Research

This article is accurate for the latest versions of EU3, Napoleon’s Ambition and In Nomine v3.2.
Please help update this page to include information on the HTTT and DW expansions.

(For strategies relating to optimizing research, see Research Strategies.)

The research system in EU3 is pretty straightforward: the tech cost is a base cost with various modifiers. These modifiers depend on:

Early research penalty
Inflation
Number of provinces owned
Research multipliers (luck, domestic sliders, national ideas, decisions, government type, events, defender of the faith)
Technology group

The ability to invest in research is less easy because of the many sources of income. Broadly, it's based on two factors:

National Income
Neighbor bonuses

Research cost in HTTT

The overall formula is:

A breakdown of the various pieces follows. Note that the modifiers are expressed in percentages, so you must convert them to decimals when applying the formula above. (For example, if in-game you have 16% inflation, you would enter ".16") One happy consequence of the associative-ness of this formula is that you can simply consider all percentage impacts identically -- that is, 5% inflation will increase the total tech cost by the same amount as a tech cost penalty of +5%. (Or by 2 additional provinces if you're over 8, etc.)

This formula is exact, so note that the main source of error is likely to be the 'inflation' parameter. (The game stores this to three decimal places in the save file but only displays it in-game to one decimal place.) All fractional results of this formula are truncated in the game for display purposes. (5278.887 becomes 5278.) Be careful to correctly convert the decimals too: 2.5% = .025, not .25 or 2.5.

Base Cost

See the table below of associated tech years and the resultant base research costs for the normal 1399 start date (modders, take note!). The formula is:

These are the basic tech costs for each tech level which are modified by all the other factors below. Note that the [Year_NextTech - Year_Start] term can't go below 0.

Tech Level	Year	Cost	Year	Cost	Year	Cost	Year	Cost	Year	Cost
	Gov't		Production		Trade		Naval		Land
0	1300	0	1300	0	1300	0	1300	0	1300	0
1	1360	6300	1360	6300	1360	6300	1360	6300	1360	6300
2	1380	2100	1380	2100	1380	2100	1380	2100	1380	2100
3	1400	2112.6	1400	2112.6	1400	2112.6	1400	2112.6	1400	2112.6
4	1410	1119.3	1410	1119.3	1410	1119.3	1410	1119.3	1410	1119.3
5	1420	1182.3	1420	1182.3	1420	1182.3	1420	1182.3	1420	1182.3
6	1430	1245.3	1430	1245.3	1430	1245.3	1430	1245.3	1430	1245.3
7	1440	1308.3	1440	1308.3	1440	1308.3	1440	1308.3	1440	1308.3
8	1450	1371.3	1450	1371.3	1450	1371.3	1450	1371.3	1450	1371.3
9	1455	701.4	1465	2198.7	1455	701.4	1465	2198.7	1465	2198.7
10	1470	2245.95	1475	1528.8	1460	717.5	1475	1528.8	1475	1528.8
11	1485	2387.7	1485	1591.8	1470	1497.3	1485	1591.8	1485	1591.8
12	1495	1654.8	1495	1654.8	1480	1560.3	1495	1654.8	1495	1654.8
13	1497	333.48	1497	333.48	1490	1623.3	1497	333.48	1497	333.48
14	1498	167.37	1498	167.37	1495	827.4	1498	167.37	1498	167.37
15	1502	679.56	1502	679.56	1500	843.15	1502	679.56	1502	679.56
16	1508	1042.02	1508	1042.02	1510	1749.3	1508	1042.02	1508	1042.02
17	1518	1799.7	1518	1799.7	1520	1812.3	1518	1799.7	1518	1799.7
18	1530	2250.36	1530	2250.36	1530	1875.3	1530	2250.36	1530	2250.36
19	1540	1938.3	1540	1938.3	1540	1938.3	1540	1938.3	1540	1938.3
20	1545	984.9	1545	984.9	1545	984.9	1545	984.9	1545	984.9
21	1550	1000.65	1550	1000.65	1550	1000.65	1550	1000.65	1550	1000.65
22	1565	3143.7	1565	3143.7	1565	3143.7	1565	3143.7	1565	3143.7
23	1585	4443.6	1585	4443.6	1585	4443.6	1585	4443.6	1585	4443.6
24	1600	3474.45	1600	3474.45	1600	3474.45	1600	3474.45	1600	3474.45
25	1610	2379.3	1610	2379.3	1610	2379.3	1610	2379.3	1610	2379.3
26	1620	2442.3	1620	2442.3	1620	2442.3	1620	2442.3	1620	2442.3
27	1625	1236.9	1625	1236.9	1625	1236.9	1625	1236.9	1625	1236.9
28	1636	2797.41	1636	2797.41	1636	2797.41	1636	2797.41	1636	2797.41
29	1644	2074.8	1644	2074.8	1644	2074.8	1644	2074.8	1644	2074.8
30	1655	2929.08	1655	2929.08	1655	2929.08	1655	2929.08	1655	2929.08
31	1660	1347.15	1660	1347.15	1660	1347.15	1660	1347.15	1660	1347.15
32	1675	4183.2	1675	4183.2	1675	4183.2	1675	4183.2	1675	4183.2
33	1690	4324.95	1690	4324.95	1690	4324.95	1690	4324.95	1690	4324.95
34	1700	2946.3	1700	2946.3	1700	2946.3	1700	2946.3	1700	2946.3
35	1709	2702.7	1709	2702.7	1709	2702.7	1709	2702.7	1709	2702.7
36	1714	1517.25	1714	1517.25	1714	1517.25	1714	1517.25	1714	1517.25
37	1719	1533	1719	1533	1719	1533	1719	1533	1719	1533
38	1723	1236.48	1723	1236.48	1723	1236.48	1723	1236.48	1723	1236.48
39	1725	620.76	1725	620.76	1725	620.76	1725	620.76	1725	620.76
40	1727	623.28	1727	623.28	1727	623.28	1727	623.28	1727	623.28
41	1730	940.59	1730	940.59	1730	940.59	1730	940.59	1730	940.59
42	1732	629.58	1732	629.58	1732	629.58	1732	629.58	1732	629.58
43	1735	950.04	1735	950.04	1735	950.04	1735	950.04	1735	950.04
44	1737	635.88	1737	635.88	1737	635.88	1737	635.88	1737	635.88
45	1743	1930.32	1743	1930.32	1743	1930.32	1743	1930.32	1743	1930.32
46	1747	1296.96	1747	1296.96	1747	1296.96	1747	1296.96	1747	1296.96
47	1750	978.39	1750	978.39	1750	978.39	1750	978.39	1750	978.39
48	1755	1646.4	1755	1646.4	1755	1646.4	1755	1646.4	1755	1646.4
49	1760	1662.15	1760	1662.15	1760	1662.15	1760	1662.15	1760	1662.15
50	1765	1677.9	1765	1677.9	1765	1677.9	1765	1677.9	1765	1677.9
51	1770	1693.65	1770	1693.65	1770	1693.65	1770	1693.65	1770	1693.65
52	1775	1709.4	1775	1709.4	1775	1709.4	1775	1709.4	1775	1709.4
53	1780	1725.15	1780	1725.15	1780	1725.15	1780	1725.15	1780	1725.15
54	1785	1740.9	1785	1740.9	1785	1740.9	1785	1740.9	1785	1740.9
55	1790	1756.65	1790	1756.65	1790	1756.65	1790	1756.65	1790	1756.65
56	1791	351.96	1791	351.96	1791	351.96	1791	351.96	1791	351.96
57	1792	352.59	1792	352.59	1792	352.59	1792	352.59	1792	352.59
58	1795	1063.44	1795	1063.44	1795	1063.44	1795	1063.44	1795	1063.44
59	1798	1069.11	1798	1069.11	1798	1069.11	1798	1069.11	1798	1069.11
60	1801	1074.78	1801	1074.78	1801	1074.78	1801	1074.78	1801	1074.78
61	1803	719.04	1803	719.04	1803	719.04	1803	719.04	1803	719.04
62	1805	721.56	1805	721.56	1805	721.56	1805	721.56	1805	721.56
63	1807	724.08	1807	724.08	1807	724.08	1807	724.08	1807	724.08
64	1809	726.6	1809	726.6	1809	726.6	1809	726.6	1809	726.6
65	1811	729.12	1811	729.12	1811	729.12	1811	729.12	1811	729.12
66	1813	731.64	1813	731.64	1813	731.64	1813	731.64	1813	731.64
67	1815	734.16	1815	734.16	1815	734.16	1815	734.16	1815	734.16
68	1820	1851.15	1820	1851.15	1820	1851.15	1820	1851.15	1820	1851.15
69	1830	3765.3	1830	3765.3	1830	3765.3	1830	3765.3	1830	3765.3
70	1840	3828.3	1840	3828.3	1840	3828.3	1840	3828.3	1840	3828.3
71	1850	3891.3	1850	3891.3	1850	3891.3	1850	3891.3	1850	3891.3
72	1880	12230.9	1880	12230.9	1880	12230.9	1880	12230.9	1880	12230.9

Group Modifier

These are the penalties associated with the various tech groups.

Size Modifier

See this table of country size modifiers based on the number of provinces you own. The formula is:

This is a penalty adjusted for the size of your country (in provinces). The piecewise layout above indicates its somewhat unexpected nature; basically, the first two provinces add 20%, and every province after that (except province #6, which counts for double for some reason) is 10% until you reach 8 provinces--at which point you have a 100% penalty (that is, your costs are double that of a one-province nation). Any subsequent provinces will add 2.5% to this modifier per province.

Early Modifier

This is a 20% penalty for every year before a tech's associated start date (note that only whole years are counted). This "start date" is actually your current tech's nominal completion date, so if it's 1583 and you're researching Gov't 24, then since your current (23) tech level's associated date is 1585 you are two years early from the normal start and will get a 40% penalty; on January 1st, 1584, this will become a 20% penalty.

General Modifiers

These are all the various additional tech bonuses/maluses achievable in the game; all such effects simply add together.

- Sliders give +3%*(Innovative vs. Narrowminded) and -4%*(Serfdom vs. Free Subjects).

- The Scientific Revolution national idea gives a -10% effect.

- Defender of the Faith gets +20% trade & production tech cost modifiers.

- Tribal governments get a +50% penalty.

- Lucky nations get a -2% bonus (of course, the player can't normally be a lucky nation).

- Various decisions will give permanent effects, and various events will give temporary ones.

Also, note that in the game there are sometimes two different labels to modifiers -- "tech cost" and "tech cost modifier". The latter often reference specific tech categories (e.g., "land tech cost modifier") and apply uniquely to them, but may be added to the former in the calculation as if there were no distinction.

Inflation

This is pretty self-explanatory -- the country's inflation rate as reported in the game. (Better if from the save file, but your error is likely to be very small if you just take it from the budget screen.)

Example

In October 1688, an 11-province Netherlands is researching Gov't 34, Land 34, Naval 31, Production 30 and Trade 31.

8.000% inflation
(-4) Innovative vs. Narrowminded and (+2) Serfdom vs. Free Subjects
enacted the Importation Act decision (+6% tech cost)
just got the Colonial Ventures event in August (-2% naval tech cost modifier for 120 days)
Defender of the Faith for the Reformed faith (+20% production & trade tech cost modifiers)

Thus, the research costs in-game are:

Gov't 34:	8319	(8319.349)
Prod. 30:	7220	(7220.475)
Trade 31:	3320	(3320.859)
Naval 31:	2656	(2656.688)
Land 34:	8319	(8319.349)

Research cost in IN

Formula for research cost equation in IN is (individual parameters discussed below):

Early research penalty * tech date modifier * country size modifier
* (tech date - previous tech date)
* ((100 + modifiers from scientific method, sliders, decisions, defender of faith and luck)/100)
/ tech group * (1 + inflation/100)

Base costs (IN)

Early research penalty modifier is:

(1+n/5),

where n is number of years early. The average year for each tech level is listed in the Tech tree. The average tech level date is the year in which research for that tech level should be completed, not started. Therefore there is no early research penalty as long as the date is greater than or equal to the average tech level date of the previous tech level. For example: Tech 21 has a date of 1550 and Tech 22 has a date of 1565. If the current date is 1550 or later, then there is no early research penalty for Tech level 22.

Technology date modifier is an addition that came with IN and it makes every next tech relatively more expensive. For example, this modifier is just a bit more than a hundred (111.89) when researching tech level 4, double that: 222.14 at tech level 23, and 407.99 for tech 72. It can be calculated by this equation:

Tech date multiplier = ((date assoc. with next tech
- 1232.4) * 0.63).

Country size modifier: the more provinces owned, the greater the multiplier to cost of research. In IN there is no cap for it while EU3 and NA had a cap of 89 provinces. It is calculated using data from table in the Research Cost - Supporting Data, and equation is:

Country size modifier = (data point for x size country)
/(data point for 1 province sized country),

where x is number of provinces a country has (note: colonies that are not cities yet do not count, as they do not increase tech cost).

Research multipliers: The research multipliers are based on the sum of the affects of the Innovation slider, the Serfdom slider, the Scientific Revolution National Idea, Defender of the Faith, Decisions and Lucky nation. The Defender of the Faith "bonus" (actually a penalty) only applies to the Trade and Production technologies. The "bonus" is a 20% increase in research costs. (This is defined in static_modifiers.txt). The Lucky nation bonus only applies to Lucky nations (which can only be AI nations). The bonus is a 2% decrease in research costs. Technology groups: The Latin tech group is the best since it essentially has no effect on research cost. All other tech levels, however, have very significant penalties on research costs, since the total cost can increase by 11 - 99% depending on the tech group. For this reason, any nation not in the Latin tech group should focus all effort on the Westernization national decision as soon as possible.

Inflation: Inflation raises the cost of all goods, including research costs.

Research cost in EU3 and NA

The full research cost equation in EU3 and NA is (individual parameters discussed below):

province cost * (tech date - previous tech date) * early research penalty
* ((100 + centralization + innovative + scientific method + defender of faith + luck)/100)
/ tech group * (1 + inflation/100)

The early research penalty is determined by:

Revised Cost = Base Cost * ( 1 + n^2 / 20 )
(where n = the number of years early)

Base Costs (EU3 and NA)

Provinces: The more provinces owned, the greater the cost of research. See the table below for cost per province. The maximum base cost per year is 500 in EU3 and NA, so adding additional provinces after 88 are "free" from a research cost point of view. In IN, however, there is no maximum base cost.

Technology Year: The average year for each tech level is listed in the Tech tree. The average tech level date is the year in which research for that tech level should be completed, not started. Therefore there is no early research penalty as long as the date is greater than or equal to the average tech level date of the previous tech level. For example: Tech 13 has a date of 1550 and Tech 14 has a date of 1565. If the current date is 1550 or later, then there is no early research penalty for Tech level 14.

Research multipliers: The research multipliers are based on the sum of the affects of the Innovation slider, the Centralization slider, the Scientific Revolution National Idea, Defender of the Faith, and Lucky nation. The Defender of the Faith "bonus" (actually a penalty) only applies to the Trade and Production technologies. The "bonus" is a 20% increase in research costs. (This is defined in static_modifiers.txt). The Lucky nation bonus only applies to Lucky nations (which can only be AI nations). The bonus is a 2% decrease in research costs. Technology groups: The Latin tech group is the best since it essentially has no effect on research cost. All other tech levels, however, have very significant penalties on research costs, since the total cost can increase by 10 - 90% depending on the tech group. For this reason, any nation not in the Latin tech group should focus all effort on the "Westernization" national decision as soon as possible.

Inflation: Inflation raises the cost of all goods, including research costs.

Research Investments

National Income:

Neighbor bonuses: Within each technology group, every nation except the tech leader receives a neighbour bonus. This is calculated using the difference between your tech level and the tech level of the tech leader within your technology group. If you receive no neighbour bonus when you mouseover your sliders from the treasury screen, then you are the tech leader for your technology group.

Research Cost Examples (EU3 and NA)

Manchu Example: 74 provinces, researching tech level 15, year 1777 (no early research penalty), centralization bonus = 0, innovative bonus = 8 (this is actually a penalty), does not have scientific method, is not defender of the faith, is not a lucky nation, Chinese tech group, inflation of .2

456.2 * (1585 - 1565) * (1 + 0^2/20) * ((100 + 0 + 8 + 0 + 0 + 0)/100) / .4 * (1 + .2/100) =
456.2 * 20 * 1 * 1.08 / .4 * 1.002 = 24684.07

Spain Example: 175 provinces, researching tech level 38, year 1747 (9 years early), centralization bonus = 0, innovative bonus = 2 (this is actually a penalty), has scientific method, is defender of the faith, is not a lucky nation, Latin tech group, inflation of 0

Government Tech:
500 * (1747 - 1743) * (1 + 9^2/20) * ((100 + 0 + 2 - 2.5 + 0 + 0)/100) / 1 * (1 + 0/100) =
500 * 4 * 5.05 * .995 / 1 * 1 = 10049.5

Trade Tech: (defender of faith penalty only applies to Trade and Production techs)
500 * (1747 - 1743) * (1 + 9^2/20) * ((100 + 0 + 2 - 2.5 + 20 + 0)/100) / 1 * (1 + 0/100) =
500 * 4 * 5.05 * 1.195 / 1 * 1 = 12069.5

Note: there are several potential rounding errors in this equation, the primary 2 being inflation and the province cost. Therefore you may not get the exact in-game cost using this equation, but you should be very close.

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