The Transformation of Archers

[Jon Shafer]

First, I must start off by saying I used to hate Archers. Abhor Archers. They were slow, they had a poor upgrade path, they weren't exactly cheap and they weren't effective (opinion )...

Which is the main problem: they weren't cost effective. Why build Archers when you can build vet Warriors and upgrade them to vet Swordsmen for chump change? Sure, China et al. can use them for an early rush on a weak AI civ, but come on now, you can basically wipe out an AI no matter what you use whenever you use it unless you're playing on Deity. Why waste shields on inferior units that don't upgrade for a long time (and upgrade to pretty crappy units even when they do) when you can build units that are more effective at the time and can be upgraded to something better?

But that was pre-Conquests.

After Conquests, I've learned to befriend the Archer, and use it more to my advantage. I'll run down the things I see as its newfound strengths and why I now find them more useful.

Range-0 Bombardment

The obvious Conquests improvement to Archers is the ability to bombard defensively. While it doesn't often prove of much use while fighting against the AI (though occasionally it does), it has much greater application in games against other humans, where the battles are bigger and bloodier, and a handful of Archers can take a few knocks off attacking units.

Changes to Upgrades

Upgrading in Conquests is now more expensive than it was in PTW, which means the Warrior-to-Swordsman upgrade scheme is no longer anywhere near as reliable as it once was. Having to fork over 40 gold to upgrade Swordsmen early on was doable, but it would cost you, as you can't really generate large amounts of gold early on without turning down research significantly... but now it's 60 gold. Seriously now... who has 120 gold to upgrade just 2 Warriors as a modern force? Upgrading is now really only effective as a means of making obsolete units useful again for a high cost, as it was designed. Not as a means to build a cheap army and then upgrade it to a modern one in quantities much greater than should normally be possible.

Also, the fact that you can't do 40-turn research any more means that if you want to turn down science to save gold... you actually have to turn down science. You can't just do a 40-turn tech while building up gold and hope to remain anywhere near the forefront of science.

Since it's no longer as economical to rely on Warrior-to-Swordsman upgrades, that leaves a void in the offensive lineup before the point where a civ has the industrial base to produce Swordsmen from scratch. This void is now filled by the Archer, as it was originally designed to do. If you want attackers in this era, they're going to have to be Archers.

Changes to Barbarians

In Conquests barbarians are a lot more of a handful than in PTW and Civ 3, mainly because almost every time a hut is popped it gives barbs. And in order to kill these guys you're going to need attackers. Previously, a couple upgraded Swordsmen could handle the minor barb threat easily enough, but now a few early Archers will have to do the job instead (due to the new huts and the other aforementioned issues). If you're going to pop a hut near one of your cities and you get barbs (as happens more often than not), you're going to need a unit to clean them up. Letting barbs wander about your empire isn't really a good idea, especially when you have a ton of Workers scurrying about (as any good civ player should).

These three main changes in Conquests have given the Archer a new light for me. Having a mixed Archer-Sword-Horse army in the middle of the Ancient Era is now a more common site and can be a wise investment on the part of the player.

[ducki]

Good stuff!

In Conquests barbarians are a lot more of a handful than in PTW and Civ 3, mainly because almost every time a hut is popped it gives barbs.

Any chance you moved up a difficulty level recently? I don't even bother with huts any more, since moving up to Emperor, because it's not worth it most of the time.

And in order to kill these guys you're going to need attackers.

Except that the nice AI that got patched into the PtW barbarians, where they actually would wander around looking for a weak spot or a stray worker or a nice tile to pillage seems to have been omitted. Now they mostly just fortify on the spot. I posted some screenshots a while back where I had an undefended capitol and lost my warrior about 6 squares away to barbs from a hut. At which point, they all just fortified.
Ignoring my empty town - I went ahead and finished a settler to see how long they'd let me go. Settled a second town, my two workers fully improved both and got within 2-3 squares of the barbs before they finally decided "Hey, we're barbarians, let's go raise Cain!"


Since I go (very)light on defense, I'll often build a couple Archers just for barb "defense" duty, and combined arms is a good thing. IIRC, 0-range bombard was primarily to help the AI, who builds lots of archers and then garrisons towns with them.

[Jon Shafer]

Originally posted by ducki
Any chance you moved up a difficulty level recently? I don't even bother with huts any more, since moving up to Emperor, because it's not worth it most of the time.

I normally play Demigod since Conquests, and ever since then huts have been useless...

Except that the nice AI that got patched into the PtW barbarians, where they actually would wander around looking for a weak spot or a stray worker or a nice tile to pillage seems to have been omitted. Now they mostly just fortify on the spot. I posted some screenshots a while back where I had an undefended capitol and lost my warrior about 6 squares away to barbs from a hut. At which point, they all just fortified.
Ignoring my empty town - I went ahead and finished a settler to see how long they'd let me go. Settled a second town, my two workers fully improved both and got within 2-3 squares of the barbs before they finally decided "Hey, we're barbarians, let's go raise Cain!"

Ignoring the smarts of the barbs, the fact that you can pop so many (especially on higher diff levels with high barb settings) means that they're inevitably going to be a huge threat. I played AU501 on Demigod, and before too long I ended up with two stacks of 8 barb Horseman on my little island. The southern stack nearly destroyed my 1-turn-left Great Library and the northern one had me pinned down where I had to use all my units for defense rather than MP, forcing me to turn up the lux slider pretty high. All-in-all, really annoying.

Speaking of which, I hadn't really noticed any sort of major difference in the barbs. Though it does still sometimes attack units fortified on hills or mountains for some reason...

Since I go (very)light on defense, I'll often build a couple Archers just for barb "defense" duty, and combined arms is a good thing. IIRC, 0-range bombard was primarily to help the AI, who builds lots of archers and then garrisons towns with them.

Right. On higher diff levels it's important to have some useful attackers around ready to kill anything that gets near. I've found that stacks of 6 or 8 barbs require more than just a couple perimeter units in order to save your cities.

[vmxa1]

I agree Trip. I never like to make archer, unless I was going for a rush. Now I make more than ever.

Ducki if you don't enjoy huts at Emperor, you will really hate them at Sid. They are prety ugly at Demi, but you can get find once in a while (non expansion). I have barbs kill archers and spears and horses routinely at Sid. You still get a 25 bonus at Demi, zero at Deity and Sid.

[ducki]

Ignoring the smarts of the barbs, the fact that you can pop so many (especially on higher diff levels with high barb settings) means that they're inevitably going to be a huge threat.

This may be true at Demigod. At Emperor, if you just let the AI do most of the popping, you don't get as many barbs, or so it seems. If I'm "running a tight ship" where losing an exploring-for-contacts warrior would really put a crimp on my plans, I flat out ignore the hut. If it's close to home, I'll gather a few archers and deal with it as late as possible.

vmxa1, it's not that I don't enjoy them, per se, just that the potential benefit from a hut(low level tech, gold, settler - yes even this one) is usually outweighed by the near certain benefit of keeping my scouting unit alive and finding other civs to trade with.

It's entirely possible my observation is skewed, but I remember when I first played PtW and the barbs were a real nuisance instead of just stupid elite-generators. I've yet to see a C3C barb "probe" my budding empire for a weak spot. Maybe I'm wearing rose-colored glasses.


Edit: In fact, maybe I should fire up PtW and have a go, since it's included in C3C.

[vmxa1]

No you are correct that the barbs are lame in C3C over all.
I opened a threat about how lame they were. It is just that as you lose your bonus, they become a problem, even if they are not very aggressive.

Huts rarely yield anything else at Sid for a non expansion civ.

[Jaybe]

Another factor with building Archers is their upgrade path ... all the way to TOW Inf.

[ErikM]

Originally posted by vmxa1
Huts rarely yield anything else at Sid for a non expansion civ.

And, incidentally, they never yield anything but deserted huts for expansionists Maybe maps if you are lucky.

[Dominae]

The use and utility of Archers has remained relatively unchanged for me: on Emperor and below, they're good to rush with, on Demigod and above they're not worth the resources.

It's true that upgrading is more expensive and this makes building units from scratch more attractive. So I can see the logic of building Sworsdmen straight-up, but I'm not sure how this transfers to Archers, too; both units are just as cost-effective as they used to be.

Well, there's the zero-range bombardment thingy, but that's not really worth 20 Shields (you might as well just build a Catapult instead). In any case defense is highly overrated; 3 Attack is much more attractive to me than the chance it taking one HP off on defense. In order to make Archers, Longbowmen, et al. really useful units, they should have given them a Bombard value equal to their Attack (like in the PTW AU mod).


Dominae

[Aeson]

I like taking a couple Archers along with an offensive stack if the terrain is rough or the route may have mountains. Even when landing on a Mountain in and early inter-island invasion, I'm convinced that replacing those Archers with Spearmen is a better idea. Archers are good on defense when you can expect only a few attacks per turn being sent against you. In massive attacks the help they give is negligible.

On flat ground (and safe numbers) it's definitely Cats.

As for upgrading, I still easily find enough gold to upgrade 10-15 Warriors by about midway through the Ancient, while staying in the tech race.

Huts on Sid can give maps, gold, or empty for expansionist. No Settlers or cities. Deity gives everything but cities. Demi-god can give all results. I don't pop huts anymore either, except in two cases: no military units yet, or the hut is being popped by building a city next to it.

[Dominae]

Originally posted by Aeson
Deity gives everything but cities.

Wow, that's actually an advantage over Demigod! Well, maybe not, because this result is probably replaced by "nothing".


Dominae

[Jon Shafer]

Originally posted by Dominae
It's true that upgrading is more expensive and this makes building units from scratch more attractive. So I can see the logic of building Sworsdmen straight-up, but I'm not sure how this transfers to Archers, too; both units are just as cost-effective as they used to be.

Statistically 3 Archers are more effective than 2 Swordsmen.

Well, there's the zero-range bombardment thingy, but that's not really worth 20 Shields (you might as well just build a Catapult instead). In any case defense is highly overrated; 3 Attack is much more attractive to me than the chance it taking one HP off on defense. In order to make Archers, Longbowmen, et al. really useful units, they should have given them a Bombard value equal to their Attack (like in the PTW AU mod).

Yes, attacking is much more potent than defending, but when facing a competant opponent you're not always going to be attacking. And yes, Cats are certainly better than Archers at bombardment, but the point is that they have multiple roles in addition to just being able to bombard.

[Jon Shafer]

Originally posted by Aeson
As for upgrading, I still easily find enough gold to upgrade 10-15 Warriors by about midway through the Ancient, while staying in the tech race.

600-900 gold? What difficulty level are you playing on?

[DrSpike]

I usually throw a couple of archers in a stack........I think it's usually worth it.

[Dominae]

Originally posted by Trip
Statistically 3 Archers are more effective than 2 Swordsmen.

True. But let's do the math:

---

Case 1: Vet Sword vs. fortified Vet Spear

Sword loses 44.2% of the time
Average Shields lost: 0.442*30 = 13.26

---

Case 2: Vet Archer vs. fortified Vet Spear

Archer loses 65.9% of the time
Average Shields lost: 0.659*20 = 13.18

---

So, you lose a grand total of 13.26 - 13.18 = 0.08 fewer Shields when you attack with 3 Archers instead of 2 Swordsmen. Wow.

Although I downplayed the role of defense in my post above, it's hard to deny the importance of Swordsmen's higher defensive value. Certainly it's worth more than 0.08 Shields, even when you take into account the Archers' bombardment ability (I'm too lazy to do that math right now). To support this claim, consider that if all you'e got is Archers you're going to need to need some Spearmen escorts (which do not really add to your offensive punch), at the cost of more Shields.

And yes, Cats are certainly better than Archers at bombardment, but the point is that they have multiple roles in addition to just being able to bombard.

Offensive bombardment is pretty good too. In the thick of battle, I find that Catapults get used more often per turn (on average) than Archers. Archers are best used for counter-attack against damaged units, but in that situation you're usually winning anyway; Catapults, on the other hand, help you crack that nut in the first place. Not to mention the fact that a Catapult's Bombard value is far more impressive.


Dominae

[Solomwi]

Aeson, no tech from huts on Sid? Not that it will ever affect me, of course.

[vmxa1]

Yes cats would be better, but you need Math first, so it won't be available as soon as archers.

I make archers when I can't make swords or horses yet.

[vmxa1]

Originally posted by Solomwi
Aeson, no tech from huts on Sid? Not that it will ever affect me, of course.

I am pretty sure I have gotten tech on maybe two occassions or there abouts. IOW if my memory is not failing again, I am sure I got some tech. I have gotten warriors a few more times. Maps are about the same as tech for me and gold once.

This is not over a heck of a lot of huts as I don't get more than 2 or 3 a game. I don't search them out above Demi.

[Aeson]

One thing to factor into the Archer/Sword equation is promotions and upgrade path. More likely to die means more likely to promote the enemy, so using Archers you can expect to have to kill more HP's. Swords also make good defenders, and so you don't need to bring as many Spears along.

Swords upgrade come earlier, and unless you are the Scandanavians, gives a more useful unit. (why aren't there any Med Inf UU's I wonder?)

600-900 gold? What difficulty level are you playing on?

On any difficulty I can get that much gold with an average start. On Sid you can't keep in the tech race unless you get the GL, so there I just horde cash and go for the GL or 50 turn IW/HBR. Deity and Demigod you still have a decent chance to keep in the tech race and sell techs around to earn that much. It costs more to buy, but the AI have more to pay.

Key below Sid is to buy or trade for techs you see that the other AI's don't have, trade that for something the first AI didn't have, and then get your money back by trading the second tech to the first AI. Since the AI can't cash rush, the gold you don't get back just sits there most of the time, waiting for the next round of trading. It may exchange hands, but the only drain on it will be upgrading (by which time you should have grabbed it back to do your own upgrading) or establishing embassies (which the AI doesn't seem to do early or often).

On Sid, go for the GL as a Commercial/Seafaring civ with a pre-build and pray no AI pops literature from a Hut. They avoid it pretty well otherwise it seems. Otherwise 50 turn it to Iron Working (or The Wheel/Horseback riding if you are the Egyptians/Hittites/Iroquois or just want Horses because they are more common) and pray the resource is within reach.

The advantage Archers have is you can put together large numbers of them rather early, but trying to play a numbers game early on Sid doesn't work. Done right you can produce more Warriors and/or as many Chariots as you could Archers, and use the cash you have to upgrade. So it's not really 3 Archers vs 2 Swords, but 3 Archers vs ~3 Swords (you can produce more Warriors, but cash is the limiting factor). The advantage Archers have is not being dependant on Iron or Horses. Straight out production, efficiency, and upgrading path, they lag behind because of upgrading.

It's pretty balanced given the tradeoffs with each approach. Archers are safer and on lower difficulty levels offer earlier advantages, but don't have the potential of the resource units.

[nbarclay]

Dominae's analysis is highly misleading. If 100 swordsmen and 100 archers each attack 100 fortified enemy spearmen, the shield losses suffered by the attacker will (on average) be almost identical in the two cases. But the losses inflicted on the defender will be vastly higher with swordsmen as the attackers. Fewer swordsmen will have to risk their lives in follow-up attacks, and the ones that do will generally be fighting more badly injured opponents (since more potent attackers not only are more likely to win but also do more damage on average when they lose). Thus, if the attacker can get sufficient local numerical superiority, swordsmen will suffer dramatically fewer losses (in shields, not just in numbers) to actually defeat the same enemy compared with archers

A more complicated issue is how many units of each type are needed to ensure victory, since that (coupled with the cost of the units) has an impact on how many catapults a player can afford to include in an offensive stack. Swordsmen cost more, but fewer are needed for follow-up attacks when an earlier attacker in the stack loses and to replace casualties. I seriously doubt that using archers would make including enough more cats in an offensive stack practical to overcome the archers' inferiority, but I haven't examined the issue in sufficient detail to be certain.

Also note that against the same opponent, an elite swordsman is more likely to win than an elite archer and less likely to die. That provides an advantage in generating leaders.

Nathan

[DrSpike]

I think all posts like Nathan's and Dominae's are, whilst interesting, beside the point, though Trip did start it with his comment defending his original post.

Ultimately they were pants, now they are less pants, for all the reasons Trip gave (though I think the barb one is questionable - don't pop the huts except with cities!). They still aren't great, but do have more uses now. I often throw a few in a stack that get built early in the game, and I don't feel as bad about it as I once would have.

It's probably just as well they were buffed. If you don't restart when you don't have iron you need something.

[Dominae]

Originally posted by nbarclay
Dominae's analysis is highly misleading. If 100 swordsmen and 100 archers each attack 100 fortified enemy spearmen, the shield losses suffered by the attacker will (on average) be almost identical in the two cases. But the losses inflicted on the defender will be vastly higher with swordsmen as the attackers. Fewer swordsmen will have to risk their lives in follow-up attacks, and the ones that do will generally be fighting more badly injured opponents (since more potent attackers not only are more likely to win but also do more damage on average when they lose).

I'm not quite certain I understand what you mean here. If you mean Swordsmen actually perform better than Archers because the former permits fewer Spearmen promotions, then I agree (I was just about to post that point before reading yours).

By the way, in your example you must mean 300 Archers versus 200 Swordsmen; obviously if an equal amount of each attack 100 Spearmen the Swordsmen will perform better!


Dominae

[Dominae]

Originally posted by Aeson
One thing to factor into the Archer/Sword equation is promotions and upgrade path. More likely to die means more likely to promote the enemy, so using Archers you can expect to have to kill more HP's.

Oh great, and Aeson beats me to it, too...

[nbarclay]

Aeson had already raised the issue of promotions. What I'm talking about is the fact that while the averge number of shields lost against your fortified spearmen is the same for archers and swordsmen, the average number of units killed and average damage caused to survivors is not. (Of course the promotions issue makes that situation even more problematical for archers than it would be otherwise, especially against a militaristic opponent.)

Converting your percentages into battles involving 100 units on each side, swordsmen would kill about 56 spearmen and leave about 44 survivors while spearmen would only kill about 34 spearmen and leave about 66 survivors. From that point, there are two basic ways the battle could go.

If the player brought a big enough stack to essentially guarantee victory, those first 100 attackers aren't anywhere close to his entire stack. At this point, the swordsmen now have an enormous advantage over the archers. The swordsmen only have to fight 44 more battles plus whatever battles are needed to finish off enemy units that win those fights, while the archers have to fight 66 more. Further, on average, the 66 units the archers have to fight will be less badly damaged than the units the swordsmen have to fight. (After all, as weaker units than swordsmen, archers not only are more likely to lose but average causing less damage when they do lose.) And as long as the player has enough units, the numerical superiority that would result from archers' being cheaper would have no direct impact on the battle. (After all, once the last enemy unit is dead, it doesn't matter how many units you have left in your stack that haven't attacked yet.) Thus, swordsmen have a rather significant advantage over archers as long as you make sure you use them in sufficient numbers. (Note that this requires only local numerical superiority at the location of a particular attack, which is often easy to achieve even when a player is weak compared with an AI in overall military power.)

The other way the battle could go is for the number of attacking units not to be sufficient to essentially guarantee victory. For example, the same shields could buy 120 swordsmen or 180 archers. In that case, the swordsmen attack would average leaving alive 24 enemy survivors that it cannot attack a second time plus whatever units survive a second attack, while the archer stack could attack all 66 survivors a second time with 14 archers left to attack the enemies that survive those battles. In that type of situation, archers' lower cost can be used to a clear advantage, although I'm not sure exactly how the two types of units would end up comparing under those conditions.

In desperate gambles when a player is in over his head, archers are probably pretty competitive with swordsmen. But as long as a player can set the tone and tempo of a war in a way that always provides clear local superiority at the point of conflict, swordsmen have a very clear advantage over archers in terms of average losses suffered in order to kill the same enemies.

Nathan

[Dominae]

I'm not really understanding your analysis, Nathan.

On average, Archers do the same as Sworsdmen offensively, Shield for Shield. Here, "the same" means number of units lost on both sides.

What I think you're trying to say is that, individually, Sworsdmen defeat Spearmen outright more often than Archers. While true, this is subsumed by the fact that Shield for Shield the units equally cost-effective. It's not really fair to compare what 100 Swordsmen can do compared to 100 Archers, because that leaves 100 Shields unaccounted for.

It's not use to consider counter-attacks, because units are just as effective on the second round of battles as the first. That's why the best way to look at it is from a Shields perspective.

The only additional factor that comes into play is that surviving units can get promoted, so Swordsmen are preferable for that perspective. But if promotions were not a factor, Archers would be more cost-effective than Swordsmen on the offense no matter how you look at it.


Dominae

[nbarclay]

Originally posted by Dominae

On average, Archers do the same as Sworsdmen offensively, Shield for Shield. Here, "the same" means number of units lost on both sides.

The way I'm reading your earlier post, you considered only the number of shields lost on the attacker's side, not the number lost on the defender's side.

Sword loses 44.2% of the time
Average Shields lost: 0.442*30 = 13.26

Enemy loses 55.8% of the time
Average shields destroyed: 0.558*20 = 11.16

Archer loses 65.9% of the time
Average Shields lost: 0.659*20 = 13.18

Enemy loses 34.1% of the time
Average shields destroyed: 0.341*20 = 6.82

Thus, either I'm misunderstnading what you wrote or swordsmen are vastly more effective as attackers than archers in terms of the kill/loss ratio in one-on-one battles. Their expected losses are about the same in shield value, but the expected value of what they destroy is almost one and two thirds times as high.

But that tells only part of the story because in a real battle of significant size, a good human player will almost certainly try to take advantage of the stack effect. If that effort succeeds (as it almost certainly will when a good human player is attacking an AI), the attacking force will be larger than its enemy, and later attackers will be able to finish off injured enemy units relatively cheaply.

Thus, I sought to consider not only an initial 100-vs.100 battle in which the AI units are undamaged but also what might happen afterward (still in the same turn) assuming the initial 100 attacking units are only part of the player's stack. If we make no assumptions regarding the size of the attacking stack other than that the player brought enough units to win, swordsmen have a considerable advantage and archers' weight of numbers will, over the course of time, be needed just to replace the greater cost of the units lost achieving the same victories. But I suspect that there might be situations where archers' greater numbers (for a given total cost in shields) could combine with the stack effect to win battles swordsmen would have lost - albeit probably winning at a rather high cost due to the poor cost-effectiveness of the initial attackers.

By the way, given the AI propensity toward using regular rather than veteran units, statistics on how veteran archers and swordsmen fare attacking fortified regular spearmen would probably give a more accurate indication of how most human-vs.-AI battles would work out. Of course in MP, the nature of combat is rather different.

Nathan

[Dominae]

Originally posted by nbarclay
Enemy loses 55.8% of the time
Average shields destroyed: 0.558*20 = 11.16

Enemy loses 34.1% of the time
Average shields destroyed: 0.341*20 = 6.82

Thus, either I'm misunderstnading what you wrote or swordsmen are vastly more effective as attackers than archers in terms of the kill/loss ratio in one-on-one battles. Their expected losses are about the same in shield value, but the expected value of what they destroy is almost one and two thirds times as high.

What your calculations above show is that Swordsmen have better odds than Archers in one-on-one battles. We all know this already. In order to argue about the cost-effectiveness of each unit, you cannot omit their relative costs in your analysis (which you did).

Shields destroyed per Swordsmen: 11.16
Shields destroyed per Archer: 6.82

3/2 Archers per Swordsmen

-> 3/2 * 6.82 = 10.23

So, Swordsmen are 8.3% more efficient in terms of Shields destroyed. That's not negligible, but certainly not noticeable in any normal game.


Dominae

[nbarclay]

Dominae, your multiplication by 3/2 reflects the fact that a larger number of archers can fight a larger number of battles. But if you perform that multiplication, you have to multiply not only the value of the enemies destroyed but also the value of the archers lost. Otherwise, you are counting the average value of units killed in one and a half archer vs. spearman battles but only counting the cost of units lost in one such battle.

But the situation is made more complex by the fact that the enemy won't have one and a half times as many spearmen just because you're using archers instead of swordsmen. Thus, some of the archer battles will be against injured units rather than against healthy ones. But in a battle of stack against stack (at least with a good human player attacking an AI), some of the swordsmen will also be attacking injured units. Which is why I went into as complex (and apparently confusing) an analysis as I did.

Nathan

[Dominae]

Originally posted by nbarclay
Dominae, your multiplication by 3/2 reflects the fact that a larger number of archers can fight a larger number of battles.

No, I'm multiplying by 3/2 because you get 3 Archers for every 2 Swordsmen (20*3 = 2*30). If you're going to do an analysis in terms of Shield cost-effectiveness (which I am), at some point you have to factor in the fact that the costs are different. This has nothing to do with number of attacks.


Dominae

[nbarclay]

You factored the cost in when you multiplied the value of a destroyed swordsman by 30 shields and the value of a destroyed archer by 20 shields. When you then multiply the value of the enemy units destroyed by the archers by 3/2, you end up factoring in the cost difference twice instead of once.

According to your statistics, the expected value of a swordsman attacking a spearman is that the swordsman will suffer a loss of 13.26 shields and inflict a loss of 11.16 shields on the enemy. The expected value of an archer attacking a spearman is that the archer will suffer a loss of 13.18 shields and inflict a loss of 6.82 shields on the enemy. These expected values already reflect the fact that swordsmen cost one and a half times as much as the other units. If that fact were not already reflected, the expected value of swordsmen lost would be only 8.84 shields.

In order for archers to average killing more spearmen than that expected value, they would have to fight more battles. That is the only way they could possibly do it. But if they would fight more battles, they would suffer more losses in addition to inflicting more losses on the enemy. The ratio of losses archers suffer to damage they inflict on the enemy does not suddenly go up by 50% just because swordsmen are more expensive than archers.

Looking at it another way, if you multiply the value of the units archers kill by 3/2 in order to account for the difference in unit costs, you are really calculating the losses inflicted on the enemy by an archer and a half, not the losses inflicted by a single archer. But an "archer and a half," when it loses a battle, costs 30 shields, not 20.

Nathan