Knights and Merchants.net Forum

I'm sorry if it looked arrogant, I just tried to show that these points are not valid in this case because they don't help in this discussion. You see more people having problems with that change in this state, but still you claim that a fictitious majority would be in favour of these changes? Don't you think we talk to others, too?

That's "right through strength". We play and the winner was right? That still proves nothing. And why does it matter how good I play? I don't want to judge myself, so please ask the people I've played with. And please stop the black-and-white thinking. This change wouldn't make anyone having no chance, you know that perfectly as your next lines prove. It shifts the balance, and I think it shifts it too much so it gets inbalanced.

Again that black-and-white-thinking where some people should be restricted from voting and others shall be allowed. Why that?

The problem that I see with you is that you are not accessible to my points. You still reject them all and rely on your replays. I even tried to access your arguments and further develop them. But I still want to carry on the discussion, really! Let's continue in the other thread. I have tried to work with your points and find that the balance is good already.

The reason why I did not yet play with you was the first offense from your side. Plus maybe the fact, that I don't have internet access on evening during workdays

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.

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.

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= 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.

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.

So my last point: If it's balanced like you claim it to be, than why is just lance + xbow? Think about that.

So my last point: If it's balanced like you claim it to be, than why is it just lance + xbow? Think about that.

What's this Sieg? viewtopic.php?f=6&t=468
Looks that your style of testing stuff is really out of context.

Economy, construction space, production times, peacetime, luck factor in battle...
Where are these in your analysis? Think about it.

So the hand-to-hand fight becomes more important in the game, just as it was in the original TSK+TPR.

Archers are useless compared to crossbowmen. I NEVER make archers while I used to make them in the past. If you have iron at your disposal, it would just be a waste of leather and timber to make archers. I once tried pikemen + archer for a change. I got slaughtered by crossbowmen + lance carrier.

If you read the post above mine you'll have an answer to your question

No, the mathematics is not dispensable, it's how the remake works. Everything inside the game is calculated by these mathematics. The fighting as well as the delivery, the harvesting. Just everything. So you are not allowed to neglect them.

The theory I presented above was the most advanced one we've ever done. It almost covers everything (except that I forgot to mention that the knight already has a 33% advantage in life points).

But I see that you don't want to continue, so I won't either.

Finally, the key point. It annoys me that you don't see that:
It's not that the lance carriers are too strong (they are not, they are balanced compared to other hand-to-hand fighters!).
It's the crossbowmen that are too strong!

We agreed on the rough estimation that crossbowmen do 2/3 of the total damage in a real battle in a real game. It's very hard to calculate the exact number, but it's a good approach to think that most armies are 50/50 between ground troops and long-range units. And the long-range units do double the damage per attack. So we end up in 67% of all damage done by archers. If you then think that the ground troops die earlier than the long-ranged units, this number rather goes up than down, so maybe the crossbowmen even account for 75% of all damage. We don't know exactly (yet ).

So the situation is the following: the crossbowmen are the deciding factor in the game. They do the damage, not the protecting units.
So the other units are only a protection for the crossbowmen. They are not meant to do the damage, they simply server the purpose of protecting the crossbowmen as long as possible so they can do maximum damage.

And this the crux of the whole thing. The balance between ground troops is of only minor interest because it's dominated by the crossbowmen. So people try to make the cheapest unit that does survive at least some bolts. And that's the lance carrier. The milita has only 1 armor, so it's not usually used, although I've met them already.

And I never said that knights are overpowered. I said they are balanced! They become overpowered if you give them one additional life point.

I see your problem. I know that you want to improve the gameplay. Casually spoken you try to do good for the game. Otherwise I would not bother discussing with you.
But I hope you see my point and understand my approach. I never was satisfied with the current situation, but I know that this origins from the long-range fighters, not from the balance of hand-to-hand fighters.

Try to think away from only the building-maps towars the fighting maps. You see the harmony there. The hand-to-hand fighters are in perfect balance! There is no need to break them. But the long-range fighters are too strong. So I dare to submit my proposal for the third time: make the long-range units weaker! So the hand-to-hand fight becomes more important in the game, just as it was in the original TSK+TPR.

Again: If they're already balanced, why does almost nobody train them?
At least with the patch people made knights, that stil didn't mean that they dealed the heaviest damage.

in the end we want the same

Well if maths did all the work why isn't it balanced yet?

you're ignoring experience

By the way you will always keep the discussion whether certain units are used as they should be. People complain about lancers now, because they are meant to counter horses, but are used against other units as well. When you implement the patch you'll see that everyone uses axefighters (no variation again), but aren't axefighters mainly meant to counter lancers (rock, paper and scissor story). People will just use those axefighters against horses as well, even though they don't have the bonus against horses...they last longer, meanwhile your crossbows can easily kill the horses.

You'll always have one unit that will be used way more than other units. Even in situations they aren't meant to be used. Yes something needs to be changed, but the patch in its current state will create a new problem while solving the other problem.

Again: If they're already balanced, why does almost nobody train them?
At least with the patch people made knights, that stil didn't mean that they dealed the heaviest damage.

The patch did NOT increase the amount of knight in my opinion.