A Retinue Composition Efficiency Metric

[Dragatus]

I understand how tactic works... In fact, I thought exactly the same thing as what you wrote here before actually using the excel to make some calculations.

It turns out cataphract mixing with cavalry (2:1) actually decreases the skirmish offense intensity from 1.325 to 1.122, if you are fighting on a terrain suitable for HA. This is because increasing the LC ratio increases the chance to trigger harass. Mixing with 2:3 ratio can make it to a roughly same value 1.338, however this will decrease the melee offense intensity from 2.189 to 1.397 (German brave general). If you mix too many LC, it basically becomes a standard cavalry. It's just not worth it. Of course, if you are fighting on a terrain not suitable for HA, mixing it with cavalry will greatly increase the skirmish offense, since you are simply adding number of LC from zero, but the cost of melee power is the same as previous case.

Similarly, I was arguing with someone on reddit about the power of pure camels after he posted this link. I always thought pure camels can't be better than Tie-Futu on equal numbers, because Harass is 300% and disorganized Harass is 100%. It turns out I was wrong, pure camels do better damage than any other units except mixed camels in Skirmish phase, and there is no risk of triggering volley. And at the same time they do same damage as housecarls in melee, so it's also no problem if the enemy numbers are too big to finish the battle in skirmish. It's completely viable, and somewhat anti-intuitive, that's why I suggest to include it.

I really appreciate the author because the excel sheet is really helpful to make quick calculations and get results which are not that intuitive.

I see now that when it comes to average results, pure Cataphract is better than I thought. That said, I would still use the 2:1 mix for the sake of reliability. With a mix you have a 100% chance that at least half your skirmish troops will be useful, though the chance that both will be useful is only 43%. With pure Catphract you have an 89% chance all your skirmish troops will be useful and an 11% chance all your skirmish troops will be useless. Personally I am risk averse and dislike gambling, so I'd take the one that never fails horribly. Especially since diferences in average efficiency are quite small.

I think the truth is a little weirder than this, as I've ranted about here. If it's tl;dr for anyone, the upshot is that War Elephants don't trigger heavy cavalry tactics because the line in the special troops file reads "base_type = heavy_cavalry" instead of "base_type = knights". I don't know whether "heavy_cavalry" is defined elsewhere for other reasons, but the heavy cavalry unit is called "knights" in the combat tactics file.

That's very interesting. I have failed to notice that bug concerning elephants and I quite like the heffelups and woozles solution to the HA bug.

 

[redtide]

I updated the documents in the original post to correct the error in handling heavy cavalry offense bonuses. I also made some things prettier.

 

[redtide]

The more I think about this, the more certain I am that you should have just multiplied the offensive and defensive efficiency rather than taking the square root. Right now if you quadruple a unit's attack you will only double it's ACREM

I'm still thinking about the best form of a combined metric. There will necessarily be some loss of resolution, and I think it's best seen as a kind of vague initial impression. The reason I took the square root is that in my conception I was pretending that ARCEM still has dimensions of dmg/cost (like cost-effectiveness), even though it actually doesn't. I don't know why, but that felt right.

But I have realized that the present form of ARCEM rewards flanks that are balanced between offensive efficiency and defensive efficiency and punishes flanks that are skewed in one direction or the other. The easiest way to understand this is by looking at the skirmish efficiency chart. Choose one of the points representing a flank and construct a rectangle using its coordinates (by drawing a horizontal line to the y-axis and a vertical line to the x-axis). ARCEM finds the length of the side of a square with an area equal to that of the rectangle. Since a squarer rectangle has a larger area, ARCEM rewards flanks that have defensive efficiencies and offensive efficiencies that are closer in value. Thus, Nubian 3:2 LS has a greater sARCEM than Longbow 7:4 LS. I don't know if that's good or bad. What do people think?

A combined metric that does the opposite would be one of the form SQRT(OE^2 + DE^2), which finds the diagonal of the rectangle, i.e. the straight-line distance between the origin and the point representing the flank. (You could divide it by SQRT(2) to force the values of the reference retinues back to 1.) Thus, Longbow 7:4 LS would have a greater value than Nubian 3:2 LS.

If you were to relate the two metrics (through division or subtraction), you would have an indication, in a single number, as to whether the flank is well-balanced between offensive efficiency and defensive efficiency or is skewed in one direction or the other.

 

[Dragatus]

Generally speaking I would recommend going for the surface area of the rectangle (or teh sdie of a square of the same surface if you must) rather than it's diagonal. Without context offense and defense should both be equally valid and they do reinforce each other as I mentioned before.

But context changes things. Skirmish units will do damage during both the skirmish and the melee phase, while melee units will only deal significant damage during melee phase. This means that for a melee focused unit skirmish defense is much more significant than skirmish offense. For example, Pikemen have 0.1 skirmish attack while Heavy Infantry have 0.25 skirmish attack, so if we just look at the ratio of the two we see that the Heavy Infantry is more than twice as good. But in reality neither will really do significant damage and what truly matters is which unit can reach melee phase with lower losses.

With skirmish units it's the opposite. Feudal armies are predominantly melee focused, so incoming damage during skirmish phase is lower than incoming damage during melee phase. This mean skirmish units can afford to have a lower defense, but since they are capable of doing notable damage during skirmish phase they will want to maximize that.

Or to put it simply, when fighting feudal levies skirmish units want to rout the enemy before melee can begin which requires a high skirmish attack and melee units want to reach the melee phase with minimal loses which requires a high skirmish defense.

What you could do to reflect this would be to have a general sACREM metric as calculated now and a specialized metric that would be OE² * DE for skirmish-focused compositions and just plain DE for melee-focused ones. Skirmish defense still matters for skirmish units, just not nearly as much as skirmish attack. But for melee units the skirmish offense can be largely ignored. Essentially we get the special metric by taking sACREM in it's current form and then multiplying it with OE for skirmish compositions and dividing it by OE for melee compositions.

Things get more complex if you also consider fighting tribals or nomads. Their armies are predominantly composed out of skirmish units so your retinue will be taking significant damage already in the skirmish phase. In such a case skirmish defense becomes as relevant as skirmish attack for the skirmish units while for the melee units skirmish defense becomes even more crucial. You could try to reflect that by using sACREM for skirmish compositions and DE² for melee ones.

But adding this anti-barbarian metric would lead to a degree of bloat in the charts and actually isn't really needed. sACREM would presumably already be listed anyway and if you square DE that doesn't change the order in which compositions are listed. If a given composition has a higher DE than another then it will also have a higher DE². And what people want to know is which one is better, not so much how far apart they are.

So my recommendation is to keep ACREM largely as it is now (except maybe drop the square root) and then list an additional 4th specialized skirmish metric.

 

[redtide]

3 morale points are substracted to the total morale of the army for each casualty (converted as percentages but this is not very important).

I've uploaded a new version (version 0.3) that incorporates morale according to the above assumption, which I'm referring to as Eslin's explanation, after what I believe to be its fullest expression. I'm not completely satisfied with this explanation, but even if it doesn't exactly match what the game does, I believe it nonetheless provides a better characterization of a flank than ignoring morale altogether. I've re-defined sARCEM and mARCEM to use morale efficiency instead of defensive efficiency.

 

[CaptainPolyp]

Thanks, I did not know this thread. I'll read it.

 

[Dragatus]

I've uploaded a new version (version 0.3) that incorporates morale according to the above assumption, which I'm referring to as Eslin's explanation, after what I believe to be its fullest expression. I'm not completely satisfied with this explanation, but even if it doesn't exactly match what the game does, I believe it nonetheless provides a better characterization of a flank than ignoring morale altogether. I've re-defined sARCEM and mARCEM to use morale efficiency instead of defensive efficiency.

The description from Eslin's thread doesn't quite match my experimental data. The part about how morale is determined does (more or less), but the part about how morale damage is applied does not.

Here's my data from around the time Conclave was released: https://docs.google.com/spreadsheet...2LlPuulvxdxvxiDqoZ-PEn7TB0/edit#gid=337772544

I modded the game and set all units to have 1 in every stat (including morale) and then watched fights between Harold Godwinson and William the Bastard. I recorded the number of troops, morale percentage, displayed maximum morale, the displayed damage and the displayed losses for 5 successive days of battle.

When doing my last round of practical retinue tests I also discovered that the number of units in an army also has some sort of impact. That's units as groups of soldiers, not different types of soldiers. An event army of 5X soldiers lost morale at a faster rate than 5 event armies of X soldiers.

 

[CaptainPolyp]

The description from Eslin's thread doesn't quite match my experimental data. The part about how morale is determined does (more or less), but the part about how morale damage is applied does not.

In the thread, Eslin reports 1 morale damage per loss. have you tried with a morale damage of 2.5? (the MORALE_DAMAGE parameter seem to be set with this this number in the current build)

When doing my last round of practical retinue tests I also discovered that the number of units in an army also has some sort of impact. That's units as groups of soldiers, not different types of soldiers. An event army of 5X soldiers lost morale at a faster rate than 5 event armies of X soldiers.

Does that mean that morale damage are applied per-unit? One loss would deal morale damage to all the army if there is only one unit, or to each unit separately if there are several?

 

[Dragatus]

In the thread, Eslin reports 1 morale damage per loss. have you tried with a morale damage of 2.5? (the MORALE_DAMAGE parameter seem to be set with this this number in the current build)

The thread mentiones Horse Lords, so 2.4 patch. At that point MORALELOSS_FACTOR was indeed 1. In the 2.5 patch when I did my morale testing MORALELOSS_FACTOR was increased to 3. I haven't done any more morale tests since then.

Does that mean that morale damage are applied per-unit? One loss would deal morale damage to all the army if there is only one unit, or to each unit separately if there are several?

If morale damage was applied to every unit the 5 units of X soldiers would lose morale faster than the one unit of 5X soldiers, but the opposite is true. I still need to investigate this thoroughly, but at first glance it appears like there may be some kind of losses in morale damage when it gets spread out among multiple units. Which in turn would inflate the combat potential of cheap unit types such as Light Infantry or Pikemen. For 1200 retinue cap you could get 1 unit of Knights or 2 units of Light Skirmish and the second option will benefit from morale loss dissipation.

 

[CaptainPolyp]

If morale damage was applied to every unit the 5 units of X soldiers would lose morale faster than the one unit of 5X soldiers, but the opposite is true. I still need to investigate this thoroughly, but at first glance it appears like there may be some kind of losses in morale damage when it gets spread out among multiple units. Which in turn would inflate the combat potential of cheap unit types such as Light Infantry or Pikemen. For 1200 retinue cap you could get 1 unit of Knights or 2 units of Light Skirmish and the second option will benefit from morale loss dissipation.

Is it consistent with rounding error then? (when rounding down)
If the number of losses per unit and/or morale loss per unit is proportional to the size of the unit, then this is highly probable that the losses per units and/or morale loss per unit are not integer values. If the (morale) losses are rounded down each day, the difference can be meaningful, although not extra big... but if you add up these small differences each days...

 

[tyler45455]

Can we get a TLDR of what the best retinue to use is?

 

[redtide]

Can we get a TLDR of what the best retinue to use is?

Depends on your criteria. For instance, a lot of people probably care more about what I call "raw power" than any of the cost-effectiveness stuff. But I've presented some prospective retinue rankings in the "figures" PDF. They're presented in a kind of "drill down" format: first ranked according to the combined metric, and then the component metrics are plotted against one another in several different charts, allowing you to focus on whichever characteristic you're interested in, e.g. melee offensive retinue-cap-usage-effectiveness. And it's still an open question whether this method can predict which flanks will have high win rates or high kills:casualties ratios.

EDIT: Oh, but I guess there is actually a single answer to this question. It's definitely camels.

 

[CaptainPolyp]

EDIT: Oh, but I guess there is actually a single answer to this question. It's definitely camels.

Maybe they will be nerfed next patch tho. (nothing announced yet but given how they are overpowered)

 

[Dragatus]

Yes, it's definitely camels. Camels are essentially Light Cavalry with double attack and I can tell from experience that they'll massacre any levies they run into. I had 50k Camel Cavalry crush a 175k Chinese army three times in my Egyptian NK world conquest.

Is it consistent with rounding error then? (when rounding down)
If the number of losses per unit and/or morale loss per unit is proportional to the size of the unit, then this is highly probable that the losses per units and/or morale loss per unit are not integer values. If the (morale) losses are rounded down each day, the difference can be meaningful, although not extra big... but if you add up these small differences each days...

No, the effect is too big to be explained by a rounding error.

[2X + 2X + 1X] vs 5X resulted in the first army winning with 52.9% morale remaining (47.1% morale lost).

[1X + 1X + 1X + 1X + 1X] vs 5X resulted in the first army winning with 56.7% morale remaining (43.3% morale lost).

[1X + 1X + 1X + 1X + 1X] vs [1X + 1X + 1X + 1X + 1X] resulted in both sides losing morale at the same rate.

[1X + 1X + 1X + 1X + 1X] vs [2X + 2X + 1X] resulted in the first army winning with 26.1% morale remaining (73.9% morale lost).

In all cases both sides were taking the same amount of damage and losing the same amount of soldiers per day. I did not record how much morale the loser had at the moment of defeat, but it had to be less than 20% (so more than 80% morale lost).

If we make the assumptions that the loser always lost 81% morale and that the number of units is the only factor, fiddle with those result a bit, and rewrite them we get:

5 units vs 1 unit resulted in the first army losing 53% as much morale as the second one.
3 units vs 1 unit resulted in the first army losing 58% as much morale as the second one.
5 units vs 3 units resulted in the first army losing 91% as much morale as the second one.
5 units vs 5 units resulted in the first army losing 100% as much morale as the second one.

The first step to understand things better would have to be to verify the assumptions. For example I'd have to test if the distribution of soldiers within the units has any effect (so for example test if [3X + 3X + 3X] loses morale at the same rate as [4X + 4X + 2X] or [7X + 1X + 1X]) and whether you get the same result when both attacking and defending. I'd also have to record the exact amount of morale in the losing flank at the time of defeat.

 

[tyler45455]

Depends on your criteria. For instance, a lot of people probably care more about what I call "raw power" than any of the cost-effectiveness stuff. But I've presented some prospective retinue rankings in the "figures" PDF. They're presented in a kind of "drill down" format: first ranked according to the combined metric, and then the component metrics are plotted against one another in several different charts, allowing you to focus on whichever characteristic you're interested in, e.g. melee offensive retinue-cap-usage-effectiveness. And it's still an open question whether this method can predict which flanks will have high win rates or high kills:casualties ratios.

EDIT: Oh, but I guess there is actually a single answer to this question. It's definitely camels.

ok what about a TLDR for a pagan HRE emperor, what unit costs the least per month while still being strong in combat.

 

[redtide]

ok what about a TLDR for a pagan HRE emperor, what unit costs the least per month while still being strong in combat.

What culture are you, and which cultures would you be willing to switch to? I haven't accounted for any religious offense, defense, or morale bonuses, but I don't think that Germanic gets any, just a levy bonus.

 

[Dragatus]

If your retinue is a small fraction of your levy, you'll do best with Light Skirmish. The only thing better would be certain cultural Light Infantry retinues (or camels).

If you want to use it as a standalone force I'd recommend a mix of Light Skirmish and Defence from among the standard retinues.

 

[redtide]

I've realized that there's an omission in the current version (0.3). The spreadsheet applies cultural building bonuses only to troops in cultural retinues and not to troops in generic retinues. I'll fix this in the next version.

 

[Hospitalier]

Thank you guys so much for trying to illuminate the combat mechanics. The combat phase always looked like spaghetti to me, very hard to understand every value, very hard to optimize. I usually just fell back to the "have more guys" thing, which disappointed me. Anyways, I think I'll try some of your combat mods when I get the chance. In the mean time, good work!

 

[es333]

Wow, this is extremely complicated. Could someone smarter than me tell which retinues are the best (strongest)?