The Transformation of Archers

[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