sturmvogel said:
I expected Portugal's population to increase, not decrease, using your system. I think you incorrectly used the most adverse divisor because Portugal's population was about 20% of Spain's in 1600 in reality and it keeps that ratio in the 1600 game data you've provided. 790,000 for Spain in game terms and 165,000 for Portugal. But you've given Portugal 26,500 population in 1419, which is just a hair short of one tenth the size of the 256,000 for the provinces that would form Spain. Since both nations would grow at the same rates, barring events like the various expulsions, that would mean that Portugal would still be a bit short of one tenth the size of Spain in 1600.
To restate the issue you've divided the Spanish 1600 EU population by roughly one third to get the 1419 data, but you've divided the Portugese data by one sixth to derive their starting population. So I think that their population total in 1419 should almost double to 52,000 or so. Perhaps 27,000 in Tago, 17,000 in Porto and 9000 in Algarve.
Now we haven't fine tuned the expulsion events, but they're going to greatly complicate our efforts to get the populations of these two countries to remain in balance since anywhere between 60,000 and 100,000 Jews fled Spain to Portugal in 1492 and some 275,000 - 300,000 Moriscos left Spain for North Africa in 1571.
Another issue is that I'm not sure exactly what territories were included in the Portugese data. It could well include Madeira, the Azores, the Cape Verde Islands and Tangiers/Ceuta, which would again greatly complicate things, or maybe not since the census was conducted by the Spanish Crown.
At any result I think we'll have to run 3 or 4 test games once we finalize the population events to ensure that we have the right figures in the proper relationship to each other.
My calculations could be a bit off, and as you say, tests should demonstrate that by 1600 mean population should have grown within (+-)5% of target, with deviations up to 20%. Portugal should have roughly 1/5 of the population in 1419 as expected in 1600. I used the value of 150,000 that you provided, not the 165,000 from the game, because that is the one you said it was correct.
But there is an aspect that is hard to put in calculations, but is both real and has a very important effect. The population of a country of 50,000 habitants, all in one province, grows much faster than the population of a country of 50,000 habitants distributed in ten provinces. Why? I don't know. The simplest explanation is that the number of fractionals kept in the calculations is limited (it appears to be 3 digits in EU2, according to save-files), and the fractions discarded quickly add up.
For example the province of 50,000 at a 5% 10-yearly growth rate, should grow by 20.85 habitants the first month. You will see a 20 increment, but part of the fraction is past over for calculation. Let's say 0.8 in our example for the sake of simplification. In the province of 5,000, the growth should be 2.085. You will lose a higher percentage of the growth when you cut the fractionals. In our example the growth would be 2, and 0.0 would pass to the population base for next month. This difference quickly adds up. If you take the population of a large province (150,000 habitants) in 1600 from a game, and the initial population, you will see that you will have to multiply the first by a factor of around 0.2, meaning that it has growth by 500%. A small province (25,000) in 1600, will show that its population has grown by only 250%.
In practical terms, this means that the population of Portugal, with 3 large provinces, grows much faster than the population of Spain, with many small provinces, and therefore the correct data for 1419 will require less population for Portugal to achieve a correct value and ratio in 1600. Tests will show it, and you can check it easily from a single savefile in 1600. Add up the populations for Spain and Portugal in that game and compare them with the respective values in 1419, and you will see that Portugal grows faster.
The islands can be kept out of the calculations, as their contribution is small. I saw that the data for Baleares was within ball park values, and that is enough for me.