Manpower Maths Revisited

[Dinner]

The following was copied word for word from the Europa Universalis forum and was done so because it might increase players understanding of the game.
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Inspired by a game playing Tibet, I've been looking at the concept of manpower as implemented in EU2. Since I couldn't find a FAQ on this subject, I decided to set up a series of experiments involving save-game mutilation to solve the mystery of how the various factors interface. I ended up with a rather elegant equation that appeals to the mathematician in me, and decided to spread the gospel

The text has been updated based on feedback on the first draft of this article: paragraph 1.1 has been thoroughly revised, and two sections have been added (sections 6 and 7). Special thanks to jdrou who mercilessly eliminated my region theory used to explain which provinces would supply manpower - and came up with some constructive ideas.

Index:
1 Province Manpower Factors
2 Province Manpower Equation
3 Conclusions
4 Total Manpower
5 Manpower Myths Laid to Rest
6 Manpower and Colonisation
7 Manpower and Conquest
8 Province Manpower Tables

Enjoy,
Peter Ebbesen.



1 Province Manpower Factors

First let us consider the manpower of individual provinces. This figure can easily be obtained by reading the ledger (13:Taxation & Production Breakdown and 31:Non-Colonial Provinces), though all figures are rounded up to one decimal precision, or inspecting a given province, in which case the number is rounded down to integer precision.

Given the findings below (that the manpower fraction is always 1/4, 1/2, 3/4, or 0) this means that the ledger will always read a whole number plus a decimal which is one of {0, 3, 5, 8}, such as 1.3, 0.5, 2.8 and so on and so forth.


1.1 Capital location

The provinces in which you can potentially receive manpower are based on the location of your capital.

You will gain manpower from any provinces you own on the same continent as your capital, the continent of a province being defined in province.csv.

You will also gain manpower from any province you own with road access to your capital.

Continents by regions




Africa (East Africa, North Africa, and West Africa)

America (Central America, North America, South America, and the Carribean)

Asia (Central Asia, China, India, Indochina, Indonesia, Japan, Middle East, and Siberia)

Europe (British Isles, Central Europe, Eastern Europe, HRE, Scandinavia, Southern Europe, and Western Europe)

Oceania (Australia, Pacific)


In other words, the border between Europe and Asia runs (North to South, European provinces): Orenburg - Astrakhan - Daghestan - Kurdistan - Sivas - Adana.

Thus, if your capital is on an island in Europe, like England, Scotland, Eire, Wales, Corsica, Sardinia, Cyprus, the Knights, or any of that crowd, you won't really gain any manpower from colonisation - except for the Azores and the Canary Islands, which count as European. Don't count on Greenland, since it is lumped as part of the American continent.

Anyways, more about colonisation and manpower in part 6.

When talking about province manpower from now on, it is assumed that the province is one that the country is eligible to receive manpower from. Otherwise it is a flat zero.


1.2 Basic manpower

Every province has a basic manpower defined in province.csv (fifth number before the type of good produced in the province). It is a positive integer (except for Terra Incognita which has manpower 0), and is the base for all that is to follow. This figure cannot be found anywhere but province.csv, since it isn't listed in any ledger or shown when inspecting a province, which is a shame. I'll denote the basic manpower mBase.


1.3 Events

The basic manpower is modified during play by the random events 'new land claimed', 'agricultural revolution', and 'establish cantonments' (1.05), and a very few nation specific events. I'll denote the modifier by events mEvent.

Note that once a province has had its manpower modified by an event, you can read the modified manpower mBase + mEvent in the save file as part of the province information.


1.4 Population size

The population of a province has an enormous impact on the available manpower applying a percentage modifier to mBase + mEvent. I'll denote this percentage pPop. The modifiers are as follows:


code:--------------------------------------------------------------------------------
Population pPop
---------------------
0- 699 0.00
700- 20000 0.25
20001-200000 0.50
200001-999999 0.75
--------------------------------------------------------------------------------



1.5 Culture

Manpower is also affected by culture. Arguably, culture is the single strongest component in determining the manpower of a province - at least if the province in question has the wrong culture Following multiplying the base manpower by the population percentage modifier, one should add the culture modifier. I'll denote the culture modifier mCul, and it is defined as follows:


code:--------------------------------------------------------------------------------
Culture mCul
-----------------------
State culture 0.0
Non-state culture -2.0
--------------------------------------------------------------------------------



1.6 Conscription center

A conscription center in a province usually has a huge impact on the manpower of a province. Experiments reveal that the province manpower modified for events, population, and culture is subjected to a simple linear transformation in provinces with a conscription center, irrespective of whether it is one of your core provinces or not. If the transformation returns a negative number, which is possible in non-state cultured provinces with low population and/or base manpower, a result of zero manpower is substituted. In other words, a conscription center is not guaranteed to increase your manpower.

State cultured provinces with a high population, high manpower, and a conscription center can supply immense amounts of manpower.


code:--------------------------------------------------------------------------------
Conscription pCon mCon
--------------------------
Present 3.0 1.0
Not present 1.0 0.0
--------------------------------------------------------------------------------



1.7 Nationalism

As of 1.05 manpower is also reduced by nationalism. Experiments show that nationalism reduces manpower by a constant, which I will denote mNat.


code:--------------------------------------------------------------------------------
Nationalism mNat
----------------------
No nationalism 0.0
0-10 years left 0.0
10-20 years left 0.0
20-30 years left -1.0
--------------------------------------------------------------------------------



2 The Province Manpower Equation

To summarize. The following factors affect the manpower of a province:



mBase, the base manpower, from province.csv

mEvent, modifications from events, additive

pPop, a multiplier dependant on population size

mCul, a modifier based on culture

pCon and mCon, two modifiers depending on the existence consciption center

mNat, a modifier for nationalism



Thus, and without further ado, I present the province manpower equation:


manpower = pCon * ((mBase + mEvent)* pPop) + mCul) + mCon + mNat


If the calculated manpower is negative due to non-state-culture, a low mBase + mEvent, or nationalism or whatever, it is set to zero.

As is clear to the observant reader, the only fractions possible are fourths, since pCon, mBase, mCul, and mCon are natural numbers, and pPop is either 0, 1/4, 2/4, or 3/4.

The manpower equation has been applied to the most typical situations, and the results can be found in the tables in section 6.


3 Conclusions

A state cultured province in a location eligible for manpower will always supply some manpower.

However, a non-state cultured province will only add to your manpower from a certain base manpower modified by events,

code:--------------------------------------------------------------------------------
Without conscription center:

700- 20000: mBase + mEvent >= 9
20001-200000: mBase + mEvent >= 5
200001-999999: mBase + mEvent >= 3


With a conscription center:

700- 20000: mBase + mEvent >= 7
20001-200000: mBase + mEvent >= 4
200001-999999: mBase + mEvent >= 3

--------------------------------------------------------------------------------


Given that outside Europe manpower greater than 3 or 4 is uncommon, it is no wonder that colonising is the way to prosperity for Asian minors with quaint few-province cultures - though there are exceptions. Isfahan with a Centre of Trade, high population, and a base manpower of 10, is a prize for anyone. With a conscription center, Isfahan can supply Persia with a whopping 23.5 manpower once it passes 200,000 people, and without it is still worth 5.5 manpower to total strangers that can draw manpower from the Middle East.)


4 Total Manpower

The manpower and the sum of province manpower can be read in the ledger. This value is modified by your domestic policy slider setting for quality, ranging from a +50% bonus at full quantity, to a -50% malus at full quality. This modified number is your total manpower. It represents how many recruits are added to your manpower pool every year (the manpower pool is limited in size to twice your total manpower), and is also added directly to your support limit (beyond your support limit, seen on the army screen, you pay extra for support of your troops).

In effect, full quantity allows you to recruit three times as many soldiers per year as full quality, and at a reduced price for infantry and cavalry, making quantity attractive both for nations with high manpower who can afford to send neverending waves of soldiers at their enemies and for smaller nations that desperately need manpower to replenish losses.


5 Manpower Myths Laid to Rest

Experiments have now shown, that

1) There is no manpower bonus for the capital province.

2) Religion has no influence on manpower whatsoever (except that converting pagans gives them your state culture, but that is a different matter)

3) Core/noncore status has no effect on manpower, save for allowing conscription centres to be built

4) Manpower is independent of difficulty level and aggressiveness setting

5) The location of a province being on the same continent as the capital is a sufficient, but not necessary, condition for supplying manpower.


6. Manpower and Colonisation

Most colonisable provinces supply the bare minimum manpower of 1. Since a province of 1,000 men supplies as much manpower as one of 19,999 one should definitely go for many small provinces rather than keep building up a few, with the possible exception of a CoT likely or enormously wealthy province like Jakarta. (Throwing excess settlers at Jakarta as well as a manufactory and a mayor will yield one very high income province a century or two down the road - but shouldn't be done at the expense of colonising virgin territory.)

For European nations colonisation supplies very little manpower unless they gain road access to India or Siberia and begin colonising. That being said, there are an awful lot of Siberian provinces, and it does add up. And for 'It All Belongs to the Dark Side' Russia, there is no excuse for not colonising the corridor.

For Asian nations, gaining an early foothold in Southern India and Indonesia will do wonders for their manpower, and they can then colonise the Siberian corridor later on.

Incas and colonisation. As any Inca player will know, once you've killed off the Chimu by 1421, you've got at least seven decades of loneliness ahead of you - no neighbours, no explorers, no conquistadors, no nothing. Spend these decades colonising the two uncolonised provinces and adding settlers to your own non-gold provinces. You will want to raise the population and thus the non-gold tax and production income as soon as possible, and it will help your manpower as well in a few centuries. You can colonise up to 5,000 inhabitants and at an average 6 percent growth rate per decade, they will cross the 20,000 manpower boundary approximately 240 years later - which is very nice (by that time you should, hopefully, have colonised at least two thirds of the Americas, and you might be facing some stiff fights). The provinces near Cuzco will grow much faster, of course. Go naval and crank out those settlers - and get more explorers (vital).


The uncomplete list of colonisable provinces with manpower greater than one:

Within each region the provinces are sorted first by manpower, then alphabetically within manpower equivalence classes.



Africa: If you can colonise it, it is probably manpower 1.

The Americas: Who cares. If you're living here you should be colonising every single province from the coast inwards to keep out those pesky Europeans rather than worry about manpower. There are a large number of manpower 2 provinces in Eastern North America - from the Mississippi eastwards, and a few in Western North America, and rest of the colonisable Americas is, with a very few exceptions such as Pampas del Sur(3), all manpower 1 provinces.

India: Bombay(2), Cochin(2), Goa(2), Kerala(2), Palakimedi(2), Pondicherry(2)

Indonesia: Bandung(3), Jakarta(3), Bandjarmasin(2), Flores(2), Jambi(2), Mindanao(2), Palawan(2), Palembang(2), Salabanka(2), Sarawak(2), Selatan(2), Sulawesi(2), Sumbawa(2)

Siberia: Surely you are joking. Manpower 1 across the board




7. Manpower and Conquest

These target lists assume that you fulfill the requirements for receiving manpower from a province.

Very High priority targets:



Any state cultured province

Any province with a conscription center and positive manpower


High priority targets, sorted by location:



England, specifically Anglia(8)

Russia, specifically Moscow(12 !), Novgorod(8), Vladimir(8), Nizhgorod(6), and a boatload of five manpower provinces

Southern and Western Europe - more high manpower provinces than you can shake a stick at. Especially in Italy, France, and Germany

Persia, specifically Isfahan(10), Tabaristan(10), Baluchistan(5), Fars(5), Hamadan(5), Hormouz(5), Mekran(5), Tabriz(5). Note to the various hordes: Move south to gain manpower

India, specifically Hyderabad(6), Maharashtra(6), Mysore(6), Awadh(5), Delhi(5), Malwa(5), Rajputana(5).

Nippon, actually not that high base values, a single fiver and some fours, but the high population size is enough to put them on the hit list - if your capital is in Asia

Egypt, Alexandria(6), Delta(6), Egypt(6), Nile(6)

Songhai and Kongo, a few five and six manpower provinces. For the truly desperate.



Medium priority targets:

Whatever remains of Europe that wasn't covered above

Low priority targets:

The rest of the world (*), including China, which warrants an explanation. While China has a large total manpower pool in the hands of China or Manchuria, it is of little help to foreigners since it is caused by a lot of manpower 3 and manpower 4 provinces, which will only supply manpower to foreigners when the provinces pass 200,000 population. This will happen eventually, but for a large part of the game they will supply zero manpower to a conqueror.

(*) That is, low priority with respects to manpower. Feel free to conquer the rest of the world for other reasons. Manifest destiny or megalomania comes to mind.


8 Province manpower tables

Using the equation derived above, I have made the following tables. Their predictions are in accord with observed evidence as of 1.05 (or until one of you sharp-eyed folks finds an exception or a typo). They assume that nationalism has died down to the level than mNat=0


code:--------------------------------------------------------------------------------
Population 700-20000

mBase | SC SC/Con | NonSC NonSc/Con
--------------------------------------
1 | 0.25 1.75 | 0.00 0.00
2 | 0.50 2.50 | 0.00 0.00
3 | 0.75 3.25 | 0.00 0.00
4 | 1.00 4.00 | 0.00 0.00
5 | 1.25 4.75 | 0.00 0.00
6 | 1.50 5.50 | 0.00 0.00
7 | 1.75 6.25 | 0.00 0.25
8 | 2.00 7.00 | 0.00 1.00
9 | 2.25 7.75 | 0.25 1.75
10 | 2.50 8.50 | 0.50 2.00


Population 20001-200000

mBase | SC SC/Con | NonSC NonSc/Con
--------------------------------------
1 | 0.50 2.50 | 0.00 0.00
2 | 1.00 4.00 | 0.00 0.00
3 | 1.50 5.50 | 0.00 0.00
4 | 2.00 7.00 | 0.00 1.00
5 | 2.50 8.50 | 0.50 2.50
6 | 3.00 10.00 | 1.00 4.00
7 | 3.50 11.50 | 1.50 5.50
8 | 4.00 13.00 | 2.00 7.00
9 | 4.50 14.50 | 2.50 8.50
10 | 5.00 16.00 | 3.00 10.00


Population 200001-999999

mBase | SC SC/Con | NonSC NonSc/Con
--------------------------------------
1 | 0.75 3.25 | 0.00 0.00
2 | 1.50 5.50 | 0.00 0.00
3 | 2.25 7.75 | 0.25 1.75
4 | 3.00 10.00 | 1.00 4.00
5 | 3.75 12.25 | 1.75 6.25
6 | 4.50 14.50 | 2.50 8.50
7 | 5.25 16.75 | 3.25 10.75
8 | 6.00 19.00 | 4.00 13.00
9 | 6.75 21.25 | 4.75 15.25
10 | 7.50 23.50 | 5.50 17.50

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EU2 AARs
WAAR of the Worlds - Maximum fortresses in 1530? Surely you are joking....
It Came From the Mountains - Tibet: Does This Herald A New Ice Age?
The Righteous BastAARds - Castile: Two Can Play That Game. *Now featuring slippergrams*
The Timurid Scientists - (completed) Winner of the first "Funniest AAR" OscAAR.
World Conquest for Dummies - (completed) Winner of "Best Completed AAR, Feb-May 2002" OscAAR

Various Useful Links
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Manpower Maths Revisited