[size=+1]The cost of historical colonization for Spain:[/size]
The conditions for this test were as follow:
1) Spain held all her European possessions at each time. Navarra from 1512, Low Countries and French-Comte from 1516, Milan from 1535, Netherlands was released in 1590, Rousillon lost in 1640, etc. This means my income was higher than what SPA AI usually gets.
2) Explorers and conquistadores were used extensively to reduce the cost of colonization. The AI never does that.
3) Provinces were considered terminally colonized when short one colonist from city if they had positive growth. Over the course of a few years they reach city on their own. That means 9 colonists if no natives, or 8 colonists if friendly/neutral natives. The AI tends to colonize all the way to city if it has not forgotten about the colony.
4) Trading Posts were established previously only if low chance of colonization, and pushed up several levels only if very low chance of colonization or very negative growth in the province.
5) Colonization was given a high priority, just below promotions, and on par with conversions. Therefore the amount of money dedicated to colonization diminished when governors became available, and when conversions were under way.
Given all the above, I consider that the cost of colonization for the AI is around 20% higher than the one reported here.
Code:
year expense colonists completed colonies (number of colonists)
1493 102 2 0
1494 142 4 0
1495 134 5 0
1496 126 5 0
1497 152 4 0
1498 131 5 0
1499 199 5 0
-----------------------------------
1490s 986 30 0
-----------------------------------
1500 205 6 0
1501 271 7 Tortuga (7)
1502 229 7 Antigua (10), Barahona (10)
1503 122 3 0
1504 193 6 0
1505 220 5 Guadeloupe (14)
1506 0 0 0
1507 187 4 0
1508 137 3 0
1509 135 3 0
-----------------------------------
1500s 1699 44 4
-----------------------------------
1510 255 6 Guantanamo (6)
1511 152 3 Puerto Rico (12)
1512 147 3 Moron (4)
1513 194 4 0
1514 174 4 0
1515 216 5 0
1516 202 5 Aires (11)
1517 256 6 0
1518 257 7 0
1519 241 7 0
-----------------------------------
1510s 2094 50 4
-----------------------------------
1520 232 5 Havana (14)
1521 234 5 St. Thomas (14), Isthmus (12)
1522 155 4 0
1523 252 6 Dominica (9)
1524 236 6 0
1525 266 5 0
1526 259 5 0
1527 257 5 0
1528 280 7 Cartagena (9)
1529 355 8 Barbados (10)
-----------------------------------
1520s 2526 57 6
-----------------------------------
1530 322 7 0
1531 300 6 0
1532 269 5 Tobago & Trinidad (10)
1533 339 6 Tehuacan (10)
1534 290 5 0
1535 417 6 0
1536 260 4 0
1537 390 6 0
1538 452 7 Caribe (12)
1539 417 8 Cuyuni (19)
-----------------------------------
1530s 3456 60 4
-----------------------------------
1540 346 7 Guatemala (12)
1541 392 8 Mazatlan (8)
1542 286 4 0
1543 283 5 Yarumal (16)
1544 216 4 0
1545 210 4 0
1546 205 4 Honduras (11)
1547 255 5 0
1548 239 4 Nicaragua (10)
1549 251 4 0
-----------------------------------
1540s 2683 49 5
-----------------------------------
1550 265 5 0
1551 254 4 Guyana (13)
1552 0 0 0 (unhappiness event)
1553 0 0 0
1554 171 4 0
1555 158 3 0
1556 246 6 0
1557 228 4 0
1558 325 8 0
1559 161 6 0
-----------------------------------
1550s 1808 40 1
-----------------------------------
1560 290 5 Yaraguai (20), Mosquitos (11)
1561 384 6 0
1562 421 6 0
1563 495 7 0
1564 472 8 0
1565 430 7 Parana (12)
1566 449 7 0
1567 432 7 0
1568 408 6 0
1569 505 8 Campeche (11)
-----------------------------------
1560s 4286 67 4
-----------------------------------
1570 194 3 0
1571 306 5 0
1572 301 5 Tocuvo (24), Yucatan (15), Valparaiso (9)
1573 130 2 0
1574 339 6 Maracaibo (18)
1575 111 2 0
1576 145 4 0
1577 112 3 Luzon (13)
1578 61 4 Copetonas (12)
1579 103 3 0
-----------------------------------
1570s 1802 37 6
-----------------------------------
1580 161 3 0
1581 272 5 0
1582 285 7 0
1583 87 1 0
1584 153 2 0
1585 216 3 0
1586 210 3 0
1587 268 4 San Matias (8)
1588 192 3 0
1589 222 3 0
-----------------------------------
1580s 2066 34 1
-----------------------------------
1590 202 3 Talca (9)
1591 140 2 0
1592 140 2 0
1593 166 3 Mindoro (11)
1594 129 3 0
1595 160 3 0
1596 178 4 0
1597 305 4 Chubut (9)
1598 302 4 0
1599 231 4 0
-----------------------------------
1590s 1953 32 3
-----------------------------------
Statistics for 1500-1599:
Total money spent in colonists: 24373 ducats
Average money spent in colonists per year: 243.7 ducats
Total number of provinces terminally colonized: 38
Average cost of colonizing one province (including partially colonized provinces in calculation): 595 ducats
Estimated average cost of colonizing one province for the AI: over 700 ducats
Average number of colonists required per province: 12 (12.5 for the AI)
Average speed of colonization in this test: 1 province every 2.6 years
Maximum speed of colonization if unlimited money and perfect DPs: 1 province every 1.7 years
Speed required to colonize 77 provinces by 1700: 1 province every 2.5 years
Comments: By spending all non-essential money in colonization, I was barely able to keep up with historical colonization during the 1500s. I was running a good economy, with controlled inflation, although short on manufactories, as I dedicated that money to colonization. This was done at the expense of not getting involved in wars. I was supposed to be fighting France in Italy, and the Ottomans in the Mediterranean but I kept out of alliances and peaceful. I did fight the rebels in the Low Countries. My trade was as always much better than for the AI. The AI is also commonly dragged to alliances wars, and wastes money in a thousand things.
Conclusion: The AI is chronically short on money for colonization. To prevent the player from colonizing the entire world, colonization has been made too expensive for the AI. The AI needs to raise 700 ducats per province that it is supposed to colonize, and this comes to about 280 ducats per year for Spain between 1500 and 1700. I seriously doubt that it can raise much more than 90-120 ducats per year for colonization, given initial census tax and AI priority for expenses. This estimate fits well with the observation of AI colonization, that is between 1/2 and 1/3 of required to be historical. The problem is going to be made more acute with the increased number of provinces in the new map, as the cost is not going to be reduced. This situation can be extended to Portugal, England, and to a lesser extent to France and Russia.
Possible solutions:
A) Reduce the cost of colonization by half. I don’t know if it is possible. I know climate and natives affect, and we do not want to change those.
B) Provide the required funds.
C) Accept that colonization will never be historical and expect the situation to worsen with the new map.