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Thread: Analysis: Mercenaries vs Demesne Levies

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    Colonel iron0037's Avatar
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    Analysis: Mercenaries vs Demesne Levies

    When is it to my advantage to hire mercenaries instead of relying on my own troops? It’s a simple enough question. Let’s see if we can we can figure it out. This is a lengthy, mathematical investigation. If math isn’t your thing, then either skip to the conclusions or stop right here.

    Problem Description
    Let’s constrain the problem with some assumptions:
    • I want to hire the Swiss Band or raise an equivalently potent army from my demesne.
    • I am sitting on a wad of cash such that money is no object. My only concern is maximizing the effectiveness of the gold I spend.
    • Since I am in no rush to field this army, build times to improve my demesne are not a concern.
    • I don’t care about my vassals’ levies. They are notoriously fickle about sending troops and get upset when I field them for too long.
    • My demesne only consists of castles that have no upgrades.
    • I’m not going to leverage any culture-specific buildings.
    Ok, if I hire the Swiss Band, I get 300 archers, 600 heavy infantry, and 600 pikemen. I won’t be able to exactly reproduce this contingent with my holdings since my demesne produces different kinds of troops in different ratios. So how do I compare apples to oranges?

    Quantifying Combat Strength
    Combat mechanics are rather complicated, but I’m going to make a rough approximation of a soldier’s value depending on his class. Let’s sum the total Attack and Defense values of each class of soldier in all three phases of combat. I’m going to call this quantity “Power.” Yes, this is not a perfect way to score combat value, but it’s far better than nothing. Examining defines.lua, we extract the following data:

    Unit - Power/Morale/Maintenance
    Light Infantry – 17/3/1
    Heavy Infantry – 19.5/5/2
    Archers – 19/1/1/
    Pikemen – 22.4/6/2
    Light Cavalry – 31/4/2
    Heavy Cavalry – 40/10/4

    Evaluating the Swiss Band under these metrics yields a Power of 30.8 ((600*19.5+300*19+22.4*600)/1000 = 30.84) and a Morale value of 6.9 ((600*5+300*1+600*6)/1000 = 6.9). So what improvements would I need to make to castle(s) to get the same Power and Morale? Let’s examine.

    The 1 Castle Demesne
    If I am a lowly count with but one castle, I have a lot of improving to do. If I want to get my levies to a Power of 30.8 and Morale of 6.9, then I need to build ALL of these buildings:
    Militia Barracks 1, 2, and 3
    Barracks 1, 2, 3, 4, 5, 6
    Stable 1, 2, and 3
    Training Grounds 1 and 2
    Castle Walls 1 and 2
    Keep 1 and 2
    This nets me an army of 228 light infantry, 528 heavy infantry, 264 archers, 156 pikemen, 204 light cavalry, and a paltry 6 knights. With morale boosts from the Training Grounds, this gives me a force of 29.25 Power and 67.5 Morale…it’s close but not perfect. There are other building combinations that yield similarly potent forces, but this is one of the more cost effective ones that yields a close Power:Morale ratio.

    Hurray, I’ve built all those buildings and can muster my own force to rival the Swiss Band. What did it cost me to do this? Would you believe 3510 gold?! Ok, ok, but the maintenance on my demesne is lower, right? Yes, it is only 1.91 gold per month instead of 6.75. So how long would I have to field both armies before it was economically advantageous to gone the demesne route? It turns out to be roughly 64 years.
    Mercenaries: 75 + 6.75*12*64 = 5259 gold
    Demesne: 3510 + 1.91*12*64 = 4977 gold
    This assumes that your levy maintenance remains fixed…it doesn’t decrease in size as the army takes losses. This is a bit optimistic; your actual mileage will vary. But even still, you will have to field your levy a LONG time before you recoup your investment.

    More than One Castle
    If I have multiple castles instead of 1, does the demesne route become more compelling? Well, yes it does. In order to get an equivalently potent army, you don’t need as many buildings. If you have 2 castles, you’ll need to spend 1610 gold upgrading each one (I’ll spare you the building list). For 3, it’s 790 gold. 4 is 320G, 5 is 220G, 6 is 100G, and you don’t need any upgrades if you have 7 or more castles. Again, these numbers can vary depending on your build strategy. In order to get a Power:Morale ratio close to the Swiss Band, my 3 castle strategy involves building Keeps, which aren’t really that cost effective. Hence the precipitous dropoff in cost between 3 and 4 castles.

    Regardless of which building route you take, we can begin to uncover a pattern of initial cost and cost over time. This is the chart that I came up with.

    As you can see, there’s a critical point beyond which the demesne investment becomes worthwhile.

    Conclusions
    Based on all the data, this is what I’ve decided.
    1) Never upgrade a castle until you have at least 4 of them. Always rely on mercenaries before then. They’re going to get you to 4 castles in a far more cost effective manner.
    2) Once you get to 4+ castles, you can begin to contemplate investing in your demesne for the long haul. But even then, it’s going to take a quarter century of warfare before you begin to break even.
    3) The smartest thing to do is to quickly max out your demesne holding limit with mercenaries.

    Future Investigation
    I haven’t thought about it as thoroughly, but it would be interesting to compare mercenaries versus building upgrades once you max your demesne out. My suspicion is that you’ll find a similar situation: improving the demesne is only advantageous over decades of warfare. It would also be interesting to evaluate temples and cities, though I suspect that they won’t help the situation.
    Last edited by iron0037; 23-02-2012 at 18:55. Reason: refined chart

  2. #2
    Quote Originally Posted by iron0037 View Post

    Future Investigation
    I haven’t thought about it as thoroughly, but it would be interesting to compare mercenaries versus building upgrades once you max your demesne out. My suspicion is that you’ll find a similar situation: improving the demesne is only advantageous over decades of warfare. It would also be interesting to evaluate temples and cities, though I suspect that they won’t help the situation.
    This is a very interesting analysis. You have to keep in mind though that 100+ years into the game, mercenaries can be very unreliable. I've been in many situations where they have all been hired out by other nations, or they are still regenerating and their band is significantly smaller than max (still full cost to initially hire though). This can be very important in a defensive war, where your personal levies are already there and don't need to be hired.

    Also, I don't see anywhere you've factored in the marshal bonus. This is huge.
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    Colonel iron0037's Avatar
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    Are you referring to the Marshall bonus for Training Troops? No, I did not include that. I suppose I could do so for the 1 castle scenario, but all it's going to do is reduce your break-even point by a decade or so. Also, you can't have your troops getting trained across multiple counties.

  4. #4
    I think it's best to hire mercenaries anytime hiring them would allow you to occupy an enemies holdings faster than you otherwise could with your own forces. At minimum, you need enough troops to siege all their counties at once. It's probably even worth it to hire enough to actually be able to assault without taking many losses. In a case like France, with an invasion CB, it's more than worth it to have about six assaulting stacks.

  5. #5
    Very interesting analysis. I have made that mistake of starting a fight, planning on hiring mercenaries, and then having a heart attack when none are to hire!

  6. #6
    Quote Originally Posted by iron0037 View Post

    Unit - Power/Morale/Maintenance
    Light Infantry – 17/3/1
    Heavy Infantry – 19.5/5/2
    Archers – 19/1/1/
    Pikemen – 22.4/6/2
    Light Cavalry – 31/4/2
    Heavy Cavalry – 40/10/4

    Evaluating the Swiss Band under these metrics yields a Power of 30.8 ((600*19.5+300*19+22.4*600)/1000 = 30.84) and a Morale value of 6.9 ((600*5+300*1+600*6)/1000 = 6.9). So what improvements would I need to make to castle(s) to get the same Power and Morale? Let’s examine.
    Why are you dividing by 1000? I thought that 1500 would be the correct number to divide by, there are 1500 solider in the Swiss band.

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    Colonel iron0037's Avatar
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    Quote Originally Posted by Von Hilficker View Post
    Why are you dividing by 1000? I thought that 1500 would be the correct number to divide by, there are 1500 solider in the Swiss band.
    If you look at the maintenance numbers, it's per 1000 soldiers. For example, it costs 1 gold per month to field 1000 light infantry. I was simply keeping the scaling consistent for power and morale. You could call it 30800 power and 6900 morale if you prefer. I just need a number from a consistent algorithm when benchmarking to my demesne.

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    Second Lieutenant JackTheRipper21's Avatar
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    I would say the castles have an extra advantage as even if you lose your entire levy they will regenerate, and you wont have to worry about spending another 75 gold to hire them or another band if they get wiped out, you just have to wait for a few months.

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    Colonel iron0037's Avatar
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    Yes, clearly there are lots of strategic considerations at play that are not accounted for here. Mercenaries aren't always available. Mercenaries require a new purchase after regeneration. Sometimes you just need troops and don't have the luxury of waiting 15 years to save up the cash to build all the buildings that are necessary.

    Again, this is simply an analysis of the economics of one strategy versus another. The point is that investing in your holdings is not something you'll recoup in 5 or 10 years. If you're going to invest, expect it to take a long time to pay for itself in gold. It may pay for itself (or cost you) in other ways though...

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    Colonel iron0037's Avatar
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    Per Cymsdale's suggestion, I have investigated the impact of a Marshall training troops. With a Level 15 Marshall, you get a 37.5% levy bonus to one province. With one castle, yes, the does have an impact as the chart in the first post now demonstrates. The break even time is 56 years instead of 63.

    I also show the situation where you have two castles in one province, both receiving the levy bonus. Any way you slice it, the break even point for 3 or fewer castles is 40+ years.

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    Using your power/morale formula, what are the most cost effective upgrades to put in across a players entire demesne as cash becomes available?

  12. #12
    Colonel iron0037's Avatar
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    Quote Originally Posted by Mus View Post
    Using your power/morale formula, what are the most cost effective upgrades to put in across a players entire demesne as cash becomes available?
    Funny you should ask. I was going to create a separate thread on the subject in a day or two...didn't want to overwhelm everyone with too many numbers all at once .

    The quick answer is that Militia Barracks 1 is easily the most cost effective building. It offers the best morale increase per gold and second best power per gold. Militia Barracks 2 is also pretty darn good. Barracks 1 and 2 offer pretty good morale per gold, but so-so power per gold. Stables are pretty good all around, but most their power is in the chase phase of combat, which (to my knowledge) doesn't matter unless you win the first two rounds.

    Training Grounds and Keeps are pretty bad investments until you've finished all the Level 3 troop buildings.

  13. #13
    When I did similar work on combat power for CK1, I accounted for the combat phases by multiplying the power of the unit by the number of phases it fought in and the reverse order of those phases (here, the first skirmish phase gets multiplied by 3, second main combat phase by 2, and pursuit by 1). This gave a strong preference to units that could break or severely impact the enemy's morale in the opening phase and win the battle faster. I doubt that would change the general flavor of your conclusions here, but it might affect your work on which improvements are best.

    Edit: rude bugger that I am, I totally overlooked thanking you for your excellent work in my mad rush to nitpick something you haven't published or possibly even finished yet. I shall report to the royal torturer immediately by way of apology.
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