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Bowmen and crossbowmen balance

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Esthlos

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Post 28 Oct 2014, 16:42

Re: Bowmen and crossbowmen balance

Good points, and probably all true, but in my opinion the most interesting one is this:

Since melee units go on front, they die first. So the player with swords/bows loses most of his valuable sword fighters, while the other player loses his much-easier-to-replace axe fighters. He still has his crossbowmen, and with some new reinforcements (assuming players' economies are equal) he might now hold the advantage.


At the moment, at least for me, Crossbowmen don't feel much superior to Bowmen in this regard.

In addition, when your front line crumbles, trying to save your Crossbowmen feels just as difficult as trying to save your Bowmen, since pretty much any unit can catch or at least keep up with both and any unit can slaughter both extremely easily, especially if you're retreating (thus offering your back).

The Dark Lord wrote:However, this theory is only valid when crossbowmen slaughter bowmen; which they, as far as I know, are incapable of...

100 battles
Team 1: 45 Bowmen (855 Corn)
Team 2: 33 Crossbowmen (858 Corn)

Team 1 (Bowmen) won 37 of them.
Team 2 (Crossbowmen) won 63 of them.

This is underwhelming indeed, when compared to how other Leather units fare against equivalent armies of their Iron corrispective.

Mmmm... what about giving Crossbowmen a chance to wound for 2 Life Points instead of 1, proportionally to how close they are to their target, maybe while lowering Crossbowmen's actual Attack stat?

They'd have a reason to stay and fight instead of turning their back and trying to flee (thus actually being able to make use of their superior armor), they'd have to take risks if you want them to be better than Bowmen, and they'd actually feel stronger, more worthy of their price, without becoming all-around better than Bowmen.
(Bowmen would still be better for fighting from long range, and would be able to slaughter Crossbowmen).

What do you think about this?
Last edited by Esthlos on 29 Oct 2014, 11:11, edited 1 time in total.
Just when you think you know something, you have to look at it in another way, even though it may seem silly or wrong. You must try! - John Keating, "Dead Poets Society"
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Ben

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Post 29 Oct 2014, 03:29

Re: Bowmen and crossbowmen balance

Wait, I still don't see what your beef is with xbows. They are fine, really!

(give me a TL;DR version, please lol)
#thunderposting #greentornado
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Esthlos

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Post 29 Oct 2014, 13:12

Re: Bowmen and crossbowmen balance

Ben wrote:Wait, I still don't see what your beef is with xbows. They are fine, really!

(give me a TL;DR version, please lol)

But a long message is more complete and clear... :(
I like longer posts. :(

Ok, short one: I think that Crossbowmen don't seem to be worth their cost, as one can just get Bowmen instead, use the Iron for the front lines, and pretty much always be better off this way.

P.S. I've been improving the test map, now it is much better and it's possible to set up the fights without editing its script. :mrgreen:
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Just when you think you know something, you have to look at it in another way, even though it may seem silly or wrong. You must try! - John Keating, "Dead Poets Society"
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Esthlos

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Post 30 Oct 2014, 17:35

Re: Bowmen and crossbowmen balance

Wanted to quantify the "reinforcements" needed for making it worthwhile to have your iron used on the ranged units.

Thus, I've been trying different Axe Fighters numbers until the win chance of both Axes+Crossbows and Swords+Bows were approximately equal.

I've tested this with the "reinforcements" already present, so the actual number of needed extra Axe Fighters would be higher.

Premise:
The "Corn equivalent" of 45 Sword Fighters is 64 Crossbowmen;
The "Corn equivalent" of 45 Bowmen is 37 Axe Fighters.

Best test result:
500 battles
Team 1: 45 Sword Fighters + 45 Bowmen (2520 Corn)
Team 2: 48 Axe Fighters + 64 Crossbowmen (2768 Corn)

Team 1 (Sword Fighters+Bowmen) won 256 of them.
Team 2 (Axe FightersCrossbowmen) won 244 of them.

On average, battles lasted 78 seconds.
(Shortest one 53 seconds, longest one 137 seconds)

There were 11 extra Axe Fighters, which is 29,73% of the ones for the equivalent would-be Team 2.
(48/33=1,2973=129,73%)

As already stated the actual number of the extra Fighters needed if they were reinforcements would be higher, but I don't know how to quantify this; still this data can be used, as it is possible to say that the minimum reinforcement force needed for the Crossbows+Axes to be as effective as Bows+Swords is +30% circa of the Axe Fighters in less than 78 seconds (or else it'll be too late).
Just when you think you know something, you have to look at it in another way, even though it may seem silly or wrong. You must try! - John Keating, "Dead Poets Society"
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Bo_

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Post 12 Nov 2014, 15:16

Re: Bowmen and crossbowmen balance

I didn't read what the discussion is about so sorry for not having any constructive argument.

I've just decided to play some more KAM.
When I left people only made axe, bow and if you wanted to do something crazy you made some knights.
Now people go for bow, lance, knight and sword.

I'd love to be able to make axe and xbow again without Sado making fun of me. Would that be possible?
Thank you guys for helping me out.
Kick fast, think Bo.
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pawel95

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Post 12 Nov 2014, 15:46

Re: Bowmen and crossbowmen balance

Bo_ wrote:I'd love to be able to make axe and xbow again without Sado making fun of me. Would that be possible?
Thank you guys for helping me out.


I guess that´s exactly the reason why the topic was made? Anyway, keep the cool posts up.
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Ben

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Post 12 Nov 2014, 17:25

Re: Bowmen and crossbowmen balance

You can make axe fighters and crossbowmen if you want, but you'll be smashed hard by anyone with massed swords in almost all situations. It's important to work with a teammate when you train lots of crossbowmen...or alternatively make some swords to add buff to your axe fighters.
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Bo_

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Post 12 Nov 2014, 20:08

Re: Bowmen and crossbowmen balance

pawel95 wrote:
I guess that´s exactly the reason why the topic was made? Anyway, keep the cool posts up.
i meant if it was viable, i wasnt assuming it Wasnt but thanks anyway
Kick fast, think Bo.
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pawel95

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Post 12 Nov 2014, 21:43

Re: Bowmen and crossbowmen balance

Thanks yes. Thank you very much :lol:
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Esthlos

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Post 07 Apr 2015, 10:58

Re: Bowmen and crossbowmen balance

Using the data from http://www.knightsandmerchants.net/forum/viewtopic.php?f=3&t=2492&start=15&sid=d252f759012ee9cd65d0cf96fd129afe#p44055 , it is possible to estimate the relative strength of Bowmen and Crossbowmen.

From the numbers in the source code (and copied in the linked thread), it follows that on average Bowmen have a Rate Of Fire (ROF) which is double that of the Crossbowmen (1,66667 vs 0,83333).
This means that in the time needed for Crossbowmen to start firing their first bolt, Bowmen are already beginning to fire their second arrow.

Using as Time Unit the time needed for Crossbowmen to complete 1 bolt firing, we can calculate that:
in 1 TU, Bowmen have a chance of wounding a Sword Fighter for
-1 HP: 25,50%
-2 HP: 2,25%

in 1 TU, Crossbowmen have a chance of wounding a Sword Fighter for
-1 HP: 36,92%
-2 HP: 0%

(Also, as a side note, in 1 TU the damage done to buildings is
by Bowmen: 2 HP
by Crossbowmen: 1 HP)

Now, the question is: is the cost difference between Crossbowmen and Bowmen enough to justify the Damage Per Second difference? Or is it too low? Or too high?
Any idea on how to calculate this?

I propose to use the Market's values, since it has been balanced around economic values and should be accurate enough.
Also, I can't think of a better solution to compare two separate production chains...

Anyway, the value in Corn if recruited through the Market only is:
19 Corn for Bowmen (4+8+7)
26 Corn for Crossbowmen (4+11+11)

Thus, we have:
Crossbowmen cost 36,84% more than Bowmen.
Crossbowmen are 33,06% more likely to wound a Sword Fighter for at least 1 HP in 1 TU.

Conclusion: math-wise, they look pretty well balanced against Sword Fighters (thanks to the Shield bonus).

Against Pikemen the balance is strongly shifted in Bowmen's favour (Crossbowmen are only 11,11% more likely to wound them in 1 TU), but in my opinion this shouldn't matter since Pikemen are also more effective melee warriors (both against Knights, thanks to their Attack bonus, and against Sword Fighters, through sheer numbers; both situations are easily verified using the Map Editor) and cheaper to recruit.

I doubt that the fact that Leather comes from the Food chain should be considered, since recruitinh Crossbowmen doesn't forbid the use of Axe Fighters (or other Leather troops) too, just as recruiting Bowmen doesn't stop you from mining and using Iron too.


TL;DR
Ratio (Crossbowmen's cost in Corn)/(Bowmen's cost in Corn)=1,3684

Ratio (Crossbowmen's chance of wounding <Target>)/(Bowmen's chance of wounding <Target>) in 1 TU=
Civilians: 1,4286
Militia: 1,4286
Axe Fighters: 1,4814
Sword Fighters: 1,3306
Bowmen: 1,1765
Crossbowmen: 1,1111
Lance Carriers: 1,1765
Pikemen: 1,1111
Scouts: 1,4814
Knights: 1,3306
Barbarians: 1,1765
Rebels: 1,4286
Rogues: 1,4286
Warriors: 1,1765
Vagabonds: 1,4286
Just when you think you know something, you have to look at it in another way, even though it may seem silly or wrong. You must try! - John Keating, "Dead Poets Society"
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Jeronimo

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Post 11 Dec 2016, 15:19

Re: Bowmen and crossbowmen balance

Damage per Second (DPS) calculations in version r6720

DPS bow against swordfighter/knight = 60/4/2.4 = 6.25
DPS xbow against swordfighter/knight = 120/3.25/4.0 = 9.23

DPS bow against axemen/scout = 60/3/2.4 = 8.33
DPS xbow against axemen/scout = 120/2.25/4.0 = 13.33
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