Research point generation

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Originally posted and researched by Fawr here. Expanded and simplified.

The Short Story

You can increase the amount of RPs that you gain by converting some of your POPs into clerks, clergy, officers, capitalists & aristocrats. Non-national pops are not included in the calculation. The % of your national population that is of each type is the critical detail; the number of POPs doesn't matter. After you get the Darwin invention clerks become 25% better and clergy becomes 25% worse.

The literacy rate also increases RPs gained, as does the education slider. This means that paying for education gives you a long-term bonus as well as a short-term bonus.

The Long Story

RP, or Research Point, is a representation of you nation's effort in research.

The exact formula is:

{RP gain} = {base RP gain} * (0.5 + {literacy}/2) * {education spending} * {civilized modifier} * {education modifier}

{literacy} is the number shown in the last window of your country tab. The factor involving literacy can range from 0.5 to 1. When you fund education over 50% literacy increases, when you underfund it it decreases every month. Improving literacy is a lenghty process so you are stuck with a low modifier if you happen to start with a low educated country. 85 years of game span is not enough to build it from zero to max.

{education spending} is the amount of money you spend on education. It's controlled by the slider in the budget tab. Only 100% spendings allow you to get the maximum out of your research base. You can lower education spendings for a while in times of an emergency but as research is so important this is not advisable. This factor can range from 0 to 1 so you can even completely stop RP generation if you don't fund education at all.

{civilized modifier} is 1 for civilized countries and 0.1 for uncivilized ones, so uncivs get ten times less RP's than civilized nations.

{education modifier} starts at 1 and two techs: Positivism (4202) and Functionalism (4203) give a bonus of 0.1 each after they are researched. Thus the education_modifier, as it is named in the savefile, can range from 1 to 1.2.

If you are unsatisfied with your researching speed at max funding and current literacy you need to promote some of your pops to different ones, better suited for research. The formula for base RP gain is:

{base RP gain} = (sum of {POP type size} * {POP type modifier}) / {total size of national POPs} * 0.75

or if you want:

{base RP gain} = (sum of {%POP type} * {POP type modifier}) * 0.75

{%POP type} is a percentage of national culture POP type population in your total national culture population. Note that POP size is something different than population (as shown in the population window in country tag). Population = {total size of POPs} * 4.

{POP type modifier} is as follows:

POP type modifier
slaves 0
farmers, labourers, soldiers, craftsmen 1
aristocrats 2
capitalists, officers, clergymen after Darwinism 3
clerks and clergymen before Darwinism 4
clerks after Darwinism 5

There is a difference after Darwinism invention is triggered. Clerks contribute 25% more, while clergymen contribute 25% less. In 1.03 it used to be twice as much for clerks and almost nothing for clergymen.

With those two techs researched and a nation full of clerks it's possible to have 3.6RP a month and after Darwinism 4.5RP a month. In normal conditions it should be doable to exceed 1RP a month by promoting big national pops to clerks and small national pops and/or minorities to craftsmen. Clergy is useful for underindustrialized nations (they don't work so there is no need to have factory slots to avoid migration/emigration) and government types that suffer from high plurality like absolute monarchies (due to consciousness reducing effect) but after Darwinism they are even less useful. Slaves, if you happen to have any national culture ones, are terrible for research. Should be gotten rid of ASAP, abolishing slavery is best of course.

If your population consists of farmers only you get 0.75RP a month at max literacy and max spending. To keep researching one tech each year you need 0.83RP a month (0.96RP/month for techs of the fourth circle and 1RP/month for techs of the fifth circle). Everything above it can be used to trade techs or if the surplus is minimal it may be stored for the future. After researching Positivism and Functionalism the amount of 0.83RP/month with only farming population is reached at 85% literacy.

Country consists of 4 POPs, before Darwinism, 60% literacy, 100% education spending, civilized.
Aristocrat POP, size 1k: 2 * 1k = 2k
Soldier POP, size 50k: 1 * 50k = 50k
Non-national craftsmen POP, size 20k: completely ignored
Clerk POP, size 5k: 4 * 5k = 20k
Sum of POP type * modifier: 2k + 50k + 20k = 72k
Total size of national POPs: 1k + 50k + 5k = 56k
RP gain = (0.5 + 0.6/2 = 0.8) * 72k / 56k * 0.75 = 0.77RP a month

I tested the stuff above with a 1 state country (no colonies). POPs in colonies could behave differently.