The neighbor bonus is a stream of technological direct investment that a country receives for free, simply by being lower tech than its neighbors. "Neighbors" in this sense is a bit obscure: it is not physically bordering countries, but rather, sets of countries (called techgroups; see below) that are established by the game. When one country in a techgroup gets ahead, its progress tends to "drag up" all the other countries in its techgroup, especially smaller countries that are more than 2 levels behind.
A country's techgroup is a set of countries that are related to each other in sharing tech levels to a certain degree. There are five techgroups in the game: latin, orthodox, muslim, china, and exotic.
Techgroups are named mainly for religions, and often the countries making up a techgroup have similar locations and religions, but there is no necessary connection. For example, the "latin" techgroup in 1419 has most Catholic countries in it, but it also contains one Sunni country (Granada), and it does not contain Lithuania, which is Catholic. The china techgroup in 1419 contains China and most of its neighbors, but it also contain Benin and some other pagan African countries.
Each country is assigned to a techgroup, normally as it is defined in revolt.txt, although a scenario may override that definition. For the most part, the techgroup a country is in cannot change. Although events may move a country to another techgroup, there are no random events which do this, and only a few countries that may move by scripted events. One example is China, which may be promoted from the "china" techgroup to the "muslim" techgroup in the event they get after Zheng Ho's voyages, if they make the non-historic "Outward Expansion" choice.
In addition to the determining which countries a country potentially can get neighbor bonuses from, techgroup also determines a number used in the calculation of neighbor bonus, called "NMR". (Nobody knows what that stands for.) This is as follows:
Techgroup NMR --------- --- Latin 1.0 Orthodox 0.9 Muslim 0.8 China 0.6 Exotic 0.1
Computing Neighbor Bonuses
Neighbor bonuses for a country are calculated for each of the four tech fields separately, as follows. First, the difference D between the country's level in that tech, and that of the most advanced country in the same techgroup, is determined. (If the country is the leader, the difference is of course zero.)
D = (Highest tech in the country's techgroup) - (country's tech)
If D>2, then the neighbor bonus is:
(D^2 + 8*D + (#countries_in_techgroup / 8)) * NMR / (2 * size_modifier)
If D<=2, then the neighbor bonus is:
(8*D + (#countries_in_techgroup / 8)) * NMR / (2 * size_modifier)
Finally, there is a maximum neighbor bonus in each tech field, 25d per month.
The #countries_in_techgroup used in the calculation is the number of countries currently in the game in that techgroup. The size modifier used for computing the neighbor bonus is determined by the number of cities (pop 1000+) the country has:
1 1.0 2 1.2 3 1.4 4 1.5 5 1.6 6 1.8 7 1.9 8 2.0 9+ 2.0 + 0.025 per city over 8