The math behind Bombardment

[Master Zen]

Hola,

can anyone explain the way bombardment works mathematically? i.e. what are the odds bombardment will be succesful, how cities add to the defense, how many HP will the bombardment take away, what the rate of fire has to do, etc.

For a specific example, how 'bout a Stealth Bomber, bombard of 8, rate of fire 3 going up against a Mech. Infantry defense of 18.

Then, what if the Mech was fortified in a metropolis?

thank you.

[Catt]

There are some knowns and some unknowns at play, but I believe it works as follows: (1) the bombardment value is the "attack" value; (2) the rate of fire is the "number of attacks;" (3) when a unit is bombarded, it gets its normal defensive bonuses; and (4) when a city is bombarded, the target is selected as either defending unit, population, or city improvement.

Using your examples of stealth bomber versus mech infantry: MI has defense of 18, plus a minimum 10% bonus (let's say it is unfortified on grassland) meaning a defense of 19.8. The bomber's bombard strength of 8 is the "attack" and the rate of fire of 3 means it will bombard three times per "attack." So, there will be three die rolls to determine whether a hit point is lost, with a chance for success of 8/27.8, or 28.7%. The end result could be anything from no HPs lost (36.2% chance) to 3 HPs lost (2.3%) - or anything in between (i.e. 1 hp lost).

Using the second example is a bit tricky. Under vanilla Civ 3, when bombard units targeting a city, it seemed that each unit would target either unit, population, or city improvement, and the chances of each such item being targeted seemed to be approximately 50%, 25%, 25%, respectively. This targeting frequency seems to have changed in PTW to be closer to 40%, 30%, 30% - though the precise percentages are not known (thanks to etj4Eagle and sumthinelse for their work on PTW bombardment ratios over at CFC ). For simplicity's sake, let's just assume here that the correct targeting ratios are indeed 40% unit, 30% population, and 30% improvement.

The mech infantry fortified in a metropolis (again on grassland) will have a defense of 42.3 (a collective 135% bonus - 100% for metropolis, 25% for fortified, and 10% for grassland). City improvements and population have a base defense of 16 -- I do not know if they receive defensive bonuses from terrain and city size -- if yes, their defense would be 33.6 - if, no, the defense would still be 16. I am going to assume that they do not benefit and leave their valkue at 16 for this example.

When your stealth bomber attacks the metropolis, the RNG is consulted and one of the three potential targets is selected. If the unit is targeted the same calculations described above are used, but with a defense value of 42.3, resulting in a 15.9% chance of bombard success for each of the 3 "rate of fire attacks" -- chances of no damage to the unit are 59.5% and chances of 3 HPs being lost is 0.4%. But if the target selected is population or a city improvement, then the chance of a successful "hit" would be 8/24 or 33% for each of three RoF's -- one would expect a successful bombardment in about 72% of the time -- this assumes that only one of the 3 rate of fire "attacks" needs to be successful in order to destroy the target, an assumption I believe is accurate but about which I claim no special knowledge.

One final twist to this long answer -- it appears that the targeting ratio against cities is unaffected by the availability of the specific target selected -- if all city improvements are destroyed (wonders, wonder-provided improvements and the palace being indestructible by bombarment) and the population has been reduced to 1 (can't go lower via bombardment), there is nonetheless still a 60% chance (30% pop and 30% improvement, based on stated assumptions) that such "phantom targets" will be attacked -- in such case, the bombardment will have failed, simply because there is nothing to destroy.

Hope that helps and wasn't too long to get through.

Catt

[Jaybe]

Also of note: Cruise Missiles target only defending units and can kill (they do not need the "Lethal Land" "Lethal Sea" bombard flags. I BELIEVE that they do not go through the target selection determination when targeting a city.

[Catt]

Originally posted by Jaybe
Also of note: Cruise Missiles target only defending units and can kill (they do not need the "Lethal Land" "Lethal Sea" bombard flags. I BELIEVE that they do not go through the target selection determination when targeting a city.

Yup - good point. I have never seen a cruise missle hit anything other than a unit (although I have also never fired a CM at an undefended city).

Your post also reminded me of one other oversight I had intended to cover: except for the CM, no bombard unit can take a unit past 1 HP under default rules. And attacking a unit outside of a city also doesn't seem to produce a "targeting choice" calculation, despite the availability of tile improvements beneath the tunit -- i.e., if our hypothetical mech infantry is unfortified on grassland, but that grassland tile also happens to have railroad, road and irrigation, than the MI will be targeted by all bombardment units until it reaches 1 HP left, then the RR (with a defense of 16?) is targeted until destroyed, then the road & irrigation as one "combined" improvement (if there were a fortress, colony, radar tower, etc., I believe that is targeted last.) With the unit down to 1 HP and all tile improvements destroyed, bombard units (other than the CM) can't even bombard the tile further.

Catt

[Master Zen]

Thank you very VERY much for that excellent explanation!!

[theNiceOne]

Great explanation Catt, I don't have much to add.

I can assure you that outside cities there is no targeting choise. If a military unit is there - it is attacked. If not, the terrain improvements is attacked.

And note that even a few (almost) normal improvements are invulnerable as well. Aqueducts and hospitals can never be destroyed (except by razing the entire city).

[epics]

YES cool post.
but I think it is very very very stupid system. In real there is no defence against air bombardment, you just get hit or not. if you get lucky, you stay alive (not very probable).

[PrinceBimz]

Catt, this subject was brought up a few times. Yours is probably the best explanation I have read about it Its just one of those things some people are just curious about and it helps to know sometimes how it all works.