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  • Upgrade Market to Rice Exchange? An objective analysis


    In this article we will objectively examine a recently brought-up topic (which must have existed for a long time) - whether it is more profitable to upgrade Markets to Rice Exchange or higher forms.

    Upgrading market to higher-level buildings has the following pros and cons:

    - Generates a steady income independent of town size
    - Boosts town development in the province

    - Requires an initial investment
    - Consumes food. Slows down town development in all provinces

    Do the Pros outweigh the Cons? Let's first simplify the question to:

    (1) Upgrade Markets to Rice Exchange
    (2) Leave Markets in the basic form

    Then if (1) proves more profitable, we will discuss whether to upgrade Rice Exchange further.

    - Provide +5 town growth bonus in the province
    - +200 commerce in the province

    Rice Exchange
    - Provide +10 town growth bonus in the province
    - +500 commerce
    - Consumes 1 food
    - Costs ~1500 koku (this value varies by the level of the Developmental Commissioner, etc.)

    So essentially upgrading a Market to Rice Exchange is about:
    (1) -1500 koku
    (2) +300 commerce in the province
    (3) +5 town growth in the province
    (4) -1 food surplus

    Let's crunch some numbers! But we need to write a good equation to represent the problem.

    Effective Tax Rate "ET%", Number of Turns "T"

    The value of commerce, just like farming, mining, and town activities, is subject to taxing. At a normal tax rate of 30%, we tax 30% of the sum of farming, commerce, mining, town. So +300 commerce transfers to 90 koku of income after 30% tax.

    But that's only in theory. In reality, we have admin cost. Normally, when we set tax rate at 30%, after admin cost, we only receive 20% of it. The missing 10% goes to the government workers who collect taxes and... have unnecessary "business trips". So +300 commerce only gives us 60 koku.

    But when we install a secret police (a Metsuke) into a province, we increases the effective tax rate even ABOVE the apparent tax rate. A level-2 Metsuke specialized in town supervision can easily achieve 30% of effective tax rate or above, at a normal tax rate of 30%.

    In our analysis, we be flexible and call effective tax rate "ET%". Our gain from upgrading to Rice Exchange is increased by 300 * ET% (per turn). Let the number of turns be "T". The total commerce-income from Rice Exchange is therefore 300 x ET% x T.

    Prediction: So how does the effective tax rate affect our decision to whether to upgrade markets? The higher the effective tax rate, the MORE actual income we receive from the +commerce building. So it should be a good idea to upgrade markets in towns we station a good Metsuke.

    Town Growth, Basic Tax Rate "BT%", Number of Provinces "P", and Number of Turns "T"

    Food surplus is a very strange concept in STW2. One food surplus gives +1 town growth in ALL provinces, not just one. You'd think that the surplus will become insignificant if it is shared by many provinces. There is one more factor to consider, that is the REDUCTION of town growth from base tax rate. For example, if you have 10 units of food surplus, but set a base tax rate (BT%) of 30%, you only receive 10 x (1-0.3) = 7 units of town growth.

    Now let's come back to Rice Exchange. Upgrading Markets to Rice Exchange costs 1 food surplus in all provinces. Let the number of provinces be "P". The effect of the food consumption of Rice Exchange (grains dropped on the floor?) is therefore -P. This food consumption is then transferred to town growth as -P x (1-BT%) = -(1-BT%)P

    But Rice Exchange also provides its own town growth boost at +5. So our final effect on town growth is 5-(1-BT%)P.

    Town growth works over time. For example, with a town growth of +7:

    On turn 1, 7 town
    On turn 2, 14 town
    On turn 100, 700 town

    The total town growth across all provinces is calculated as (let the number of turns be T):

    {[5-(1-BT%)P] + [5-(1-BT%)P x T]}/2 x T

    But that's not our income yet. Town activity is also subject to the average effective tax across all provinces (ET-AVE%). This is different from the effective tax rate in the previous case, since we probably can't put the same Metsuke into all provinces. (But if we don't use any Metsuke, ET-AVE% is probably identical to ET%).

    So our income (if negative, a loss of income) from upgrading the rice exchange over T turns is:

    Extra Profit = -1500 + 300 x ET% x T + {[5-(1-BT%)P] + [5-(1-BT%)P x T]}/2 x T x ET-AVE%

    Now we can make some charts!

    But since there are two many variables, we have to fix the others and only examine one or two at a time.
    First, let's look at the effect of number of provinces.
    We will reasonably assume the following:

    Base Tax Rate (BT%) = 30%
    Effective Tax Rate (ET%) = 37% -- a good Metsuke should be able to achieve it
    Average Effective Tax Rate (ET-AVE%) = 21% (22 provinces), 22% (16 provinces), 23% (10 provinces)
    Number of Provinces (P) = 22, 16, 10
    Number of Turns (T) = 1 to 100

    Chart 1 - Metsuke in the Province

    The precense of Metsuke boosts the income of the province in which he is stationed.

    Let's take the green line (16 provinces) for discussion. The initial deficit of 1500 (the cost of the Rice Exchange building) will be slowly pay off. At about turn 17, the Rice Exchange option breaks even. From then on they earn more profit over Market alone, but this extra from Rice Exchange max off at turn 73 or so. Then slowly we head back to deficit that goes deeper and deepr due to the loss of long-term town growth. (We still make money, just not as much as if we leave Market in the basic form.)

    As we have more provinces (the red line), the benefit of town growth is more pronounced. At 22 provinces (the magic number to pause before Realm Divide on Domination), the extra profit of the Rice Exchange is only positive between turn 20 and 45, and the extra profit is just a few hundred koku at best.

    But if we have less provinces (the orange line, 10 provinces), upgrading to Rice Exchange sounds like a great idea. The extra profit beats the alternative for a long time. However, by staying small, we already lose income from collecting less tax from additional provinces in the first place. So why would we purposely stay small?

    I guess most people's question on Rice Exchange is on whether we should upgrade Markets in all provinces. But obviously we at most can only have 5 Metsuke supervising towns. So most provinces would be without a Metsuke. Let's look at the no metsuke situation.

    Base Tax Rate (BT%) = 30%
    Effective Tax Rate (ET%) = 20%
    Average Effective Tax Rate (ET-AVE%) = 20%
    Number of Provinces (P) = 22, 16, 10
    Number of Turns (T) = 1 to 100

    Chart 2 - No Metsuke in the Province

    Without Metsuke, the extra commerce offered by Rice Exchange is subject to the regular 20% effective tax rate in the province. And we have a very surprising result: Rice Exchange does not turn ANY extra profit at any time.

    Think of what you can do with those 1500 koku per province!

    I think the verdict is quite clear now so we can reach a conclusion:


    (1) ONLY upgrade a Market to Rice Exchange if there is a good Metsuke stationed in the province. Since at most we have 5 Metsuke, we will at most upgrade 5 Markets to Rice Exchange. Naturally, this better happens in our richest provinces (very fertile soil, gold mine, etc.) to maximize the additional profit.

    (2) Don't bother upgrading the Market in any other provinces.

    (3) Even with Metsuke, it is only more worthwhile to upgrade a Market to Rice Exchange if we play a shorter campaign and have a low number of provinces for the majority of the game.

    (4) Never upgrade the market if you will finish the campaign in the next 15 turns.

    (5) Don't upgrade the market if the game will last very long.


    Let's compare Market vs. Merchant Guild:

    - Provide +5 town growth bonus in the province
    - +200 commerce in the province

    Rice Exchange + Merchant Guild
    - Provide +20 town growth bonus in the province
    - +1000 commerce
    - Consumes 2 food
    - Costs ~4750 koku (again, this value varies by the level of the Developmental Commissioner, etc.)

    So essentially upgrading a Market to Rice Exchange is about:
    (1) -4750 koku
    (2) +800 commerce in the province
    (3) +15 town growth in the province
    (4) -2 food surplus

    So we can simply make a few changes of the equation and make the same plots.

    Extra Profit = -4750 + 800 x ET% x T + {[15-(1-BT%)P] + [15-(1-BT%)P x T]} x T x ET-AVE%

    (1) With Good Metsuke (37% Effective Tax Rate)

    We can indeed see that there is an improvement of profit across the board. For the 10-province scenario, we get an extra profit of 9000+ (achieved 92 turns after the construction is completed) for upgrading to merchant guild. Note that if you only put a mediocre Metsuke, say one that makes an effective tax rate of 30%, our extra profit is cut by half, down to 4700 koku. (This is not per turn, but in total.)

    For the 22-province scenario that is at least the typical case for a domination game, there is only a small extra profit of less than 2000 koku between 20-70 turns after the completion of the buildings. And if your Metsuke is mediocre (30% effective tax rate), you actually lose extra profit compared to vanilla Market.

    (2) No Metsuke (20% Effective Tax Rate)

    Now this looks very familiar. Even for the 10-province scenario, the best profit is "88" koku achieved 67 turns after the completion of the buildings. That's... not a lot. In general it is simply bad news across the board.

    So the verdict is out. We can draw our conclusions on Merket vs. Merchant Guild. It pretty much looks like the conclusion for Market vs. Rice Exchange. So we will just summarize it below:


    Upgrade to Merchant Guild if you have a very good Metsuke (high effective tax rate) stationed in the castle town, and if you like to expand slowly. Otherwise, it is more profitable to leave it as Market.
    This article was originally published in forum thread: Upgrade Market to Rice Exchange? An objective analysis started by Maltz View original post
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