EU4 Advanced Economics 2. Buildings Part I

What provinces should you develop? What buildings should you build? Are Manufactories overrated? Should you get a loan or debase currency? These questions are answered over a series of guides. For players looking for nothing less than mathematical precision in their EU4 economy management.

Introduction

Constructing various buildings is a major way to boost the income of your empire.



We will investigate the various types of income-boosting buildings and assess how cost-efficient they are.

• Buildings that boost Tax Efficiency (Churches, Cathedrals) are henceforth referred to as 'Tax Efficiency buildings'.
  
• Buildings that boost Production Efficiency (Workshops, Counting Houses) are henceforth referred to as 'Production Efficiency buildings'.
  
• Buildings that boost Trade Power (Marketplaces, Trade Depots, Stock Exchanges) are henceforth referred to as 'Trade Power buildings'.
  
• Buildings that lower State Maintenance (Courthouses, Town Halls) are henceforth referred to as 'State Maintenance buildings'.

France at the 1 Nov 1444 start date is used as an example.

Tax Efficiency, Production Efficiency and State Maintenance buildings are discussed in Part I.
Trade Power buildings are discussed in Part II.

Tax Efficiency buildings

Churches become available at Admin Tech 4 (Year 1453), cost $100 and raise provincial Tax Efficiency by 40%.

Cathedrals become available at Admin Tech 19 (Year 1648), cost $300 and raise provincial Tax Efficiency by 60%.

Open Buildings tab, click Church and align the provinces by Improvement value.


Paris is supposed to be the most cost-efficient province to construct a Church. It is projected to raise provincial Tax income by $0.26.

Here is an Excel table calculating the actual change in tax income for the top 10 provinces from the list, from Paris to Montpellier.

• For provinces controlled by Clergy, autonomy is assumed to be 0, as Clergy estate does not affect tax income.
  
• Teff = Tax Efficiency
  
• Teff of 1.15 is assumed in this table (+0.25 for City, +0.75 for Core, +0.15 from Clergy Estate). Changing Teff does not affect d$T/m and (d$T/m)/Cost however.
  
• $T/m = Monthly Tax income
  
• d$T/m = Difference in monthly Tax income before and after building a Church
  
• (d$T/m)/Cost = Difference in monthly Tax income divided by the cost of a Church ($95).
  
• Embracing Renaissance institution confers -5% construction cost. Since the majority of a EU4 campaign occurs after the Renaissance Institution, I assume -5% construction cost in all of my Excel table calculations.
  
• ROI(yrs) = Return on investment. Number of years it takes for the building to start producing profit i.e. to break-even. Decimal points omitted. Note that the 1-year construction period is not considered, so you need to add 1 more year if you want to count from the construction start date.
  
• Last profitable year = the last date when the building can be finished and still expect a profit before the campaign ends in 1821. Not applicable in non-Ironman games. Cells highlighted in red mean that the last profitable year occurs before the building becomes available i.e. it's not worth it. Decimal points omitted.

You can see that d$T/m (the column highlighted in green) matches Predicted increment (also highlighted in green), meaning that the game makes an accurate prediction of the increase in Tax income after building a Church.

(d$T/m)/Cost (the column highlighted in yellow) matches Predicted order (also highlighted in yellow), meaning that the game aligns the provinces in the correct order of cost-efficiency.

Paris should be the first province to have a Church built, as that will give you the most value for your ducats.

Next, let's look at Cathedrals.

• In the (d$T/m)/Cost column, the cost is set as $285 ($300 - 5% from Renaissance Institution).

Predicted increments are accurate. The predicted order is accurate.

You can see that the cost-efficiency of a Cathedral is exactly 1/2 of a Church. Therefore, as a general rule, if you had $300 ducats to invest, it is better to build 3 separate Churches rather than 1 Cathedral. For example, in the 1444 France scenario, constructing 3 Churches in Paris, Reims and Lyonnais will give you an income boost of 0.26 + 0.20 + 0.17 = $0.63/month. But constructing 1 Cathedral in Paris will only boost your income by $0.40/month.

Now, let's consider a situation where a province already has a Church, and you want to upgrade it to a Cathedral.

• In the (d$T/m)/Cost column, the cost is set as $190 ($200 - 5% from Renaissance Institution).

Predicted order / Predicted increment columns are absent in this table because no Churches are present in the Year 1444. But we can still calculate the hypothetical cost-efficiency of upgrading a Church to a Cathedral.

You can see from the table that the cost-efficiency of upgrading a Church to a Cathedral is exactly 1/2 of constructing a Cathedral outright.

Note that in this table, except for Paris and Reims, the Last profitable years occur before Cathedrals unlock, in the Year 1648. This means that the upgrades are not worth it for provinces other than Paris and Reims. For example, imagine Lyonnais has a Church that is upgraded to a Cathedral as soon as Cathedrals becomes available in the Year 1648. From 1649 (it takes a year for the construction) it will take 181 years to break even, in the Year 1830. This is after the campaign end date (1821 for Ironman games), so a player is better off saving up the $200 rather than using it to upgrade the Church in Lyonnais.

Production Efficiency buildings

Workshops become available at Admin Tech 6 (Year 1479), cost $100 and raise provincial Production Efficiency by 50%.


Counting Houses become available at Admin Tech 24 (Year 1715), cost $400 and raise provincial Production Efficiency by 100%.



Paris is supposed to be the most cost-efficient province to construct a Workshop. A Workshop there will raise provincial Production income by $0.23/month.

Let us see if the predictions given by this tab are accurate. An Excel table is made for the top 10 provinces from the list.

• For provinces controlled by Burghers, autonomy is assumed to be 0, as Burgher estate does not affect Production income.
  
• GPeff = Goods produced modifier
  
• Peff = Production Efficiency
  
• Production Efficiency increases throughout the game from Admin Technology. In this table, Peff is set at 1.12%, since that is the value at Admin Tech 24 when Counting Houses become available. Changing Production Efficiency has no influence on d$P/m or (d$P/m)/Cost however, so although the Peff assumed in this table (1.12) is different from the Peff in 1444 France (1.02), one can still test the accuracy of the predicted income boosts as given by the Buildings tab.
  
  Note that in this guide series, Technology level 24 (Year 1715) is used as a benchmark timepoint for Production Efficiency (12% from Admin Tech 24) and Trade Efficiency (14% from Diplo Tech 24). This is because out of all the income-boosting buildings, Counting Houses are the last to unlock, at Admin Tech 24 in the Year 1715. Using a common timepoint allows a fair comparison between the cost efficiencies of the various income-boosting buildings.
  
  
• $P/m = Monthly Production income
  
• d$P/m = Difference in monthly Production income before and after building a Workshop
  
• (d$P/m)/Cost = Difference in monthly Production income divided by the cost of a Workshop ($95)
  
• Embracing Renaissance institution confers -5% construction cost. Since the majority of a EU4 campaign occurs after the Renaissance institution, I assume -5% construction cost in all of my Excel table calculations.
  
• ROI(yrs) = Return on investment. Number of years it takes for the building to start producing profit i.e. to break-even. Decimal points omitted. Note that the 1-year construction period is not considered, so you need to add 1 more year if you want to count from the construction start date.
  
• Last profitable year = the last date when the building can be finished and still expect a profit before the campaign ends in 1821. Not applicable in non-Ironman games. Cells highlighted in red mean that the last profitable year occurs before the building becomes available i.e. it's not worth it. Decimal points omitted.

You can see that d$P/m (the column highlighted in green) matches Predicted increment (also highlighted in green), meaning that the game makes an accurate prediction of the increase in provincial Production income after building a Workshop.

(d$P/m)/Cost (the column highlighted in yellow) matches Predicted order (also highlighted in yellow), meaning that the provinces are aligned in the correct order of cost-efficiency.

Paris should be the first province to have a Workshop constructed, as that will give you the most value for your ducats.


Next, let's look at Counting Houses.

• In the (d$P/m)/Cost column, the cost is set as $380 ($400 - 5% from Renaissance Institution).

Predicted increments are accurate. The predicted order is accurate.
The cost-efficiency of a Counting House is exactly 1/2 of a Workshop. Therefore, as a general rule, if you had $400 ducats to invest, it is better to build 4 separate Workshops rather than 1 Counting House.

For example, in the 1444 France scenario, constructing 4 Workshops in Paris, Lyonnais, Chartres and Montpellier will give you an income boost of 0.23 + 0.21 + 0.12 + 0.12 = $0.68/month. But constructing 1 Counting House in Paris will only boost your income by $0.47.

Furthermore, in this table, except for Paris and Reims, the Last profitable years occur before Counting Houses become available in the Year 1715. This means that the Counting Houses are not worth it for provinces other than Paris and Reims.


Now, let's consider a situation where a province already has a Workshop, and you want to upgrade it to a Counting House.

• In the (d$P/m)/Cost column, the cost is set as $285 ($300 - 5% from Renaissance Institution).

Predicted order / Predicted increment columns are absent in this table because no Workshops are present in the Year 1444. But we can still calculate the hypothetical cost-efficiency of upgrading a Workshop to a Counting House.

The cost-efficiency of upgrading a Workshop to a Counting House is lower than constructing either of the buildings outright.

Also, except for Paris, Last profitable years occur before Counting Houses become available in the Year 1715, which means that upgrading Workshops to Counting Houses are not worth it for provinces other than Paris.

Tax Efficiency buildings and Production Efficiency buildings show similar rises in income per ducats spent. However, Tax income is cut by non-accepted cultures or religious intolerance, so tax buildings should only be built in provinces that have both appropriate culture and religion. Production income on the other hand is not affected by culture or religion.

Another perk of Production Efficiency buildings is that they synergise well with Manufactories - this is discussed in EU4 Advanced Economics 4. Manufactories.

State Maintenance buildings

Let's talk about buildings that reduce State Maintenance.


Courthouses become available at Admin Tech 8 (Year 1505), cost $100 and lower State Maintenance by 25%.


Town Halls become available at Admin Tech 22 (Year 1687), cost $200 and lower State Maintenance by 50%.

The formula for calculating State Maintenance is not explained clearly in EU4 Wiki.

"+0.007 per development level" is not a modifier. It is a base value upon which all other modifiers are applied (all modifiers are additive, not multiplicative).

For example, see Lyonnais in 1444 France:

Development of Lyonnais = 20
Modifier due to distance from capital (the formula for calculating distance from the capital is unknown) = +6.90%
Modifier due to producing Paper as a resource = -10%
So the formula for calculating the State Maintenance of Lyonnais is
(20 x 0.007) x (1 + 0.069 - 0.1) = 0.13566 per month.

With a Courthouse (-25% modifier), the formula will become
(20 x 0.007) x (1 + 0.069 - 0.1 - 0.25) = 0.10066 per month.

For 1444 France, this is the alignment given in-game when building a Courthouse, in the order of cost-efficiency:


This Excel table calculates the actual change in State Maintenance, for the top 10 provinces from this list:

• Existing modifiers = including distance from capital, bonus from resource etc.
  
• dSM = change in State Maintenance after constructing a Courthouse
  
• dSM/Cost = change in State Maintenance divided by the cost of a Courthouse ($100 - 5% from Renaissance Institution)
  
• ROI(yrs) = Return on investment. Number of years it takes for the building to start producing profit i.e. the number of years it takes to 'break-even'. Decimal points omitted. Note that the 1-year construction period is not considered, so you need to add 1 more year if you want to count from the construction start date.
  
• Last profitable year = the last date when the building can be finished and still expect a profit before the campaign ends in 1821. Not applicable in non-Ironman games. Cells highlighted in red mean that the last profitable year occurs before the building becomes available i.e. it's not worth building it. Decimal points omitted.

Apart from lowering maintenance costs, State Maintenance buildings have an added benefit of speeding up drops in province autonomy. Although a useful trait, it is not considered in the cost-efficiency analysis of State Maintenance buildings in this guide.

Predicted changes in State Maintenance (columns highlighted in green) are slightly inaccurate. For example, Predicted change for Orleanais should be displayed as 0.02 but is displayed in-game as 0.03 (remember that the game discards 3rd decimal points rather than rounding up or down).

Predicted order (columns highlighted in yellow) is accurate.

You can see that the cost-efficiency of a Courthouse is quite low compared to buildings that raise Tax/Production Efficiency. Considering that they become available in the Year 1505, there is only a small time window, during the 1500s, when you can build Courthouses and expect a profit.

Let's now look at Town Halls. This is the aligned list of cost-efficiency when building a Town Hall:

Note that this alignment is different from Courthouse. With Courthouse, Paris was at the top of the list, but here, Lyonnais is. Also, Nemours, 8th on the list for Courthouses, has dropped out of this list.

This is because with Paris and Nemours, building a Town Hall brings State Maintenance to 0. Since State Maintenance cannot be below 0, there is a cap on how much State Maintenance can be lowered. For example, in Paris, a Town Hall would bring State Maintenance down by 0.06 to 0. In Lyonnais, it will drop by 0.07. A Town Hall in Lyonnais therefore saves you more ducats than one in Paris.

The following is an Excel table that calculates the cost-efficiency of Town Halls:

• In the dSM/Cost column, the cost is set as $190 ($200 - 5% from Renaissance Institution).

Predicted increments (highlighted in green) and predicted order (highlighted in yellow ) are accurate.

The cost-efficiency of Town Halls are abysmal. They become available in the Year 1687, but the last profitable years occur before that, for the provinces used in this French example. Town Halls are not worth building in any of these provinces.

The following table is what happens when you upgrade a Courthouse to a Town Hall:

• In the dSM/Cost column, the cost is set as $90 ($100 - 5% from Renaissance Institution).

For all provinces in this table, the cost-efficiencies are too low to justify an upgrade. For example, imagine Paris has a Courthouse that is upgraded to a Town Hall as soon as Town Halls become available in the Year 1687. From 1688 (it takes a year for the construction) it will take 328 years to break even, in the Year 2016. This is after the campaign end date (Year 1821). A player is better off saving up the $100 rather than spending it on the upgrade.

In addition, as your empire expands, you may need to un-state existing States so that you can state newly conquered, more lucrative provinces. Any existing Courthouses / Town Halls will then lose value, as non-State provinces have 0 maintenance.

In order to maximise the utility of Courthouses and Town Halls, choose a state that is:

• Incurring high maintenance costs (eg. high development, far away from capital, have a State Edict).
  
• You don't plan to un-state it anytime soon.

Real example

So far I have been using 1444 France as an example. Let's load up a more realistic example so that we can verify our findings. This is my Venice > Italy Ironman game, in the Year 1653.


I mentioned previously that upgrading Tier 1 buildings to Tier 2 (eg. Church to Cathedral, Workshop to Counting House, Courthouse to Town Hall) are less cost-efficient than constructing Tier 2 buildings outright.

But this scenario suggests otherwise. When I try to build a Cathedral, the top 10 suggestions, from Crete to Pisa, are all upgrades (cost $192). Kirshehir, where building a straight Cathedral is suggested (cost $288), is only 11th on the list.


Why do upgrades dominate the list? There are two major reasons:

1. Some provinces may simply be out of building slots, so do not appear on the list. An example in my Italy game is Ferrara.


Ferrara does not have a Church. It would receive a tax income boost of $0.35 per month with a Cathedral (and therefore top the list by a big margin), but it does not have a spare building slot so is not on the list of suggested provinces.

2. If you have been investing regularly on constructions throughout your campaign, provinces that would benefit the most from Cathedrals would already have Churches built there.

Have a look at the distribution of Churches and Cathedrals in my Italian empire:

• Blue = Cathedral present
  
• Dark green = Church present
  
• Light green = neither Church/Cathedral present
  
• Yellow = neither Church/Cathedral present, no spare building slot

Churches and Cathedrals are concentrated in provinces with high development (northern Italy, Balkans, Egypt). Provinces with neither of those buildings (African coast, Anatolia and Crimea) have low Base Tax values, so even a Cathedral will not boost their tax incomes that much.

Kirshehir, being a relatively underdeveloped province, would definitely benefit from having a Cathedral built there, but the resulting boost in tax income will still not be as much as, say, upgrading the Church in Novara, a richer province in northern Italy.


As proof, I tried destroying existing Cathedrals in the northern Italy region:

Provinces such as Verona, Genoa and Milan now appear at the top of the list, proving that constructing Cathedrals outright is more cost-efficient than upgrading existing Churches.

Similar phenomena are observed with Production Efficiency & State Maintenance buildings.

To recap, upgrading Tier 1 buildings to Tier 2 is less cost-efficient compared to constructing Tier 2 buildings outright. However, in real game situations, upgrades may still dominate the top of the list of suggested provinces. Follow the list, and you will not go wrong.

Conclusion

• For Tax Efficiency, Production Efficiency and State Maintenance buildings, the predicted boosts in income are displayed (almost) accurately. The order of provinces given by the Buildings tab are accurate. Provinces at the top of the list should be prioritised when choosing a province to construct a building.
  
• 1st tier buildings (Church, Workshop, Courthouse) are often more cost-efficient compared to 2nd tier buildings (Cathedral, Counting House, Town Hall). Even if they have become obsolete, they can often boost your income more than their successors.
  
• Courthouses and Town Halls are far less cost-efficient compared to Tax/Production Efficiency buildings. It can take 200-300 years before they start producing returns. I say stay away from them unless you have run out of all other investment options.

To be continued in Part II.

Links to the rest of my guides: EU4 Advanced Economics
1. Province development
2. Buildings Part I
3. Buildings Part II
4. Manufactories
5. Light Ships

[Clausewitz]

Hey, just one thing: You treat courthouses and town halls only for their economic returns, but they have the benefit (for me the main one) of reducing the governing cost of of the province. I.e. they take less government capacity for states.
I understand You focus primarily on economic side, but
a) the second thing is worth at least noting (as mentioned before, for me the reduction of state maintenance is secondary benefit of this building at best)
b) less governing cost means You can have more states, which does impact Your economy. This is very hard to measure though.

[jddoty25]

Imagine using math for a video game
this post was made by a joke
this post IS a joke
please laugh I'm trying help

[Captain Izolenta]

Great work m8!