Research cost
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[edit] Research Costs
The cost of research is based on many factors: The number of provinces you own, the time between tech level dates, the current date relative to the tech level date, research multipliers, tech group, and inflation.
The full research cost equation 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 average year for each tech level is listed in the Tech tree.
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 (which is really 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, so I haven't explicitly tested this factor myself). The bonus is a 2% decrease in research costs.
The tech groups are:
| Group | Multiplier |
|---|---|
| Latin | 1.0 |
| Eastern | 0.9 |
| Muslim | 0.8 |
| Indian | 0.5 |
| Chinese | 0.4 |
| African | 0.2 |
| New World | 0.1 |
Note that the inflation is rounded for display (i.e. actual inflation of 1.588 will display as 1.6)
The base cost per year is based on the number of provinces you own. See the table below cost per province. The maximum base cost per year is 500, so adding additional provinces after 88 are "free" from a research cost point of view. This cost is then multiplied by the number of years between the tech level data and the previous tech level date.
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 >= 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.
The early research penalty is assessed by modifying the base research cost according to the following formula :
Revised Cost = Base Cost * ( 1 + n^2 / 20 ) (where n = the number of years early)
Example 1: Manchu, 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
Example 2: Spain, 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.
See Research Cost - Supporting Data
[edit] Province Cost
The following table shows the cost of research based on the number of provinces owned:
| Provinces | Cost/year | Verified |
|---|---|---|
| 1 | 125 | * |
| 2 | 150 | * |
| 3 | 175 | * |
| 4 | 187.5 | * |
| 5 | 200 | * |
| 6 | 225 | * |
| 7 | 237.5 | * |
| 8 | 250 | * |
| 9 | 253 | * |
| 10 | 256.3 | * |
| 11 | 259.4 | * |
| 12 | 262.52 | |
| 13 | 265.64 | |
| 14 | 268.76 | |
| 15 | 271.8 | * |
| 16 | 275 | * |
| 17 | 278.12 | |
| 18 | 281.3 | * |
| 19 | 284.42 | |
| 20 | 287.54 | |
| 21 | 290.66 | |
| 22 | 293.78 | |
| 23 | 296.9 | |
| 24 | 300.02 | |
| 25 | 303.14 | |
| 26 | 306.2 | * |
| 27 | 309.2 | * |
| 28 | 312.32 | |
| 29 | 315.44 | |
| 30 | 318.56 | |
| 31 | 321.68 | |
| 32 | 325 | * |
| 33 | 328.12 | |
| 34 | 331.24 | |
| 35 | 334.36 | |
| 36 | 337.48 | |
| 37 | 340.6 | |
| 38 | 343.72 | |
| 39 | 346.84 | |
| 40 | 349.96 | |
| 41 | 353.08 | |
| 42 | 356.2 | |
| 43 | 359.32 | |
| 44 | 362.44 | |
| 45 | 365.56 | |
| 46 | 368.68 | |
| 47 | 371.8 | |
| 48 | 374.92 | |
| 49 | 378.04 | |
| 50 | 381.16 | |
| 51 | 384.28 | |
| 52 | 387.4 | |
| 53 | 390.52 | |
| 54 | 393.64 | |
| 55 | 396.76 | |
| 56 | 399.88 | |
| 57 | 403 | |
| 58 | 406.12 | |
| 59 | 409.24 | |
| 60 | 412.36 | |
| 61 | 415.48 | |
| 62 | 418.6 | |
| 63 | 421.7 | * |
| 64 | 424.82 | |
| 65 | 427.94 | |
| 66 | 431.06 | |
| 67 | 434.18 | |
| 68 | 437.3 | |
| 69 | 440.42 | |
| 70 | 443.54 | |
| 71 | 446.66 | |
| 72 | 449.78 | |
| 73 | 452.9 | |
| 74 | 456.3 | * |
| 75 | 459.42 | |
| 76 | 462.54 | |
| 77 | 465.66 | |
| 78 | 468.78 | |
| 79 | 471.9 | |
| 80 | 475.02 | |
| 81 | 478.14 | |
| 82 | 481.26 | |
| 83 | 484.38 | |
| 84 | 487.5 | |
| 85 | 490.62 | |
| 86 | 493.74 | |
| 87 | 496.86 | |
| 88 | 499.98 | |
| >=89 | 500 | * |
* These numbers were verified in-game. The remaining numbers are an estimate based on an increase of 3.12 per province. The 500 maximum was verified with nations that were much larger than 89 provinces. So while the 500 maximum has been verified, the fact that it is reached at 89 provinces is based on the estimated increase of 3.12.
