Map Database  •  FAQ  •  RSS  •  Register  •  Login

Swordfigters vs. Pikemen

<<

Esthlos

User avatar

Knight

Posts: 600

Joined: 23 Jun 2013, 16:02

KaM Skill Level: Beginner

Post 01 May 2015, 18:50

Re: Swordfigters vs. Pikemen

The Dark Lord wrote:I think that with such a large number of bowmen, the impact of the shield bonus is smaller. I wonder what the results would be with only 45-50 bowmen on each side.

It seems you are actually right, at least as far as test 1 goes... shouldn't the opposite happen? :O :?
(Now that I think of it, it would be a good idea to run consecutive tests with one setup, in order to determine the variance still given by random factors)
(EDIT: tested the results of series of 500 1v1 battles between Militia; it seems that the win percentages from these tests have a standard deviation of 2,29%)

With 45 Bowmen, 15 columns formation, troops split into single units:

Test 1:
Pikemen won 270 out of 500 battles (54%).
Sword Fighters won 230 out of 500 battles (46%).

Average duration: 74 seconds
Shortest fight: 44 seconds
Longest fight: 184 seconds

Test 2:
Pikemen won 195 out of 500 battles (39%).
Sword Fighters won 305 out of 500 battles (61%).

Average duration: 83 seconds
Shortest fight: 52 seconds
Longest fight: 131 seconds

Ben wrote:Haha,this looks pretty funny. I imagine lots of soldiers running around like ants ^^
Do you have the "simulation" on a scripted map? If so, I'd like to watch it ;)


map
You do not have the required permissions to view the files attached to this post.
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"
<<

Esthlos

User avatar

Knight

Posts: 600

Joined: 23 Jun 2013, 16:02

KaM Skill Level: Beginner

Post 06 May 2015, 10:50

Re: Swordfigters vs. Pikemen

TL;DR The Shield bonus seems to be not enough for Iron troops.

Long version:
By these results, it seems that the more Bowmen are involved, the better Pikemen perform against Sword Fighters... but, theorically, the opposite should happen, since Pikemen have no shield and Bowmen have a high rate of fire (which makes them better versus troops with lower defence).

Now, some math: by the law of large numbers, we can assume that Bowmen's hit chance against the various troops equals the average number of wounds inflicted by 100 arrows.

Dividing this by the number of Life Points every unit has, we have that, on average, 100 arrows kill:
    10,00 Lance Carriers
    6,67 Axe Fighters
    5,00 Scouts

    6,67 Pikemen
    5,00 Sword Fighters
    3,75 Knights

Now, the percentage of killed soldiers ties inversely with their total number (the higher the total number of soldiers, the lower is the percentage of deaths represented by the above numbers), which in turn ties inversely with their economic worth (the costier they are, the less you can make of them).

(Since we are comparing units from the same production chains, then any imprecision in the economic values from viewtopic.php?f=26&t=2624#p44414 applies to both sides and mostly factors out.)

So, let's multiply the average kills by each unit's economic worth:
    130 Lance Carriers
    113 Axe Fighters
    135 Scouts

    147 Pikemen
    155 Sword Fighters
    158 Knights

Now, what are these numbers? Well, they represent the relative impact of Bowmen's presence against each foe: the higher the number, the more relatively effective are Bowmen against that unit; as you can see, Bowmen are still more effective against Sword Fighters than against Pikemen, even with the Shield bonus, due to the sheer cost difference between the two warrior types.

Since the situation is reversed for Lance Carriers and Axe Fighters, I'd suggest making the shield bonus a percentage increase in defence rather than a flat bonus: this would leave the situation unchanged for Leather troops but reverse it for Iron troops.

As a side note, it should also make Crossbowmen way better than Bowmen against shielded foes, without changing their powers in any other case.

Lastly, interesting the results for Cavalry units; sadly, though, Horses are from a production chain different enough to make this comparison very uncertain as far as Cavalry units go.

Of course, this can be done for Crossbowmen too:
    260 Lance Carriers
    302 Axe Fighters
    360 Scouts

    293 Pikemen
    382 Sword Fighters
    388 Knights
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"
<<

The Dark Lord

User avatar

King Karolus Servant

Posts: 2094

Joined: 29 Aug 2007, 22:00

Location: In his dark thunderstormy castle

KaM Skill Level: Veteran

Post 06 May 2015, 15:26

Re: Swordfigters vs. Pikemen

Esthlos wrote:By these results, it seems that the more Bowmen are involved, the better Pikemen perform against Sword Fighters... but, theorically, the opposite should happen, since Pikemen have no shield and Bowmen have a high rate of fire (which makes them better versus troops with lower defence).

I disagree; your results were according to my predictions as you can see a few posts back. Why you ask? Because so many bowmen make the shield patch insignificant. Imagine 10 bowmen and 10 sword fighters against some pikes and 10 bowmen. It is unlikely that those 10 bowmen will inflict much damage on those sword fighters. Now imagine 1000 bowmen and 10 sword fighters against some pikes and 1000 bowmen. It is likely that none of those melee troops ever get close to any bowman because they get overwhelmed by arrows.
Now this is an extreme(ly bad) example, but I think it does explain my reasoning. With many bowmen, the chance they inflict damage on sword fighters increases and the shield patch becomes less significant.
<<

Esthlos

User avatar

Knight

Posts: 600

Joined: 23 Jun 2013, 16:02

KaM Skill Level: Beginner

Post 06 May 2015, 18:01

Re: Swordfigters vs. Pikemen

The Dark Lord wrote:
Esthlos wrote:By these results, it seems that the more Bowmen are involved, the better Pikemen perform against Sword Fighters... but, theorically, the opposite should happen, since Pikemen have no shield and Bowmen have a high rate of fire (which makes them better versus troops with lower defence).

I disagree; your results were according to my predictions as you can see a few posts back. Why you ask? Because so many bowmen make the shield patch insignificant. Imagine 10 bowmen and 10 sword fighters against some pikes and 10 bowmen. It is unlikely that those 10 bowmen will inflict much damage on those sword fighters. Now imagine 1000 bowmen and 10 sword fighters against some pikes and 1000 bowmen. It is likely that none of those melee troops ever get close to any bowman because they get overwhelmed by arrows.
Now this is an extreme(ly bad) example, but I think it does explain my reasoning. With many bowmen, the chance they inflict damage on sword fighters increases and the shield patch becomes less significant.

What you wrote makes sense, of course: my post though was to bring up that the Shield bonus may be not enough when compared to the larger HP pool of the cheaper Pikemen.

I brought this up because I made other tests: in particular, I found it significative that Sword Fighters actually seem to tend to utterly destroy Pikemen when no ranged support is involved at all (if I recall correctly, Sword Fighters won 85% (!) circa of the fights with the setup from the last "test 1" - except that there were no Bowmen), better than they do when few Bowmen take part in the fight.

I wondered if it could be proven in an objective, mathematical way and, if I'm not wrong, it seems it actually can be, thanks to the fact that ranged units get no direction modifier (which instead makes things way more complex for melee units).
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"
<<

The Dark Lord

User avatar

King Karolus Servant

Posts: 2094

Joined: 29 Aug 2007, 22:00

Location: In his dark thunderstormy castle

KaM Skill Level: Veteran

Post 06 May 2015, 18:32

Re: Swordfigters vs. Pikemen

Hmm, I looked into it again, but I find some of your calculations/assumptions very arbitrary. But it is interesting.
<<

Esthlos

User avatar

Knight

Posts: 600

Joined: 23 Jun 2013, 16:02

KaM Skill Level: Beginner

Post 06 May 2015, 20:32

Re: Swordfigters vs. Pikemen

The Dark Lord wrote:but I find some of your calculations/assumptions very arbitrary.

Which? (?)
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"
<<

Esthlos

User avatar

Knight

Posts: 600

Joined: 23 Jun 2013, 16:02

KaM Skill Level: Beginner

Post 08 May 2015, 16:32

Re: Swordfigters vs. Pikemen

The Dark Lord wrote:Hmm, I looked into it again, but I find some of your calculations/assumptions very arbitrary. But it is interesting.

By the way, this can also be done with 0% arbitrarity.

Here we go:
Since this thread is "Swordfighters vs. Pikemen", these two units will be the only ones taken in consideration.

By the law of large numbers, we can assert that the average number of wounds inflicted by 100 arrows equals Bowmen's hit chance.

Thus, the average number of wounds inflicted by 100 arrows is
15 against Sword Fighters
20 against Pikemen

Since both unit types have 3 Life Points, they both need 3 wounds to die.

Thus, we can say that the average number of kills per 100 arrows is
5 against Sword Fighters
6,67 against Pikemen

Please note that this does not take in account that arrows may not hit always the same units, which spreads out the damage and lessens the losses; assuming the damage doesn't spread out biases this comparison in Sword Fighter's favor; this means that, if Pikemen end up resulting better, the result will be certain, while if they don't then the result will have a slight chance of being such due to this bias.

The percentage of soldiers lost purely due to Bowmen's intervention equals "average number of kills" times "X" (times 100, since it's a percentage and not a ratio) divided by "number of warriors of the types in the comparison", where X is a coefficient accounting for those factors that apply to both sides, such as the duration of the fight or the actual number of Bowmen and thrown arrows.

The number of warriors of the types in the comparison equals "Y" divided by "units' economic requirements", where Y is the economical output of their hometowns, which must be assumed equal for both sides for this comparison to be as unbiased as possible.

Now, the units' economic requirements are:
1 Recruit, 2 Iron Defences, 1 Iron Weapon for Sword Fighters
1 Recruit, 1 Iron Defence, 1 Iron Weapon for Pikemen

Iron Weapons and Iron Defences come from the same production chains up to the very last step, which means that their relative worth is easily calculated by taking in account the different production times.
The difference in the last step's buildings' size will be ignored in order to make the comparison simpler and because it is very rare that the available space is so limited that this becomes an impactful factor; anyway, when it does come into play, it favors Pikemen, which means that ignoring it yet again slightly biases this comparison in Sword Fighter's favor.

Thus, 1 Iron Protection is worth 1,24 Iron Weapons.

Recruits are instead from a completely different production chain; what we know for sure is that they are worth less than Iron Weapons, since Schools work very fast and Gold is usually more available than Iron and can be produced much faster and in higher quantities.
Thus, we'll work with the bounds of certainty of their value: 0 ≤ Recruit ≤ 1 Iron Weapon

With these values, we can say that
1 Sword Fighter's worth is between 3,48 and 4,48 Iron Weapons
1 Pikeman's worth is between 2,24 and 3,24 Iron Weapons

Thus, the ratio of their economic worths is between 0,64 and 0,72 (Pikeman/Sword Fighter)

The ratio of the number of warriors of the types in the comparison thus equals the "inverse of the ratio of their worth" (this being a ratio, Y gets factored out for being both at the numerator and at the denominator).

Thus, the total number of Pikemen is between 1,38 and 1,55 times that of Sword Fighters; for simplicity the total number of Sword Fighters will be called "N".

Thus, the ratio of soldiers lost purely due to Bowmen's intervention for sure
is 5·X/N for Sword Fighters
lies between 3,22·X/N and 3,62·X/N for Pikemen

In percentages:
500·X/N % of the Sword Fighters
something between 322·X/N % and 362·X/N % of the Pikemen

500·X/N is always higher than both 322·X/N and 362·X/N , for any N ≥ 1 and X > 0 (which are their limit: N can't be less than 1 or else there are no warriors in the fight, X can't be 0 or less or else it means that no arrows have been shot during the battle).

Thus, we can say with certainty that Pikemen as a whole are more durable than Sword Fighters against Bowmen.

Which they aren't supposed to be, as far as I know.

EDIT: Fixed a few mistypings.
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"
<<

tonc5

Laborer

Posts: 14

Joined: 01 Oct 2016, 03:51

KaM Skill Level: Average

Post 21 Oct 2016, 04:15

Re: Swordfigters vs. Pikemen

Why are they even called "Pike men"? There holding halberds you fools.
<<

Ben

User avatar

Prince Lothar

Posts: 3553

Joined: 08 Jan 2009, 23:00

Location: United States of America GMT-5

KaM Skill Level: Beginner

Post 21 Oct 2016, 04:27

Re: Swordfigters vs. Pikemen

Pikemen are usually misnamed in most games it seems. Pikes are very long...like a phalanx ;)
Liberté, Égalité, KaM
<<

tonc5

Laborer

Posts: 14

Joined: 01 Oct 2016, 03:51

KaM Skill Level: Average

Post 22 Mar 2017, 01:00

Re: Iron Production

T*AnTi-V!RuZz wrote:Pikes talk cooler than swordsmen.

The admin has spoken.
Hecka true.
<<

Refan

Laborer

Posts: 10

Joined: 23 Dec 2014, 11:43

KaM Skill Level: Average

Post 17 Jun 2017, 13:31

Re: Swordfigters vs. Pikemen

Swords man is way Cooler and far BETTER then PIKEMEN ever will be. Shield ftw.
Previous

Return to General / Questions

Who is online

Users browsing this forum: No registered users and 3 guests