Factory balance

[MichaelEbert]

for a competitive hoi game, faction power should be (roughly) adjusted, so it's not completely one-sided. eg: how should we make this v3 factory ratio (v3 column) convert?

Name    | V3 | v1 |Ratio| /3 |$/9|
England |1450| 415| 3.5 | 138|161|
Bohemia |1250| 455| 2.7 | 152|139|
Algeria | 545| 130| 4.2 |  43| 61|
Iberia  | 515| 121| 4.3 |  40| 57|
Ukraine | 497| 143| 3.5 |  48| 55|
Novgorod| 455| 136| 3.3 |  45| 51|
Rijnland| 395| 110| 3.6 |  37| 44|
Italy   | 317|  68| 4.7 |  23| 35|
India   | 205|  50| 4.1 |  17| 23|
Croatia |  74|  20| 3.7 |   7|  8|
Greece  |  25|   8| 3.1 |   3|  3|
Korea   |   7|   3| 2.3 |   1|  1|

[MichaelEbert]

combine 2 formulas: (a) to minimize large power discrepancies, and (b) to keep nations of roughly even powers together. (a) could be max_hoi4power(n) = hoi4_power(n-1)+hoi4_power(n-2) (b) could be max_hoi4power(n) = (vic3power(n)/vic3power(n-1)*max_hoipower(n-1)

[MichaelEbert]

hmm taht would still leave bhoemia and england with >1k v3 factory equivalent.

max_hoi4power(n) = 4/3 * log2(hoi4_power(n-1)-0.5) + 1

Playing around in desmos, this gives approximately linear growth for 100% - 120% power, and then decreasing after that. 2.0 => 1.6, 3.0 =>1.9. 2x power is reached when initial power is 3.3x.