In the file 00_defines.txt, there is the following line:



"MILITARY_POWER_EXPONENT = 0.75 # math: power = ( ( effective_health * damage_per_day ) ^ exponent ) * scale"



This is wrong. The exponent should be 0.5. This not a matter of opinion or game mechanics, and is easily provably theoretically and demonstrable practically: For large numbers and when all units can engage, you need 4 times the firepower per unit to fight to a draw with twice the numbers. For the theory behind it, the most straightforward reference is to "Lanchester's Square Law". This particular example is shown in the third graph on the sidebar in the English Wikipedia article. A relevant quote:



"Note that Lanchester's square law does not apply to technological force, only numerical force; so it requires an N-squared-fold increase in quality to compensate for an N-fold decrease in quantity."



I tested in game by checking the displayed power of a starting fleet with kinetic weapons (98), then editing the save file to add 60 levels of the repeatable kinetic damage tech to increase damage by a factor of 4. This should double the fleet power to 196. Instead it increases it to 277, which indeed means it is being multiplied by 4^0.75, so this exponent is actually being used.



This probably responsible for most of the problems with higher tech fleets not being as powerful as their fleet power would indicate versus larger numbers of lower tech units, and will hose any AI calculations that rely on fleet power. It's also probably why the old 'basic corvettes are best' problem wasn't spotted by the devs earlier.



More seriously, a designer at some point thought it was possible for some exponent other than 0.5 to work. This is like trying to get a distance calculation right with an exponent other than 0.5 in the Pythagorean formula. Presumably others have been trying to patch problems and introduce ad-hoc correction factors based on an incorrect model. Unfortunately, no possible linear correction factors will be useful outside of a narrow range if the exponent is wrong.



This is of some urgency for the 1.9 patch--whatever model is used for balancing small fleets vs large fleets will perform progressively worse as the (health * damage) of individual ships moves farther away from whatever standard test they use if they don't fix the formula.