Infrastructure damage in battles is calculated based on units sent, units defending, randomness, victory type, and the amount of infrastructure in the city.
Victory type is between 0 and 3, and corresponds to Utter Failure, Pyrrhic Victory, Moderate Success, Immense Triumph respectively.
The general formula for ground battles, airstrikes, and naval battles is:
min(((Attacking Units - (Defending Units * 0.5)) * Unit Damage) * RAND(.85,1.05) * (Victory / 3), City Infra Limit, Total Infrastructure)
Ground Battles
Soldier Infrastructure Damage: 0.000606061
Tank Infrastructure Damage: 0.01
City Infra Limit: (City Infrastructure * 0.2) + 25
Airstrikes
Aircraft Infrastructure Damage: 0.35353535
City Infra Limit: (City Infrastructure * 0.5) + 100
When infrastructure specifically is not being targeted, infrastructure damage is divided by 3, with the exception of dogfights, which divide damage by 2.
Naval Battles
Ship Infrastructure Damage: 2.625
City Infrastructure Limit: (City Infrastructure * 0.5) + 25
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Missiles and Nuclear Weapons destroy an amount of infrastructure dependent upon the amount of infrastructure in the city targeted, the city's population density, and randomness.
The general formula is:
min(RAND(Base Infrastructure Damage, max(Max Infrastructure Damage, Population Density * Pop Density Factor)), City Infrastructure Limit, Total City Infrastructure)
Missiles
Base Infrastructure Damage: 300
Max Infrastructure Damage: 350
Pop Density Factor: 3
City Infrastructure Limit: (City Infrastructure * 0.3) + 100
Nuclear Weapons
Base Infrastructure Damage: 1700
Max Infrastructure Damage: 2000
Pop Density Factor: 13.5
City Infrastructure Limit: (City Infrastructure * .8) + 150