Cavalry vs. Sword vs. Halebard test in r3897

[Krom]

I have set up a test map with 2 groups, 24 men in each, 8 men per row, facing each other. Player1 attacks Player2. Then I run it 50 time each in a pure simulation (no screen display).

Cavalry - Swordsmen: 50 wins, 5-22 units left alive;
Swordsmen - Halebardmen: 49 wins, 8-21 units left alive;
Halebardmen - Cavalry: 48 wins, 5-20 units left alive;

As you can see the balance is almost Paper-Rock-Scissors without giving extra +1hp to swordsmen

[sado1]

But did you try reversing the attack sides? As far as I hear, the result of the battles depends on who's attacking.

[Krom]

Thats not gonna change the fact that each unit type is better at fighting other unit type roughly the same as it is worse at fighting 3rd unit type. A > B > C > A loop.

Now second attacked first:
Cavalry - Swordsmen: 50 wins, 7-22 units left alive;
Swordsmen - Halebardmen: 50 wins, 6-22 units left alive;
Halebardmen - Cavalry: 50 wins, 6-20 units left alive;

[The Dark Lord]

If every unit costs the same these results would be fair, but sword fighters are really expensive and knights are even more expensive (but you get more speed in return). 24 sword fighters cost you 72 iron. You can make 36 crossbowmen or pikemen from that, which would be 50% more units. That's a large number. To balance things out, you should have more sword fighters left vs pikemen than pikemen vs knights. In other words, they need some kind of bonus. Not a large one like +1 life, but at least something is required.
Also, in my eyes those results are way too random. 8-21 units alive? 8 or 21 on a scale of 24 is quite a difference...

[Bo_]

Yes it was already 'rock-paper-scissors' in real numbers and in 1 vs 1 battle. Also important is the number of soldiers, so you have to make adjusted numbers. I've calculated it, let's call it PK for Pikemen and knights, PS between pikemen and swordmen, and SK for swordmen and knights.
So this adjusted number gives you the equal number of soldiers for the same cost/time, using the market values.

For pikemen and knights: Amount of knights; let's say 10, multiplied by 1.765 (See feedback and discussion, page 5, for calculation), gives you the equal amount of pikemen: 18. 18 knights defeats 10 knights.

For Pikemen and swordfighters: Amount of swordmen, let's say also 10, multiplied by 1.529, gives you the equal amount of pikemen: 15. 15 pikemen can defeat 10 swordmen, so here it doesn't fit anymore in you rock-paper-scissors.

Then for swordfighters and knights: 10 knights multiplied by 1.25 gives you 13 swordfighters. Here 10 knights will most likely win.

So, in equal amounts pikemen are stronger than knights and swordfighters, and knights are stronger than swordfighters. No 'rock-paper-scissors' like you say.

With the +1 hp: Knights are stronger than swordfighters, swordfighters stronger than pikemen and pikemen stronger than knights.

Ok I agree +1 hp may not be the best sollution but I still think that it was better.

IMO this also explains why lances and pikemen are so op now, and why it's only about lances + crossbow.

There's also 1 more very important factor and that's range soldiers. Since they do 50% of the damage, the strentch of a unit is less important, it's more about endurance of 1 unit and the amount of them, wich made lances and pikemen a bit useless in the core battle with the +1 hp. But not as a tactical unit against knights.
But since too many players want lances to be the main unit, it wouldn't be possible with that change.

[Krom]

Thats where KaM battle system, based on random kicks in. KaM battle results were and are always a little "fuzzy". These 6-21 values are bounds, average would be 12-13. But yes, thats how it goes.

MrBo, so you mean equally valued forces are 10 Cavalry / 15 Swordmen / 18 Halebardmen ?

[Bo_]

No, 10 knights, 13 swordmen and 18 halebardmen.
I've calculated those using market values.

Still it's not 100% correct since it doesn't calculate the building cost or the amount of building space you have. In most maps you can have for example 2 weapon smiths and 2 armor smiths, for xbow or pikemen, but not 2 weapons smiths and 4 armI or smiths. (For knights and sword fighters)
Or for axefighters you need the double amount of armory, wich would be 8, and requires also a lot of space. For knights you should also know that stables work slowly, 4 corn for 1 knight, knowing that between each time the animal breeder feeds a horse, wich takes time, he also waits before starting to feed again. Don't forget that some buildings are more expensive to build than others.
So those tiny things aren't calculated in the market, but they also influence the amount of soldiers you can have after pt.

The numbers I gave are for the exact market values, they are way more accurate than just saying 1 vs 1.

[Siegfried]

Indeed it does make a change whether your unit attack or defend (this means they'll do the first attacking strike). But for the Paper-Rock-Scissors this should not be crucial. And as Krom shows, it indeed is not in the old system.

The other point is the cost. But the cost are to be seen in relation to their vulnerability towards arrows and bolts. To understand this, you have to think like Bo does and think about the number or long-ranged units you usually face. He says that long-range units usually do 50% of the damage, which is not correct. I guess he meant that 50% of the attacks are done by long-ranged units. But then you have to consider that archers have an attack point of 60, which already is higher than the highest value (that of knight+swordman, which is 55) have. Crossbowmen even have 120. So if you assume that you're facing a troop with mixed archers and crossbowmen, their average attack already does 164% of the damage of the other troops. If you only face crossbowmen, you'll suffer 218% of damage.

The long-ranged units are the dominating and battle-decising units in the game and will always be. So the costs have to be seen in relation to that and not to the other units. And what do we find then? We find that the lance carriers/pikemen have nothing to avoid being hit by an arrow other than the usual chance to miss.
The swordmen is more expensive, true, but he has the storm attack to rush towards the archers and kill them. This makes it worth one additional equipment.
And the knight, on top of each other, has additional lifepoint + a permanent movement advantage, which makes it more maneuverable during the whole game. So the chance to get hit by an arrow/bolt is permanently lowered. This, of course, must be more cost-intensive.
The pikemen costs 3 resources, the swordmen 4 and the knight 5 - if you only count the resources inside the barracks. And this is the only number that we really can rely on.

The other number heavily depends on your way of designing your economy system. And thus I once again have to doubt the numbers that Bo provided.

Let's do the math:
To equip one pikemen you need:
A recrut, 1 pike and 1 iron armament. To produce the iron things you have to have at least the following buildings: iron mine (1x), coal mine (3x for reasonable speed), iron smithy (2x), weapon smithy (1x) and armour smithy (1x) + plus some resources to feed them, which is not important if you only compare iron units but becomes important if you compare it to wooden troops. So in total you need 9 chests plus a few timber and stone and some time (I don't count this for now)
To equip a sword fighter:
you need the same plus one additional coal mine and a second weapon smithy (two iron smithies are enough to deliver the three weapon smithies). So you need 11 chests.
To equip a knight:
you need the same as the sword fighter plus one additional farm and the stables. So 13 chests.

So the numbers are correct in the following: PS = 1.22; SK = 1.18; PK = 1.44
But - as explained above - you have to take into account that in average the long-range-units make double the damage as the ground-troops. And you have to take into account, that pikemen die easily while swordsmen have a rather inefficient counter and the knights have a permanent counter to long-ranged troops. But what number to apply there? How large is the chance that the crossbows will miss a knight vs. a pikemen? I don't have the accurate numbers, so I can't continue the calculation.

But I can't help but stress that you have to see the higher costs in relation to the long-range-units that make 2/3 of all damage!! And there, the expensive troops are way better than the pikemen.

So if you additionaly bereave the rock-paper-scissor-advantage from the pikemen, this unit is useless. Because either way it loses against all units.

[Krom]

@MrBo: I see your point and that is another thing we need to take into account when balancing armies

[Lewin]

Also, in my eyes those results are way too random. 8-21 units alive? 8 or 21 on a scale of 24 is quite a difference...

Those numbers aren't a good indication really. As soon as one group outnumbers the other group, they will circle around the back of the smaller group and kill them much quicker. So if one side gets "lucky" at the start and make some fast kills you'll find that they don't take many casualties because they can quickly finish off the opponents once they outnumber them (especially since strikes from the side/back do more damage than from the font)

[Bo_]

Siegfried about your PS, PK and SK, you should name them differently, my SK, PK and PS are exact when building infinite soldiers so let's say PS1, PK1, SK 1 for you, and PS∞, PK ∞ ans SK ∞ for me. To make it less complicated let's use AA as general term. (Adjusted amount). In AA∞ The costs of the units and buildings producing the weapons isn't important anymore compared to AA1, where the costs of buildings is bigger than the costs of your soldier.
Except that when you said

So the numbers are correct in the following: PS = 1.22; SK = 1.18; PK = 1.44

you wanted to make all those buildings again for every soldier you build? Buildings can make more than just 1 soldiers.

I've also calculated your numbers again, see below, so we can all see how you got them.
In general: AA defines how high the cost of a unit is compared to an other unit.
I'll calculate it for 1 soldier again, using MV instead of GC. (MV = market value, GC = Gold chest)
To calculate MV see this page.

When including them for 1 soldier, like you did you would have for PK:

Know that 1 gold chest = 2.5 MV

(calculation: 1 coal ore = 2 MV
1 gold ore = 2 MV
So: ((2 + 2) + 1)/2 = 2.5 MV )


1 knight = 1 Recruit (2.5 MV) + 1 sword (20 MV) + 1 shield (20 MV) + 1 iron armor (20 mv) +1 horse (12.5 MV) + 3 blacksmtihs (7.5 MV) + 1 weapon smithy (2 MV for stone + 4 MV for timber) + 2 Armor smithy(12 MV) + 2 iron smelter (5 MV) + 2 Iron smithy ( 12 MV) + 1 farm (6 MV) + 1 farmer (2.5 MV) + 1 stable (6 MV) + 1 animal breeder (2.5 MV) + 2 iron mines (8.66 MV) + 4 coal mines (17.33 MV) + 6 miners (15 MV)

= 175 MV.

1 pikemen = 1 Recruit (2.5 MV) + 1 pike (20 MV) + 1 iron armor (20 mv) + 2 blacksmtihs (5 MV) + 1 weapon smithy (6 MV) + 1 Armor smithy (6 MV) + 2 iron smelter (5 MV) + 2 Iron smithy ( 12 MV) + 2 iron mines (8.66 MV) + 4 coal mines (17.33 MV) + 6 miners (15 MV)

= 117.5 MV.
So AA for 1 knight, compared to 1 pikeman = 175 MV / 117.5 MV = 1.489, so almost your 1.44, but that's because I didn't calculate serfs.

When calculating PK for more soldiers: PK = (x(75) + 100) / (x(42.5) + 75), with x = amount of soldiers.

So for 2 soldiers it gives us: PK = (2(75) + 100) / (2(42.5) + 75) = 1.562.

In general for AA this means: (X(Cost per soldier A) + (Cost of the buildings for soldier A))/ (X(Cost per soldier B) + (Cost of the buildings for soldier B))

For PK it means that the longer the game lasts, the more knights you need to have an equal amount of pikemen, compared to their cost. (I'm not talking about strentch now)
So the first knight you build is as expensive as 1.44 pikemen, while the 1 000 000 000th knight you build is as expensive as 1,764 pikemen.


=> How long a game has last defines how much cheaper pikemen have become compared to knights.

That's interesting isn't it?

It gets realy interesting when you start to compare leather units with iron units...

But I'll do that later.

[Bo_]

Indeed it does make a change whether your unit attack or defend (this means they'll do the first attacking strike). But for the Paper-Rock-Scissors this should not be crucial. And as Krom shows, it indeed is not in the old system.

Yes it does make a change, but since the system says that pike eat knight, knight eat sword and sword eat pike, do you see a reason why knights would attack pike, or pike swordfighters?

The other point is the cost. But the cost are to be seen in relation to their vulnerability towards arrows and bolts. To understand this, you have to think like Bo does and think about the number or long-ranged units you usually face. He says that long-range units usually do 50% of the damage, which is not correct. I guess he meant that 50% of the attacks are done by long-ranged units. But then you have to consider that archers have an attack point of 60, which already is higher than the highest value (that of knight+swordman, which is 55) have. Crossbowmen even have 120. So if you assume that you're facing a troop with mixed archers and crossbowmen, their average attack already does 164% of the damage of the other troops. If you only face crossbowmen, you'll suffer 218% of damage.

Well if 50% damage is correct or not doesn't matter, it depends on how much range that person has so you can't calculate it exactly.
The point is that the more damage is dealed by range, the less important the strentch of melee becomes.
Let's call damage dealed by melee RD (Real melee damage)
You could say that RD = (strentch of melee * Number of melee) / (Number of Range * Strentch of range).
I think if you combine this with your numbers we could have exact numbers.

The long-ranged units are the dominating and battle-decising units in the game and will always be. So the costs have to be seen in relation to that and not to the other units. And what do we find then? We find that the lance carriers/pikemen have nothing to avoid being hit by an arrow other than the usual chance to miss.
The swordmen is more expensive, true, but he has the storm attack to rush towards the archers and kill them. This makes it worth one additional equipment.
And the knight, on top of each other, has additional lifepoint + a permanent movement advantage, which makes it more maneuverable during the whole game. So the chance to get hit by an arrow/bolt is permanently lowered. This, of course, must be more cost-intensive.
The pikemen costs 3 resources, the swordmen 4 and the knight 5 - if you only count the resources inside the barracks. And this is the only number that we really can rely on.

The other number heavily depends on your way of designing your economy system. And thus I once again have to doubt the numbers that Bo provided.

Well the reason we started to compare the costs between 2 melee was because people claimed knights to be op and pikemen/lances useless, you know that.
If you realy think we should compare with their costs, the AA between a pikeman and a xbow is, and will always be 1 since they need the exact same amount of resourcers and buildings.
For other units it's the same as when you compare them to pikemen.

Then we're also talking about soldiers who're actualy in battle, cause let's be honest, 90% of the damage by archers is dealt once melee has started fighting with eachother.
So I don't think making swordfighters 40% more expensive is worth the 5% less arrows they take by sometimes performing a storm attack, that even causes your swordfighters to take more damage than they win because they get easily in 1 vs 3 melee battle after being spread by that storm attack.
Don't forget players usualy have melee beside their range to protect them from incomming attacks.
Then about knights, I agree they can manouvre, so you won't use them in the core battle, but more as range-hunters. But that's tactic, we aren't talking about that.

Then about saying resources: So you're saying that 1 gold chest is worth as much as 1 sword and 1 horse? If that's you're argument to claim we shouldn't rely on my numbers, I'm sorry but I realy don't agree with that.

[Siegfried]

I did try to not make any implications, but this is not entirely possible. So I took the chest as a reference because of the simple reason that this resource is the limiting and thus most precious resource in the game.

I don't really like to take the MV because it's calculated in with a different aspect which I will explain soon. There are so many arbitrary numbers in there, for example why a basis of 2 for non-renewable compared to renewable? Why the +1 for a process step? These numbers are optimized for trading, not for an exact analysis of the game.
But we just have to agree on a collective basis, so why not try the MV once? I like your calculations, let's go on with it

I see one point in your calculations that I can't accept. And this is the fact, that you take 20MV for an iron military unit. This price clearly was set for trading purpose only. It's way too high because of the simple reason that you cannot trade all your iron resources. In this price, there already is included a share of the smithies, the citizens etc. etc.
So I'd agree with your calculation, but we have to decide whether we completely rely on the trading costs, but then we have to neglect the building costs. Or we have to rely on the building costs.

Let's do the latter. So let's calculate one iron military unit. For that, you need one coal (2MV) and one iron. For the iron, you need one coal (2MV) and one iron ore (2MV). So Iron has 5MV. Thus one military resource has to have 8MV.
The horse will be calculated analogous to the pig, which means 4 processing steps and 4 corn. This means costs of 8MV for the horse, too.

So let's do your calculation for K1:

1 knight = {1 Recruit (2.5 MV) + 1 sword (8 MV) + 1 shield (8 MV) + 1 iron armor (8 mv) +1 horse (8 MV) }+ [3 blacksmtihs (7.5 MV) + 1 weapon smithy (2 MV for stone + 4 MV for timber) + 2 Armor smithy(12 MV) + 2 iron smelter (5 MV) + 2 Iron smithy ( 12 MV) + 1 farm (6 MV) + 1 farmer (2.5 MV) + 1 stable (6 MV) + 1 animal breeder (2.5 MV) + 2 iron mines (8.66 MV) + 4 coal mines (17.33 MV) + 6 miners (15 MV)]

The costs in {} are the cost for a single soldier. The costs in [] are the costs for the building etc., this costs will be shared by all soldiers if we calculate K=
The number inside [] is 100,5 MV
The number inside {} is 34,5

So K1 = 135

Let's do this for P1:

1 pikemen = {1 Recruit (2.5 MV) + 1 pike (8 MV) + 1 iron armor (8 mv)} + [2 blacksmtihs (5 MV) + 1 weapon smithy (6 MV) + 1 Armor smithy (6 MV) + 2 iron smelter (5 MV) + 2 Iron smithy ( 12 MV) + 2 iron mines (8.66 MV) + 4 coal mines (17.33 MV) + 6 miners (15 MV)]
The number inside [] is 75
The number inside {} is 18,5

So P1 = 93,5

So PK1 = 135 / 93,5 = 1,44
which - solely by chance! - is the exact same number that I get when I take chests as the basis for all cost.

For PK= the costs for houses can be neglected, because the number inside {} is multiplied with infinity. We get then
PK= equals 34,5 / 18,5 = 1,86

OK so far. We've already mentioned the bonus speed for cavalry. Let's keep that at the back of our mind.

There are two additional features that have not been approached so far.
1. the overall fire power of units. So far, we mostly concentrated on the counter only, but this is only half of the story in a regular game. Knights don't only attack sword fighters or pikemen (they are to be avoided, obviously), but also other troops. For example scouts, axe fighters, militia, archers or crossbowmen. Or even civilians (and houses).
And for attacking the non-specialized units, you can rely on the attacking power.
The attacking power for a knight is 55
The attacking power for a pikeman is 35
Comparing only these two values we find the ratio of 1.57 (which is close to PK3 btw.)

If you'd want a fair trade, you'd have to normalize the PK= to the firepower, let's call it the normalized firepower nPK. Therefore you'll find nPK= = 1,86 / 1,57 = 1,18

This number is the 'power per cost'. And this means, that a knight is only 18% stronger than a pikeman compared to the cost (in the case of infinite built knights). If you don't build infinite knights, this number is even lower.

This firepower is real. If a knight wants to kill an archer, he has to hit him 3,6 times on average. If a pikemen wants to kill an archer, he has to strike 5,7 times. You find this nPK= in this difference. This value is real, whereas the PK= is only a theoretical construction.

2. the likelihood to benefit from lifepoint recovery.
A knight has 4 lifepoints. He can profit from recovery if he lost one already. At this stage, he has 3 lifepoints left.
A lifepoint is recovered each 41 frames iirc. I'm not sure if this value has changed since. And I'm not completely aware of the length of a single attack, iirc it was like 8 frames or so.
This means, if a knight survives 5 attacks (with his 3 lifepoints left), he'll get one lifepoint back.
The knight has an armor value of 3, most of the times he is attacked from the front, thus the multiplier is 1. Let's assume the stronges standard-unit attacking the knight, that's the crossbow with an attack unit of 120 (all other are lower!!). The change that a hit takes away one lifepoint therefore is 120/3 = 40%.
The change that the knight dies is therefore p(live) = (5 over 3) * 0,6^3 * 0,4^2 + (5 over 4) * 0,6^4 * 0,4 + (5 over 5) * 0,4^5 = 68% {die note (5 over 3) is not the fractionbut the binomial coefficient}
So the knight survives the hardest attack with a chance of 68%
If the attacker is weaker, the chance is even higher.

Let's do the math for the pikeman. He has only 2 lifepoints left andneeds to survive 5 strikes. The chance to survive is
p(live) = (5 over 4) * 0,6^4 * 0,4 + (5 over 5) * 0,6^5 = 34%
Again, if the attacker is weaker, more pikemen will survive and gain one additional lifepoint.

For the sake of comparison, let's assume the attacker is just a pikemen/scout/axe fighter, which all have an attack value of 35, thus the hitting chance is 11,7%.

The likeliness to survive for a knight and pikemen are:
p(live, knight) = 99%
p(live, pikemen) = 89%
So still you'll lose one pikemen out of a group of ten but all knights survive.

So, let's conclude:
The power per cost ratio is 18% more expensive for a knight. But for this 18% you'll get:
- twice the speed, which allows you to run away, flank the enemy troops, be less likely to be hit by arrows
- the likeliness to benefit from lifepoint regeneration is much higher, it never drops below 68%! So the knight can already be seen equivalent to having > 4,68 life points whereas the other iron troops have an equivalent of > 4,34 lifepoints, which is 1,3 life points in difference, not only 1! Of course this depends on the attacking group, but never is less than 1,1 life points. If attacked from the side, the benefit for the knight is even above the 1,3 life points.
-> thus more knights survive a real battle; and as we learnt (ask Lewin) already one troop will make a huge difference because he will start to attack the enemy from the diagonal or even the side, thus benefitting by a factor of 2 up to 5.

Or summed up:
The real lifepoints for knights is approximately 10% higher than the real lifepoints for the other iron troops, thus reducing the 18% cost overrun to small 8% (rounded). In this calculation, the vulnerability agains pikemen is already included!! And for the 8% you'll get a unit that has double the speed compared to the pikemen and the rest of all troops.
Therefore the knight is already perfectly balanced!

Just for the sake of comparison: if you take the +1lifepoint for the knight and not the pikemen, first of all the power increases (by 25%) and second of all, it even more benefits from lifepoint regeneration, making it almost impossible to get killed by a single attacking unit.
Therefore the power to cost-ratio goes well below 100%, so lp+1 makes the knight the cheaper unit compared to pikemen. Plus it has the increased speed! This means you'll get a benefit for even lower cost - that's far away from being balanced.

All these later conclusions have already been made with infinite troops calculations. If you go to a finite number of troops, the ratios are even worse for pikemen, making them already to a weaker unit than discussed here.

[The Dark Lord]

Knight imba

[sado1]

I know it's incredibly mean to laugh at someone who tries to make something good for the balance of this game, and writes a post that takes 3,5 screens of my laptop.

However, I can't resist to praise this little bit of trolling Dark made above.