when the unit scale changes from Large (which is widely recognised as the most used in MP environment) to Huge (which, in the opinion of some players, provides a more realistic and entertaining experience). Since I don't like to base my discussion on random things out of thin air, here I'm going to use both theoretical and experimental approach. I'm also going to use pictures beautifully crafted in Paint, and some simple math that I hope is not going to scare anyone.

Some theory


Switching from Large to Huge causes all units to double their numbers. The main assumption of the report is that the size increase of the square formation of a unit is uniformly distributed on its lateral dimensions; that is, the shape of the square itself, i.e. the ratio of rows over columns, remains the same (as shown in the next figure). I'll mention and discuss the validity of this assumption later on. Note that I wrote a completely random number as percentage inside the squares, just for example.


From this hypothesis we can derive the coefficient that multiplies rows and columns in the change from Large to Huge. Let r be the rows of the formation, and c its columns; then the total number of men in the unit n (the unit "area") is n = r × c .

This is valid for both Large and Huge unit size.

We also know that nH = 2nL , where the subscript H or L is related to Huge or Large scale, respectively; units in Huge scale have double the men compared to Large scale.

Therefore, if the unit keeps the same shape as assumed before, this means that the ratio between rows and columns remains the same: therefore

nH = rH × cH = 2 rL × cL =  2 rL ×  2  cL


This equation holds that doubling the number of men inside a unit results in an increase of its rows and columns by a factor  2 . This result is true only if the unit shape is not modified, as I stated before.

Movement and troop positioning


The capitalization of the map space is an essential feature of tactical encounters in EB; this holds true especially for steppe factions, but it is arguably one of the most pressing thoughts in general, and any good commander should start thinking about it since the deployment phase. A Large unit size allows for an emptier battlefield, while Huge size units fill a greater amount of available space. It is sufficient to imagine a the size of phalanx units in Large and in Huge scale: in the second case it is much harder to flank a compact phalanx line, introducing some tactical problems especially in team games with two or more players on each side.

Nonetheless, unit size influences not only the space filling of the whole army, but also the behaviour of single units. The bigger is a unit, the more difficult and time-consuming its movement is. Since in the RTW engine the speed of each soldier is fixed regardless of the unit size, one can intuitively say that complex manoeuvres such as wheeling or changing unit facing are slower in Huge scale. In general, Huge unit size results in clumsier and overall slower movements, and it is easy to see a cohesive formation break up when marching; this factor that can prove determinant for winning or losing. In Huge size you have more time to think early, but less time to react later.


Strategy is the art of making use of time and space.
I am less concerned about the latter than the former. Space we can recover, lost time never.

Napoléon Bonaparte

As an example, I can analyse semi-quantitatively the unit wheeling. The next figure shows a counter-clockwise wheeling. In custom battles, the wheeling does not follow an arc, but instead a (approximatively) straight line. It is clear that, while carrying off this manoeuvre, the men who have to travel the most are the ones the farthest from the centre of rotation. Therefore, the wheeling will be completed only when the men on the far right would have travelled the path connecting the two D vertices. As the unit size increases, the length of this path changes.


From trigonometry we know that
D = R × sin θ

where D is the distance from the two D vertices and R the radius of the wheeling.

When we change unit size, θ remains the same, while R is modified since the row of the formation is lengthened as I stated before.

The order of magnitude of this increase can be a factor  2 , if O = A: if the unit wheels over one of its corners, the manoeuvre takes the maximum amount of time. Instead, if the centre of the wheeling is far away, the time increase is often negligible, because the segment OA is far longer than the length of the rows of the formation.

From this fact it comes natural to imagine that accomplishing complex and, in particular, quick manoeuvres is more difficult in Huge scale than in Large scale. This provides a slower reaction to tactical necessities and puts the player in the need of planning carefully his orders, as already mentioned previously. For instance, escaping from an incoming charge while minimizing casualties becomes harder, because the fast wheeling required to move away from the trajectory of the charging unit is slower in Huge scale: a proper and timely micro- and macro-management of units is even more important.

Combat


It is known that the sheer number of men inside a unit does not influence the outcome of a fight, as long as stats and morale are considered: the stats remain unmodified, and morale is influenced by the percentage of men still fighting, not their absolute number. This is the reason why battles fought in Huge scale are generally slower than battles fought in Large scale: it is necessary to kill more men in order to achieve the same percentage of kills on the same unit and break its morale. This balances in some way the slower pace of unit movement on the battlefield. This consideration influences only the timespan of a fight, not its outcome.

There are nonetheless two aspects which are actually influenced by the unit size. They are the charge and the javelin volleys, and I'm going to prove why, and how much, these aspects are influenced.

(a) Charge


If we assume that the charge (e.g. from a cavalry unit) is carried off by the first row of men, we can safely imagine that the change in the rows and columns dimensions may modify the outcome of said charge. More precisely, we can say that the number of inflicted casualties during a charge is not doubled by the increase from Large to Huge, but is multiplied by our usual factor we're familiar with, that is  2 .

(b) Javelin volleys


The larger the unit scale, the more crowded the battlefield is. This fact can be exploited by javelin-armed units. If accuracy is not influenced by the unit scale (i.e. javelins are thrown in the same "area", or with the same dispersion), then javelins can be much deadlier in Huge unit scale, because in proportion more javelins are going to hit a soldier.

Case study 1: charges


Firstly I want to provide some insight into the effects of the charge and how it changes when we switch from Large to Huge.

The tests are made separately with a unit of Agema Klerouchon Hippeon and a unit of Hetairoi, on the Grassy Flatland map. Their opponents are:

  • Parthohellenikoi Thureophoroi (sword-armed infantry with javelins);
  • Kardaka Arteshtar (Hoplites with spear as primary and longsword as secondary);
  • Gund-î-Nizagan (Spearmen);
  • Kamboja Asvaka Ksatriya (Light cavalry).

For each type of opponent four tests are made. The charge is executed frontally, after giving the attack order with a single right-click; each unit is eager/fresh at the moment of impact. Each weird AI behaviour (e.g. running sideways and exposing the flank of the unit) is ignored, and the test repeated. The number of casualties caused by the charge is written down after 10 seconds from the impact.

Of course, to stay true to the initial assumption, the formation is kept the same for both unit scales.

Case study 2: javelins


The differences from Large to Huge regarding javelin casualties are studied with the help of a human opponent (thanks to ZEVA-Phillip V for his precious contribution).

For each unit size three units are taken into account: Thureophoroi (medium accuracy), Peltastai (high accuracy) and Peltastai Makedonikoi (ultra high accuracy). Each unit is shooting rounds of javelins from maximum distance in the back of a unit of Galatikoi Klerouchoi: this is done to maximize both the number of casualties and the influence of accuracy (accuracy matters the most when shooting at max distance). Three rounds of volleys are shot for each unit, and then a mean of the casualties is computed.

Experimental results


Below there are two histograms, one for each cavalry unit; they show the average number of casualties for both Large and Huge settings, in cyan and red respectively. There is also a green bar, an expected value for Huge setting: it was obtained multiplying the casualties obtained in Large by  2 .



Casualties inflicted by Agema Klerouchon Hippeon (top figure) and Hetairoi (bottom figure) when charging four different units, in both Large and Huge scale, together with expected values for Huge scale.

We can see that the experimental data for Huge scale are for the most part in good accord with the expected values. One notable exception is the case of the Kambojas: here the casualties greatly exceed the expected numbers, for both the charging units. It's challenging to understand why this happens: I suspect this has to do with unit density. I honestly have no idea whatsoever for explaining the casualties of the Kardaka when charged by the Hetairoi.

Disclaimer for boring people (click to expand)



Regarding what happens with javelins, it's not interesting to show raw data for the casualties. As a matter of fact, in Huge scale there are double the javelins than in Large, so a direct comparison is useless; furthermore, the attack values are different among the units I used. For this reason, it's better to renormalize the data: I divided the average number of inflicted casualties by the number of men in the unit and the missile attack value, so that I get the measure of the "killing efficiency" of the single soldier, regardless of the unit scale and the attack value.

For example, if a unit of Peltastai in Large scale kills an average of 9 men with each round of javelins, then I divide this number by 90, which in Large scale is the number of men a Peltastai unit is comprised of. As a result I obtain 0.1 = 100 10-3: this number is the measure of the "killing efficiency" of a single Peltast in Large scale. Then I divide again by 6, which is the missile attack of the Peltastai; this number is then compared with the equivalent for Huge scale.


Casualties inflicted by javelinmen with medium, high and ultra high accuracy, divided by the number of men in the unit and the missile attack value, for both Large and Huge scale.

It is evident that in Huge scale javelins are more efficient, because each volley kills more enemies per man and per attack point. If there was no difference between the settings, one should have expected roughly the same amount of kills per man and per attack point ( = roughly twice as many kills in Huge than in Large).

However, the data show how in Huge scale javelins are much more efficient, especially for lower accuracy units. In fact, the increase of kills per man for Thureophoroi (medium accuracy) is around 300%, while for the Pheraspidai (ultra high accuracy) the increase is less than 100%. I think the reason for this lies in the fact that at very high accuracy the increase of the number of men in the target unit does not matter as much, since the javelins are less dispersed anyway.

It is very interesting to see how the change from Large to Huge scale results in a somewhat rigid shift in the line of the casualties as a function of accuracy. This rigid shift benefits more the lower accuracy units, as already mentioned: the huge difference in efficiency between the Thureophoroi and the Pheraspidai in Large scale (2.32 vs 7.28, Pheraspidai are over three times more efficient) is greatly reduced in Huge scale (6.72 vs 12.5, less than double the efficiency).

Conclusions


From what we saw, we can now derive two main facts:
  1. Charges are less effective in Huge scale than in Large scale, in proportion to the number of men in a unit;
  2. Javelins are more effective in Huge scale than in Large scale, in proportion to the number of men in a unit.

This leads to two important conclusions.

First: when you choose the class of cavalry you want to field, you need to consider that light and medium mounted units are less viable in Huge scale: their charge is less powerful, and then in the resulting melee they get cut down to pieces by superior units. Conversely, elite cavalry is more effective in Huge scale, because after having charged they have sufficient staying power to fight competently in hand to hand. Concerning infantry, their "passive" reaction to the charge tells us that elites are again a superior choice in Huge rather than in Large scale, for the very same reason: if they suffer a charge, it cuts down less men in percentage, and in melee elite infantry can punish almost every cavalry unit.

Second: a correct use of javelineers in Huge scale (especially if concentrating fire on a single target) can be much more devastating than in Large scale, because of the impressive increase in kills per man. In this case, regular units gain in efficiency much more than elite units, even if the sheer amount of kills per man is lower. This means that units with lots of javelins, even if characterized by lower accuracy, are actually more effective than elite ranged units with fewer javelins.

There are of course other considerations that can be done, such as a more in-depth analysis of the space filling for both unit scales, but I think I reached the maximum tolerable length for this article, so I'm calling the day for now. If there are any suggestions regarding other aspects that you think can influence the outcome of a battle, please feel free to share your ideas: I'd be glad to expand this study on topics that I may have overseen.

Cheers!

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