Upgrade Market to Rice Exchange? An objective analysis

Hello,

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:

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

Cons:
- 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.

Market
- 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. Admin costs goes up with the number of provinces. At just 1 province, the admin cost is 0. At 50 provinces, the admin costs goes up to more than 60% of the tax rate (but does not affect bonus tax rates from characters, retainers, and arts).

In mid-game, when we set tax rate at 30%, after admin cost, we only receive about 20% of it (more than 20% for early game, less than 20% for late game). 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.

Updated: The Reduction of Growth "RS"

The actual town growth is affected by the base tax rate. After collecting a few dozen provinces of data, I cannot figure out the exact equation to calculate it (there seems to be hidden factors), but the following equation provides a very good estimate:

Let S = Sum of Town Growth Factors

This includes:
Town Growth from Infrastructures (Market, Ports, Roads)
Town Growth from Food Surplus
Town Grwoth from Other Factors (event, etc.)

Let RS = the Reduction of Sum of Town Growth
Real Town Growth = (1-RS)

At 0% Base Tax Rate, RS = 0% S (full town growth)
At 10% Base Tax Rate, RS = 6% S
At 20% Base Tax Rate, RS = 14% S
At 30% Base Tax Rate, RS = 26% S
At 40% Base Tax Rate, RS = 55% S
At 50% Base Tax Rate, RS = 100% S

But at very low province count (such as just 1 province), the above equation does not hold. Rather, we have a fixed value of reduction.

At 0% Base Tax Rate, RS = 0
At 10% Base Tax Rate, RS = 0
At 20% Base Tax Rate, RS = 1
At 30% Base Tax Rate, RS = 2
At 40% Base Tax Rate, RS = 9
At 50% Base Tax Rate, RS = 16

But since most of the time our territory count is rather high, and our tax rate is set at 30%, we may as well use the general case above.

Now let's come back. If you have 100 units of town growth potential from food surplus and town buildings, but set a base tax rate (BT%) of 30%, you only receive 100 x (1-0.26) = 74 units of town growth.

OK! 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 -(1-RS)P

But Rice Exchange also provides its own town growth boost at +5. That +5 is reduced by base tax rate to 5(1-RS) as well. At 30% base tax rate, we get 5 x 0.74 = 3.7 units of town growth.

So upgrading to Rice Exchange's final effect on town growth is (1-RS)(5-P). At 30% base tax rate, it is 0.74 x (5-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):

(1-RS) x [(5-P) + (5-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 + (1-RS) x [(5-P) + (5-P) x T]/2 x T x ET-AVE%

Now we can make some charts! (And they are now updated to remove errors and improve accuracy!)

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%
Number of Provinces (P) = 22, 16, 10
Number of Turns (T) = 1 to 100

With Good Metsuke:
Effective Tax Rate (ET%) = 32% (22 provinces), 34% (16 provinces), 36% (10 provinces)
Average Effective Tax Rate (ET-AVE%) = 20% (22 provinces), 22% (16 provinces), 24% (10 provinces)
Reduction of Sum of Town Growth from Base Tax Rate (RS) = 0.26

https://forums.totalwar.org/vb/attac...1&d=1330637459

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 slowly pay off. At about turn 17, the Rice Exchange option breaks even with the no upgrade option (which means they make the same amount of money).

From then on, they earn more profit over Market alone, but this extra from Rice Exchange max off at turn 58 or so at about 1400 koku (which is not a lot, really), and slowly head to deficit that goes deeper and deepr due to the loss of long-term town growth. After turn 95 or so, Rice Exchange actually makes less money than market alone. 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 campaign), the extra profit of the Rice Exchange is only positive between turn 20 and 60, and the extra profit is just several hundred koku at best.

But if we have less provinces (the orange line, 10 provinces), upgrading to Rice Exchange sounds like a great idea when we put a good Metsuke there. 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%
Number of Provinces (P) = 22, 16, 10
Number of Turns (T) = 1 to 100

Effective Tax Rate (ET%) = 20% (22 provinces), 22% (16 provinces), 24% (10 provinces)
Average Effective Tax Rate (ET-AVE%) = 20% (22 provinces), 22% (16 provinces), 24% (10 provinces)

https://forums.totalwar.org/vb/attac...0&d=1330637459

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 after we grow reasonably large.

Extra profit we make at the 10 province case is also very small. It is a very questionable decision to lose 1500 koku now only to gain that same extra koku back 80+ seasons later. 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:

CONCLUSION

(1) 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. The loss of 1500 koku in early game makes a much bigger impact than the gain of 1500 koku in mid- or late-game.

(4) Never upgrade the market if you will finish the campaign in the next 20-25 turns. (It only makes more money 15-20 turns after its completion. The construction of Rice Exchange takes another 5 seasons.)

There is one important piece of information missing. The benefit of upping a Market to a RE is 300 commerce and +5 town growth at the cost of 1 food. The benefit of going from Market to Merchant Guild is +800 commerce and +15 town growth for only 1 more food (edit: IE 2 food more than a Market).

If Merchant Guilds did not exist, Rice Exchanges would be close to worthless.

Edit: No, they would be completely worthless. What do you know.

Edit2: No, they are actually only close to worthless and at least not counterproductive unless you blitz (excluding the taking-up-a-building-slot-thing, but I guess the market would anyway)

Let's compare Market vs. Merchant Guild:

Market
- 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 + (1-RS){[15-2P] + [15-2P] x T} x T x ET-AVE%

https://forums.totalwar.org/vb/attac...9&d=1330709692

(1) With Good Metsuke (32-36% Effective Tax Rate)

We can indeed see that there is an improvement of profit across the board. Actually, in all situations we are still earning extra profit 100 turns after the completion of the Merchant Guild. If we stay small, our extra profit could go into tens of thousands! This is great.

But if we expand rapidly to 22 provinces, upgrading to Merchant Guild makes just less than 5000 extra koku 60 turns after its completion. Maybe we can invest that money somewhere else where we can see a big difference sooner.

https://forums.totalwar.org/vb/attac...2&d=1330709692

(2) No Metsuke (20-24% Effective Tax Rate)

This looks better than Rice Exchange alone, but is it better enough? For the 10-province scenario, we only earn 5000 extra koku about 60 turns after buildings are completed. And if our territory grows big, we still lose profit from the expensive investment.

CONCLUSION

Upgrade to Merchant Guild if you have a 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.

So where else can we spend the money? There are two especially good investments for early-mid game:

(1) Army. More cities = more tax & more resources to sell. This is especially critical in early game. If there is no concern for conversion, it is a very good idea to go crazy on Ashigaru armies and keep taking cities until you pause before the Realm Divide (and then you can slim down your military to focus on infrastructure).

(2) Trade Fleet. Huge return of profit quickly. The western clans should go after this as soon as possible.

Perhaps upgrading the markets in very fertile provinces/gold mine parked with good Metsuke is the way to go for eastern clans to prosper. For example, if I were Uesugi, I would hire a lv 2 Metsuke from my ex-vassal province (after it is defeated by Hojo or someone) and park the Metsuke in Sado (gold mine) with a merchant guild there.

This is pretty important stuff. I can see a lot of people getting absolutely flabbergasted by the extent to which food and market structures affect your economy. Heck, I am flabbergasted about the extent to which Rice Exchanges are worthless. They're actually worse than worthless in that they not only take up a building slot, they also cost you money. That's pretty important stuff and perhaps an explanation as to why a lot of people struggle with lategame economy. I used to always get 4-5 MGs eventually with just about any faction as a preparation for RD but heck, my good Metsuke seem a lot better off in the field except maybe 1 in a goldmine province.

I never really made merchant guilds early with land-based factions but that's mostly due to their cost and relatively high tech requirement early on where you'd rather just expand with most of the factions. Its interesting to note that if you dont plan out your every move to accomodate them, then they're also barely effective at best and a liability at worst. I used to swear to teching Tax Reform before Equal Fields as the income bonus is vastly stronger, but Equal Fields' effect on your middle-lategame econ (if you upgrade farms helluva early) might be a lot more effective than given credit for - even if you slowly creep forward as a faction like Date or Ikko.

In fact, the only argument that seems to be left for even bothering with them (MGs) with a faction like, say, Tokugawa or Hattori, is that you're planning on doing an Kabunakama+Shobai District with a r4+ Metsuke and you want the town to start growing very early on to cap out the bonus, but even then its not even a given.

Thanks for setting up all the graphs, Maltz! Nothing says conclusion like numbers.

In depth and well done. I decided to promote this to an article. Check it out: https://forums.totalwar.org/vb/conte...ctive-analysis

Quote:

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Originally Posted by Maltz

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

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I keep looking at this and I don't understand. Why isn't it just (5-(1-BT%)P)*T?

This is the sum of all town income from turn 1 to turn T. So it is an average of the two ends times the turn number. This is the same formula we use to calculate the area of a trapezoid (a+b/2) x h (height).

Thanks, I see it now, it's just average total town value times turns. But I believe it should be [5-(1-BT%)P] x T instead of [5-(1-BT%)P x T], right?

Yep you are right. I made a mistake in writing the formula (now corrected).

Update: all of the above posts have been updated with the correct formula and more accurate approximations. The conclusion is largely the same, but under certain situations upgrading Markets to higher levels can be a good idea.

This now makes a lot more sense. I was truly blown away by the complete inefficiency of Rice Exchanges. This... I dont know... "feels" more in line with what it "feels" like in the game.