I wrestled with this one the last time I played with Great Britain. In the past, my inclination always has been to replace the gunsmith under the rather blithe assumption that the higher taxation rate of European governance structures would more than make up for the loss of gunsmith income in the median term. I also got rid of the gunsmith because I didn’t want the religion penalty associated with having the region’s populace be animist; nor did I care to construct a church building strong enough to overpower the animist effects of the gunsmith. [Note: see the bottom of the article for the base formula]
I’ve just conquered Cherokee Territory and Kain Tuck Territory, though. I decided to crunch some numbers and see if I could determine whether there would be some fiscal criteria for keeping or eliminating the gunsmith. I notice that many of the players here are in their teens. For those of you who have wondered whether algebra actually can serve a useful problem solving purpose in real life, I have a serviceable example.
For those who aren’t familiar with the Native American nations buildings, the gunsmith functions very differently from a European governance structure. Unlike European governance structures, the gunsmith gives no taxation bonus. The gunsmith acts more like a combination barracks and factory, allowing the capitol to recruit a variety of troops and adding $800 to the regional tax base. Replacing a gunsmith with a European governance structure means giving up that $800 source of regional wealth in exchange for better taxation. In short, one trades a greater tax base for a greater level of taxation. Obviously, this trade becomes worthwhile only if the regional wealth from sources other than the gunsmith is pretty high. But how high?
I set up an equation (in consultation with my wife, who enjoys math more than I do) based on the particulars of my game. The tax rate in Cherokee Territory with the gunsmith is 15.9%. The tax rate with a state house, which is the middle of three tax-increasing governance structures available, is 20.2%. The regional wealth with the gunsmith is $800 greater than it would be without the gunsmith. I made the variable, x, the amount of regional wealth required for the region with a state house to generate as much tax revenue as the same region with the gunsmith.
20.2% * x = 15.9% * (x + 800)
I find percentages messy, so I turned the percents into decimals.
.202x = .159(x + 800)
I simplified the right-hand side of the equation.
.202x = .159x + 127.2
I subtracted .159x from both sides.
.043x = 127.2
I divided both sides by .043.
x = 2958
x + 800 = 3758
So, when the tax base of Cherokee Territory reaches $2958 with a state house in place, the territory will generate the same tax revenue as when the tax base is $3758 with the gunsmith in place. This calculation doesn’t mean that replacing the gunsmith with a state house becomes a good investment as soon as the tax base of Cherokee Territory reaches $2958. The calculation means that I can start to calculate the ROI (return on investment) for building a state house when the tax base of Cherokee Territory reaches $2958 because I won’t lose money. A state house costs $3500 to establish ($500 for the magistrate, $1000 for the governor’s residence, $2000 for the state house), so the regional tax base is going to have to be significantly greater than $2958 for me to see a reasonable ROI.
I can repeat this process whenever I capture a region with a gunsmith at whatever levels of taxation apply and for whatever governance structure I intend to put into place instead of the gunsmith. Let’s say that I capture Northwest Territories, which is generally pretty poor. I want to replace the gunsmith with a governor’s residence. Let’s imagine that the tax rate with the gunsmith is 15.0%, while the tax rate with the governor’s residence is 17.0%. (I’m imagining that I have 35 or more regions when this happens.)
.170x = .150(x + 800)
.17x = .15x + 120
.02x = 120
x = 6000
In other words, Northwest Territories would have to have a tax base of $6000 before a governor’s residence would generate the same revenues as the gunsmith. It’s hard to imagine this happening in an ordinary game. Therefore, it’s not always worthwhile to replace the gunsmith based strictly on tax revenues.
Getting back to Cherokee Territory, I wanted to get some idea of when I might establish a favorable ROI. Cherokee Territory has a couple of investments I intend to pursue regardless of the tax rate in the region. I fully intend to develop Rabbit Ridge into a cotton warehouse. Once Autiamique becomes a town, I’ll develop a craft workshop (weavers) there. There are a couple more variables involved, such as town wealth and decreasing tax rates as more regions come under French control. For the moment, though, I’ve ignored those other factors. I made a couple of assumptions about the price of cotton as I develop Rabbit Ridge and added in the value of the craft workshops. For the purpose of this analysis, Cherokee Territory with a cotton warehouse and craft workshop (weaver) added to the tax base is worth $4031. With a gunsmith, Cherokee Territory is worth $4831. Tax revenues with a state house are $814. With a gunsmith, revenues are $768. $46/turn in additional tax revenues yields an ROI (against the $3500 to construct the state house) of 76 turns. This is not favorable. I subtracted the $480 needed to bring the gunsmith back into operation from the cost of the state house, and I still got an ROI of 65. Upping the ante a bit to have a state capitol in Cherokee Territory, I got an ROI of 45. This is better but still not competitive with other investments.
The issue of faith and public order needs to be considered. If I have to keep a colonial militia regiment in Chicasa to keep order in Cherokee Territory due to religious unrest, the maintenance cost of each regiment needs to be deducted from the tax revenues generated by the region with a gunsmith. The same applies to the town watch. If I need to keep troops in Cherokee Territory to keep the peace, the equation changes rather quickly. Until that point, though, it’s hard to see how I will justify paying for European structures.
At the end of the day, though, I’ll revisit Cherokee Territory once the warehouse and new industry are in place. Town wealth is increasing rapidly and will continue to increase as I improve my enlightenment technology. By the time the cotton warehouse and workshops are in place, town wealth may have changed the equation considerably. In the meantime, I’ll make the most of that $800 in gunsmith wealth.
For those of you who might be interested in using this formula in your own campaigns, I have drawn out the blank model below:
x = the level of regional wealth at which a European governance structure generates the same tax revenues as a region with a gunsmith
[tax rate w/ European gvt bldg] * x = [tax rate of region with the gunsmith] * (x + 800)
Players can easily test a variety of tax rates to determine when a given European governance structure will generate as much revenue as the region with a gunsmith. Obviously, the higher the tax rate of the European governance structure, the lower the regional wealth has to be. However, I want to emphasize again that finding the point of equal revenue (x) is not the same as finding a desirable ROI. Until the region reaches the point of equal revenue, there is no ROI because the investment will lose money rather than making it. A favorable ROI for a governance structure, which I consider to be 30 turns or less, may be many turns in future after the region in question reaches the point of equal tax revenues.
The musket is for fixing and softening the enemy. The bayonet is for destroying him.
I’ve just conquered Cherokee Territory and Kain Tuck Territory, though. I decided to crunch some numbers and see if I could determine whether there would be some fiscal criteria for keeping or eliminating the gunsmith. I notice that many of the players here are in their teens. For those of you who have wondered whether algebra actually can serve a useful problem solving purpose in real life, I have a serviceable example.
For those who aren’t familiar with the Native American nations buildings, the gunsmith functions very differently from a European governance structure. Unlike European governance structures, the gunsmith gives no taxation bonus. The gunsmith acts more like a combination barracks and factory, allowing the capitol to recruit a variety of troops and adding $800 to the regional tax base. Replacing a gunsmith with a European governance structure means giving up that $800 source of regional wealth in exchange for better taxation. In short, one trades a greater tax base for a greater level of taxation. Obviously, this trade becomes worthwhile only if the regional wealth from sources other than the gunsmith is pretty high. But how high?
I set up an equation (in consultation with my wife, who enjoys math more than I do) based on the particulars of my game. The tax rate in Cherokee Territory with the gunsmith is 15.9%. The tax rate with a state house, which is the middle of three tax-increasing governance structures available, is 20.2%. The regional wealth with the gunsmith is $800 greater than it would be without the gunsmith. I made the variable, x, the amount of regional wealth required for the region with a state house to generate as much tax revenue as the same region with the gunsmith.
20.2% * x = 15.9% * (x + 800)
I find percentages messy, so I turned the percents into decimals.
.202x = .159(x + 800)
I simplified the right-hand side of the equation.
.202x = .159x + 127.2
I subtracted .159x from both sides.
.043x = 127.2
I divided both sides by .043.
x = 2958
x + 800 = 3758
So, when the tax base of Cherokee Territory reaches $2958 with a state house in place, the territory will generate the same tax revenue as when the tax base is $3758 with the gunsmith in place. This calculation doesn’t mean that replacing the gunsmith with a state house becomes a good investment as soon as the tax base of Cherokee Territory reaches $2958. The calculation means that I can start to calculate the ROI (return on investment) for building a state house when the tax base of Cherokee Territory reaches $2958 because I won’t lose money. A state house costs $3500 to establish ($500 for the magistrate, $1000 for the governor’s residence, $2000 for the state house), so the regional tax base is going to have to be significantly greater than $2958 for me to see a reasonable ROI.
I can repeat this process whenever I capture a region with a gunsmith at whatever levels of taxation apply and for whatever governance structure I intend to put into place instead of the gunsmith. Let’s say that I capture Northwest Territories, which is generally pretty poor. I want to replace the gunsmith with a governor’s residence. Let’s imagine that the tax rate with the gunsmith is 15.0%, while the tax rate with the governor’s residence is 17.0%. (I’m imagining that I have 35 or more regions when this happens.)
.170x = .150(x + 800)
.17x = .15x + 120
.02x = 120
x = 6000
In other words, Northwest Territories would have to have a tax base of $6000 before a governor’s residence would generate the same revenues as the gunsmith. It’s hard to imagine this happening in an ordinary game. Therefore, it’s not always worthwhile to replace the gunsmith based strictly on tax revenues.
Getting back to Cherokee Territory, I wanted to get some idea of when I might establish a favorable ROI. Cherokee Territory has a couple of investments I intend to pursue regardless of the tax rate in the region. I fully intend to develop Rabbit Ridge into a cotton warehouse. Once Autiamique becomes a town, I’ll develop a craft workshop (weavers) there. There are a couple more variables involved, such as town wealth and decreasing tax rates as more regions come under French control. For the moment, though, I’ve ignored those other factors. I made a couple of assumptions about the price of cotton as I develop Rabbit Ridge and added in the value of the craft workshops. For the purpose of this analysis, Cherokee Territory with a cotton warehouse and craft workshop (weaver) added to the tax base is worth $4031. With a gunsmith, Cherokee Territory is worth $4831. Tax revenues with a state house are $814. With a gunsmith, revenues are $768. $46/turn in additional tax revenues yields an ROI (against the $3500 to construct the state house) of 76 turns. This is not favorable. I subtracted the $480 needed to bring the gunsmith back into operation from the cost of the state house, and I still got an ROI of 65. Upping the ante a bit to have a state capitol in Cherokee Territory, I got an ROI of 45. This is better but still not competitive with other investments.
The issue of faith and public order needs to be considered. If I have to keep a colonial militia regiment in Chicasa to keep order in Cherokee Territory due to religious unrest, the maintenance cost of each regiment needs to be deducted from the tax revenues generated by the region with a gunsmith. The same applies to the town watch. If I need to keep troops in Cherokee Territory to keep the peace, the equation changes rather quickly. Until that point, though, it’s hard to see how I will justify paying for European structures.
At the end of the day, though, I’ll revisit Cherokee Territory once the warehouse and new industry are in place. Town wealth is increasing rapidly and will continue to increase as I improve my enlightenment technology. By the time the cotton warehouse and workshops are in place, town wealth may have changed the equation considerably. In the meantime, I’ll make the most of that $800 in gunsmith wealth.
For those of you who might be interested in using this formula in your own campaigns, I have drawn out the blank model below:
x = the level of regional wealth at which a European governance structure generates the same tax revenues as a region with a gunsmith
Players can easily test a variety of tax rates to determine when a given European governance structure will generate as much revenue as the region with a gunsmith. Obviously, the higher the tax rate of the European governance structure, the lower the regional wealth has to be. However, I want to emphasize again that finding the point of equal revenue (x) is not the same as finding a desirable ROI. Until the region reaches the point of equal revenue, there is no ROI because the investment will lose money rather than making it. A favorable ROI for a governance structure, which I consider to be 30 turns or less, may be many turns in future after the region in question reaches the point of equal tax revenues.
The musket is for fixing and softening the enemy. The bayonet is for destroying him.
[This message has been edited by webstral (edited 07-13-2011 @ 02:00 AM).]