How the number of knights affects gold earned in a region

[Eldargard]

I was reading an argument in another thread about whether a region made more or less money as it gained knights. So I decided to play around a bit using the region one of my characters has as a baseline and the formula's on the wiki page.

Of course, there are better and worse size/efficiency/lords_tax combos available with some being noticeably more profitable than others. I created a script to calculate every combination (16524 combos) of estate size (23%-40%) for one lord with an estate and one knight with an estate for every tax rate from (0%-50%) and found that total gold production for the region could range from 228 to 240 depending on estate sizes and tax rates. For this example I just picked fairly even values that I might imagine a player using.

I have also rounded down in every case so these values will tend to be lower than higher. None of this takes food production into account either.

To start, here is the basic region stats that will stay the same for all examples:

Code: [Select]

456 Region Gold
14% Tax Rate
70% Region Production

This is how the region looked when I took it over. The Lord earned 160g, the knight 77g for a total of 237 gold for the entire region.

Code: [Select]

Tax on Knight Earnings: 25%
Lord: Size - 40% Efficiency - 83%
Knight 1: Size - 40% Efficiency - 83%
Wild: Size - 20%
If the region has no knights the Lord will earn 196 gold for a total of 196 gold for the entire region.

Code: [Select]

Tax on Knight Earnings: 25%
Lord: Size - 40% Efficiency - 83% 196
Wild: Size - 60%
The text three samples have the goal of ensuring all knights earn 77 gold if at all possible

With two knights earning 77g each the lord would earn 124g for a total of 278 gold for the entire region.

Code: [Select]

Tax on Knight Earnings: 16%
Lord: Size - 34% Efficiency - 89%
Knight 1: Size - 33% Efficiency - 90%
Knight 2: Size - 33% Efficiency - 90%

With three knights earning 77g each the lord would earn 71g for a total of 302 gold for the entire region.

Code: [Select]

Tax on Knight Earnings: 1%
Lord: Size - 22% Efficiency - 100%
Knight 1: Size - 26% Efficiency - 97%
Knight 2: Size - 26% Efficiency - 97%
Knight 3: Size - 26% Efficiency - 97%
With four knights earning 77g each the lord would earn 4g for a total of 312 gold for the entire region.

Code: [Select]

Tax on Knight Earnings: 1%
Lord: Size - 0%
Knight 1: Size - 25% Efficiency - 100%
Knight 2: Size - 25% Efficiency - 100%
Knight 3: Size - 25% Efficiency - 100%
Knight 4: Size - 25% Efficiency - 100%
The next three samples have the goal of ensuring the lord continues to earn 160g if at all possible.

Two knights could each earn 59g if the lord maintained 160g for a total of 278 gold for the entire region.

Code: [Select]

Tax on Knight Earnings: 36%
Lord: Size - 34% Efficiency - 89%
Knight 1: Size - 33% Efficiency - 90%
Knight 2: Size - 33% Efficiency - 90%
Three knights could each earn 47g if the lord maintained 161g for a total of 302 gold for the entire region.

Code: [Select]

Tax on Knight Earnings: 40%
Lord: Size - 22% Efficiency - 100% 161
Knight 1: Size - 26% Efficiency - 97% 47
Knight 2: Size - 26% Efficiency - 97% 47
Knight 3: Size - 26% Efficiency - 97% 47
Four knights could each earn 37g if the lord maintained 161g for a total of 309 gold for the entire region.

Code: [Select]

Tax on Knight Earnings: 48%
Lord: Size - 8% Efficiency - 100% 161
Knight 1: Size - 23% Efficiency - 100% 37
Knight 2: Size - 23% Efficiency - 100% 37
Knight 3: Size - 23% Efficiency - 100% 37
Knight 4: Size - 23% Efficiency - 100% 37

[Anaris]

I've never been happy about the way estate efficiency handling ended up. It would make me much happier if it were absolutely, 100% clear that every knight you add to the region increases every estate's productivity, at least a little.

(I'd also like to add the ability for Dukes to own land in multiple regions in their duchies, and Rulers to do so throughout the realm...but that's only peripherally related. )

So, at some point (in my copious spare time...) I will be revisiting estate calculations, and while I'm not sure precisely what math I'll use, my intention is to adjust it so that:

1) Having lands designated as "wild" is generally worse than having them made into a vacant estate
2) Having more knights is generally strictly better than having fewer, on a gold-per-peasant basis

All that said, beware of creating scripts to calculate things in BattleMaster unless you are absolutely 100% sure of the algorithm used. There are lots of places where it's more complicated than it looks on the outside. I don't remember offhand if this is a case where the math used is more complicated than what can be relatively simply observed with a few data points; it's possible that your numbers here are all correct. Just be careful of it in general.

[Eldargard]

The numbers in this post we're all calculated by hand using the formulas on the wiki. Since I was unsure how bm code did rounding (at what steps at with what method) I just rounded down between steps. My little script also uses the formulas on the wiki and seems to match the predictions on the estate management page but I just accept that he figures are ballpark and look more for trends than not.

[Chenier]

I thought it was pretty straightforward that more knights meant more total gold? Who challenged this and how?

The more complex question was rather if more regions meant more total gold, assuming the same number of knights. I've argued a few times that, in many cases, taking up a new region can actually make a realm poorer. This is usually the result of a realm that is at its optimal density, or below it, gaining regions of below-average wealth value, leading to the transition of knights from high-wealth high-efficiency high-tax city estates to low-wealth low-efficiency low tax border lordship.

1) Having lands designated as "wild" is generally worse than having them made into a vacant estate
2) Having more knights is generally strictly better than having fewer, on a gold-per-peasant basis

I'm not sure if this was brought up before, but I think that worse than wild lands would be empty estates where the lord kicks out any noble that picks them up, because they are just meant to increase his revenues and aren't really meant for others, due to them being more profitable to him than wildlands would be.

[Anaris]

I thought it was pretty straightforward that more knights meant more total gold? Who challenged this and how?

Right—more total gold.

I want more knights to mean more gold per percent of estate—so that if the Lord has a 20% estate, and 1 knight has a 10% estate, and the Lord's weekly tax just from his estate averages 150, then another knight takes a 10% estate, the Lord's weekly tax goes up to 155. And the other knight's weekly tax goes up. Thus, not only would Lords who want to benefit the realm try to take on more knights, Lords who want to make a load of money on their own will, too..

The more complex question was rather if more regions meant more total gold, assuming the same number of knights. I've argued a few times that, in many cases, taking up a new region can actually make a realm poorer. This is usually the result of a realm that is at its optimal density, or below it, gaining regions of below-average wealth value, leading to the transition of knights from high-wealth high-efficiency high-tax city estates to low-wealth low-efficiency low tax border lordship.

Urgh. That's getting into questions of min-maxing I'm not sure we really need to deal with, as long as our player density is as low as it is. Just because it's possible that adding a region to the realm could reduce total realm gold doesn't mean that a) people will work out the math of it to know, or b) that they will think it's enough of a reduction to care even if they do do the math.

I'm not sure if this was brought up before, but I think that worse than wild lands would be empty estates where the lord kicks out any noble that picks them up, because they are just meant to increase his revenues and aren't really meant for others, due to them being more profitable to him than wildlands would be.

If there's even a hint of that happening, then I will do two things:

1) I will implement a change whereby any time a Lord kicks a Knight out of their estate, that portion of the region is locked as wild lands for at least 2 weeks. (Or whatever I calculate it will take to offset the extra gold he could get from it.)
2) I will kick that particular Lord into next century for being a bloody !@#$%^&.

[Chenier]

Right—more total gold.

I want more knights to mean more gold per percent of estate—so that if the Lord has a 20% estate, and 1 knight has a 10% estate, and the Lord's weekly tax just from his estate averages 150, then another knight takes a 10% estate, the Lord's weekly tax goes up to 155. And the other knight's weekly tax goes up. Thus, not only would Lords who want to benefit the realm try to take on more knights, Lords who want to make a load of money on their own will, too..

I don't understand the nuance, isn't this pretty self-evident too? Up to the cap, the smaller the estate, the more efficient it is, thus them more gold per % of size it generates.

If there's even a hint of that happening, then I will do two things:

1) I will implement a change whereby any time a Lord kicks a Knight out of their estate, that portion of the region is locked as wild lands for at least 2 weeks. (Or whatever I calculate it will take to offset the extra gold he could get from it.)
2) I will kick that particular Lord into next century for being a bloody !@#$%^&.

Gamey min-maxing response #2: creating a ton of tiny estates that no knight would like to take, in order to increase gold output for the lord.

Urgh. That's getting into questions of min-maxing I'm not sure we really need to deal with, as long as our player density is as low as it is. Just because it's possible that adding a region to the realm could reduce total realm gold doesn't mean that a) people will work out the math of it to know, or b) that they will think it's enough of a reduction to care even if they do do the math.

It has secondary side-effects, though. As realms grow, they average income decreases, but their expenses increase. They grow more difficult to defend, and so militia is used more, which in turn reduces wealth even more. I think it's part of the reason why Dwi has such a stalemate, despite the aggregate data suggesting the League greatly overpowers Luria. The increase in average realm size has made all realms less potent, allowing them to field much less mobile CS/gold output. All while facing much higher defender forces then were previously seen.

Just because the players don't realize it, or don't consider it, doesn't mean it's not detrimental to gameplay.

[Indirik]

There was talk of changing estates so that they are based on number of peasants, rather than percentage of region. If this was done, you could code estates to have a minimum number of asked peasants. Therefore you couldn't create an estate that gave someone 3% of a !@#$ty bad lands region. The lord then couldn't create lots of little, worthless estates. You could code in an efficiency penalty for too many tiny estates, due to administrative overhead.

[OFaolain]

At present, estate tax settings can be set such that every knight can only ever add wealth without taking any from the lord; wild lands and empty estates are taxed at 50% and the maximum tax setting for estates is 50%. If your tax rate is at 50% then any knight who takes an empty estate is creating his entire income simply by being in the estate. This is generally not feasible in rural regions with low income but in lower-density realms (for example on Dwilight) where you might only have knights in your cities then it can work quite well.

And this is assuming the lord wants to maximize his own income, for a building project for example. But if he's trying to fund the army he can lower the tax he levies from his knights to increase their income; it's a very flexible system, though I've asserted that simply having several knights is its own reward.

[Anaris]

I don't understand the nuance, isn't this pretty self-evident too? Up to the cap, the smaller the estate, the more efficient it is, thus them more gold per % of size it generates.

You're still missing it.

I'm saying I would change the code so that the same estate you have today would start making more money, without the Lord making any changes to that estate, just because another knight took an estate in the region.

Gamey min-maxing response #2: creating a ton of tiny estates that no knight would like to take, in order to increase gold output for the lord.

a) So I'll make sure that the boost to the Lord's estate doesn't come until the estates are filled.
b) What Indirik said.

It has secondary side-effects, though. As realms grow, they average income decreases, but their expenses increase.

I am not convinced that this is a strong enough effect to cause any practical problems.

And if it does, then...fine, you've expanded as far as your existing noble base will allow.

I don't have a problem with the idea that, given a certain number of noble characters in a realm, there is some fixed maximum number of regions they can hope to control, and/or a maximum above which new regions are no longer adding any meaningful benefit to the realm. I don't think it's at all unreasonable to say that a realm of 10 people should fall apart if it tries to control 30 regions.

[Chenier]

Time for a new pie-shaped continent to come replace all of the old ones!

[Sacha]

Threads like these give a good example of why we're bleeding players, IMO. We're only propagating the notion that you should play BattleMaster with a calculator and a stack of spreadsheets.

[Anaris]

Threads like these give a good example of why we're bleeding players, IMO. We're only propagating the notion that you should play BattleMaster with a calculator and a stack of spreadsheets.

Ugh. I know. That's part of what I'm trying to fight.

Unfortunately, I don't believe it's possible to avoid situations where someone with a calculator and a stack of spreadsheets can squeeze out an extra 5-15% efficiency from the game. Which means that people willing to put in that kind of effort will have a real edge.

All I can do is try to make the kinds of things they do to achieve those sorts of optimizations the same kinds of things that people would want to do otherwise. At least where it doesn't require twisting the code (and the conceptual framework) into lots of little pretzel-shapes to do it.

[Sacha]

This is idle hope most likely, but... Is there any conceivable way we could ever go back to the way things were before estates and complex tax calculations and all that jazz? I adored the old commie tax distribution.

[Lorgan]

You don't need to "hack" into the code with a calculator to squeeze every last possible coin out of your region. Trial, error and dedication is all it takes. And everyone can do that.

I also should note that there are already a lot of benefits to having plenty of knights and it shouldn't be overdone or realms with few nobles are doomed to fall in boring, lopsided wars.

[Anaris]

You don't need to "hack" into the code with a calculator to squeeze every last possible coin out of your region. Trial, error and dedication is all it takes. And everyone can do that.

Of course anyone can do that. That's not the point. The point is people shouldn't have to do that to be able to have a chance in the game, because not everyone has hours and hours to waste with that trial and error.

I also should note that there are already a lot of benefits to having plenty of knights and it shouldn't be overdone or realms with few nobles are doomed to fall in boring, lopsided wars.

All else being equal, a realm with fewer nobles should lose to a realm with more.

A realm with 5 nobles should not, ever, have a shot in hell at beating a realm with 40.

I have absolutely no problem increasing the marginal utility of additional nobles—especially increasing it for the Lords who will be taking them as knights.