Re: Cavalry vs. Sword vs. Halebard test in r3897
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
The +1 for a process step should be logic, why? You need time to transport and transform the resources. You need space for those buildings and need to feed those workers.
A perfect example for this is Strait of Sharks. A map where you have in your storehouse 9000 corn, 16000 coal, 9000 iron (not even iron ore), 9000 treetrunks and 15000 stone.
So since you claim the +1 to be useless for an accurate value, why can't players have 3000 soldiers after pt? I'll tell you why. The smithy's also need TIME to transform those resources into weapons. You can't ignore that in a value.. Why do you think players are making lances now, instead of axefighters? That 1 extra cost for the shield is realy not the cause, believe me. It's because you need more armories to make those shields, wich requires SPACE and costs for that building, you don't have infinite space. Why do you think it's so hard to have horses? Not necesairly for that 4 corn, but for the very long time it takes for your animal breeder to transform 4 corn into 1 horse.
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.
Yes I made a mistake on that, it's 8MV, thanks for correcting.
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.
Also I noticed that since 1 chest = 2.5 MV, and the buyfactor is also 2.5, you can check MV by just buying anything at the market with gold chests. But notice then that it may not be 100% accurate, like with stone as example.
I used MV because it's less confusing.
But then, the only thing you're doing rewriting this:
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.
If you hit an archer from behind you usualy just 1 hit, if it's a knight, lance or pikeman. Also when a knight snipes into a town, isn't that the use of towers? 1 knight needs to kill a lot of civilians before he wins something out of the whole sniping opperation, once it's in a base it easily gets killed. Let me tell you, I love building knights, they control the game because of their speed IF you can use them right and IF you're the only one having knights. If both players have knights, or scouts, your whole sniping operation just won't be possible, hunting range will be way more difficult, don't forget the lances. So yes knights are good, expensive but very hard to control.
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.
You can have as many theories as you want, as long as knights are very rare in the game I don't think it makes sence of trying to prove that.
It takes too long for them too build. Also, would you like your slowly trained knight to be killed by just 1 crossbow? That would make no sence.
So what I mean, yes mathematics are great, but you have to stop at some point. This goes too far, because now on every calculation you make you have to add so many other things that it's realy not worth it. In Kam the amount of units is way more important than how strong they are, wich doesn't mean that strentch isn't important. So yes, you corrected my calculations about the costs, and it's interesting to read but it realy won't help you in the game, believe me on that. I would love to discus with you about those maths in Kam, but not if it is as an argument to prove anything, because we can't, not at this point.
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.
Twice the speed yes, but it's also the more expensive horse. It's like you're ignoring the time it takes to train a horse, to have knights as your main unit you would need 3 stables, 5 farms. And those buildings take a realy huge amount of space. You should also include space in you costs calculations.
The likeliness to benefit for a life regeneration, let's just translate it by a knight will usualy not be taken down when passing by range units. Since it's impossible to spam knights you won't use them in the core battle, and also for the reason that knights or scouts in battle are too easy to catch wtih lances-pikemen.
Then the diagonal attack, well like I've said over a hundred times, you can't spam knights like other units. When having lances, pikemen or even axefighters, you will start enemy from the diagonal side most likely like that then by using knights.
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 problem is you can't calculate these things, if you could well go on, but you'll see, knights are not that balanced compared to their price. Maybe yes in theory, but it's not the AI who's playing, it's still about human players.
So my last point: If it's balanced like you claim it to be, than why is it just lance + xbow? Think about that.