Bombardment Investigation

In a recent thread "Tell me why" Sumthinelse mentioned that he did not believe bombardment results were working like normal A & D values. So I have begun a little investigation of those values and here are the initial results.

The first test used bombers against a stack of musketmen. The bombers were modded to have ROF of 1 (so that I could more easily mark hit and miss). Also the bombers were given 3 moves and the blitz ability (this so that 20 bombers became 60 and saved me having to click the mouse 40 more times to place the other bombers).

I had 125 hits and 65 misses for a 65.79% hit percentage. Bombers have an A value of 8 and musketmen have a D value of 4. They are located on a deseret so that D(1+B)=4.4. This gives an expected percentage of 64.52% The empiracal value is 1.97% higher than the theoretical one (fairly close).



The second test I did was to look at bombing of improvements. Here I placed irrigation on desert tiles.

I destroyed tile improvements 61 times and missed 127 times. I kept track of how many times I missed on each tile improvement so have a 95% confidence interval as well.

The average defense value (with any bonus) was 16.7 +/- at 95% confidence (standard deviation was 15.9. If we assume that the bonus value of 10% is applied then you get 15.3 for the base defense value (18.9-10.2 at 95% confidence). Which does include the 16 which buildings and people are at.


While the terrain value needs a little work and I want to also check the selection percentages in cities, you can see that for units out in the open it is strictly P=Ab/[Ab+D(1+B)] where Ab is the bombardment attack value. I will also make a check to ensure that ROF simply is the die thrown twice.

Edit: found a sign error in my math which gave the wrong defense values for the irrigation test (oops).

Edit fixed the error for the defense value, it should be 15.3 not 115.1. Thanks sumthinelse for catching that typo.

Okay just completed some more tests where I increased bombers ROF up to 2 (so that way every hit would count against the regular musketmen). Under this situation I got the following results

A = 8
D = 4 with 10% terrain (desert bonus)

16 at 0 hits -> 11.9%; expecting 12.6%; -5.9% error
67 at 1 hit -> 49.6%; expecting 45.8%; 8.4% error
52 at 2 hits -> 38.5%; expecting 41.6%; -7.46% error

This does seem to suggest that ROF just acts like multiple bombardment rounds, nothing magical happening. The magnitude of my error results just from using a small sample size.

Now reducing the data down to individual bombardment rounds, there are 171 hits out of 270 tries. Combining this with my previous trial gives 296 hits out of 460 tries for a hit percentage of 64.3% (off by -.26%). Back calculating the defenders D value I get 4.03, which is very close to the actual value of 4.

Therefore it looks conclusize that unit bombardment acts just as any other combat round. The only differenc is that the ROF value limits the rounds of combat and the attacker takes no damage.

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Now onto bombing irrigation, again with ROF 2. This time with my 60 bombing runs I destroyed 106 desert irrigations. It took an average of 0.7 bombing runs per terrain improvement. This gave an utter miss percentage of 41.1% per bombing run. Since the probability of completely missing is just the square of the miss percentage for one round, the per round miss probability is 64%. This gives a defensive value 14.3 or 13.0 if we assume a 10% terrain bonus. (this value is within the 95% confidence band of my previous test with a ROF of 1).

Again it looks like ROF just acts like multiple die rolls with destroying terrain improvements. The only difference is that here there is no bonus for hitting with both dies.

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Next up is to place warriors on those irrigated tiles and then bomb them. This will check to see if the underlying improvement will get hit while the unit is still there. And if so find what the prob of hitting unit verse terrain is. I will also repeat the test with cities (civilians and buildings in this case).

Good tests. I believe that the unit will always be hit and not the terrain for the next test. I may be wrong on this but thats what I think.

Originally posted by Yzman
I believe that the unit will always be hit and not the terrain for the next test.

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Yeah, that's the reason you wana fortify units on all ur important strategic resources. That'll prevent bombers from severing your roads/railroads to em, at least until ur enemy gets troops in there to try to dislodge them.

OK, so far this formula does correlate with my results, except for one detail which I will state at the bottom.

For a catapult (4) vs. non-fortified warrior on grassland I got something like 80% hits. Your formula gives 78%

Same except fotified: 72%, your formula gives 75%.

cat vs. fortified warrior on mountain: 62%, your formula 64%.

OK, now for the problem I promised. The defense for a warrior in a size 1 town with zero improvements (the same as grassland for normal attacks) is 1.35 but a catapult hits the warrior something like 20% of the time. So instead of 4/(4+1.35)=.74, we have to either add the citizen defense bonus 16: 4/(4+16+1.35)=.19

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or for a military unit in a town set defence=min(normal defense,16). It's about the same for a warrior but for a fortified mech infantry it would be either 16 or 40.3, a big difference!

I don't know why the formula didn't occur to me. Doh!

Suggestion: write the formula as P=Ab/(Ab+D) where D contains all the defense bonuses. To get D you could go to the civ3 combat calculator for units outside a town and for units inside a town apply the 16 defense bonus (although I'm not sure which way to do that yet). Bombarding a mech infantry in a town would be a useful test.

"115.1 for the base defense value" ?????? Do you mean 15.1?

But great work!!! Thanx!!!

Wow guys... and i thought i was a nerd! lol j/k

I am having trouble with making it come out right for:

attacker: catapult (4)

defender: mech infantry fortified (defense 24.3)

in size 1 city

no improvements.

Result: 15 hits/400 tries, .0375

Using a formula I suggested above 4/(4+16+24.3)=.09, clearly wrong.

How do I get a probability of .0375

Maybe there is some algorithm for it to select a target such that it selects a citizen most of the time, but then since there is only one citizen, when it does select a citizen "bombard fails."

eagle: good luck on the bombing of cities, it may be a little more challenging to figure it out!

Originally posted by sumthinelse
Maybe there is some algorithm for it to select a target such that it selects a citizen most of the time, but then since there is only one citizen, when it does select a citizen "bombard fails."

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This is the answer. I'm too busy at work to search for the details (can be found somewhere here at CFC), but when you bombard a city, there is first a random selection of target, either improvement, citizen or defener. IIRC, the chances are 25%, 25% and 50% (but I don't remember which of the three that has 50%).

Then, when target type is selected, the bombard becomes an automatic miss if that target type is unavailable (citiizen in a size 1 city, improvement in an improvement-less city, defender in an undefended city). Only after all this is the bombard calculated as normal, now against the defender if he was selected.

To look again at you numbers: If the defender has a 25% chance of being selected, then against a warrior the hit % should be 25% of the first calculated, i.e., 0.74/4 = 0.18 which is close to the 0.20 you got.

For the MI it should be (4/4+24.3)/4 = 0.0353, which again is close to the 0.0375 you got.

Originally posted by DiamondzAndGunz


Yeah, that's the reason you wana fortify units on all ur important strategic resources. That'll prevent bombers from severing your roads/railroads to em, at least until ur enemy gets troops in there to try to dislodge them.

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no so! It maybe gives more of a chance of the unit being hit instead of terrain but not always

another excellent test, thanx etj4eagle. I will link to this in the FAQ.

Originally posted by DaDrunkenFish


no so! It maybe gives more of a chance of the unit being hit instead of terrain but not always

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You have the chance of destroying an improvement only when all enemy units stacked there have 1hp. This is the reason why AIs always protect their radar towers by defenders. You must:
1. Bombard them first.
2. Destroy rails.
3. Destroy roads and mine/irrigation.
4. ... and finally destroy the tower.

Originally posted by TheNiceOne

This is the answer. I'm too busy at work to search for the details (can be found somewhere here at CFC), but when you bombard a city, there is first a random selection of target, either improvement, citizen or defener. IIRC, the chances are 25%, 25% and 50% (but I don't remember which of the three that has 50%).

Then, when target type is selected, the bombard becomes an automatic miss if that target type is unavailable (citiizen in a size 1 city, improvement in an improvement-less city, defender in an undefended city). Only after all this is the bombard calculated as normal, now against the defender if he was selected.

To look again at you numbers: If the defender has a 25% chance of being selected, then against a warrior the hit % should be 25% of the first calculated, i.e., 0.74/4 = 0.18 which is close to the 0.20 you got.

For the MI it should be (4/4+24.3)/4 = 0.0353, which again is close to the 0.0375 you got.

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Thanx! The 25% number does seem to work for a unit in a city.

I am using PTW -- the editor has the same defense values for citizen and improvement, 16, as civ3. The results I am getting for hits on improvements and citizens don't match up very well with 25% or 50% though. For example, out of 200 bombards with a catapult 17 citizens were killed and 14 buildings destroyed. Maybe it's more like 25%/35%/40% for unit/building/citizen?

Of course 200 trials may not be enough

But I searched and found one place where somebody said 25%/25%/50% but no reason was given for these numbers. There must be a better post about this somewhere.....

Well I just finished some more tests that I ran this morning.

First of all these were run with ROF=1, A=100 for the bombers
and the defense value of citizens and buildings at 2 and no town, city or metro bonuses. (as misses don't tell me anything).

First one was bombing warriors standing on top of irrigation. Out of 102 attacks the irrigation was never hit. (2 of those were misses). Therefore it is true that a unit will always be targetted over an improvement. The only thing I have not tried is bombing 1 hp units to see if this still holds true

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Second test was bombing cities. This city had 60 warriors, 50 civilians (at D=2) and 17 buildings (D=2) w/ no defense bonuses. Each time I attacked till I destroyed 15 buildings. Out of 211 trials I hit the warrior 97 times, civilians 65 times, buildings 49 times and did not miss.

This gives the following percentages:
Unit: 46%
Civilian: 30.8%
Building: 25%

This does seem close to the 50:25:25 ratio. Though it would also seem to suggest that 45:30:25 is the correct U:C:B ratio.

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For the third test I made the city a size one city. This time in 75 attacks I had 21 misses or about 28%. This is close to the 30% from above, so TheNiceOne is correct in that the civilian was still being targetted.

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For the fourth test I repopulated the city to size 50, but removed all improvements. In this case there were 17 misses in 65 attacks (26.2%). Again TheNiceOne appears to be correct and the non-existant buildings were still being targetted.


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And for the fifth and final test I was curious if the game would attempt to select GW as targets. Resulting in a hightened failure rate. In this situation the pop 50 city got every GW plus a marketplace. I run 4 games, in which I attack a total of 24 times and did not miss once. While this is a very small sample size it would seem to indicate that the game is correctly not targetting GW's.

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The short conclusion of these tests is that bombardment does use the combat formula that we all now and love (or hate). But that there is an zeorth step involved when you bombard a city. In this case the defender must first be selected by chance and the game does not take into account whether or not valid targets exist of that defender type.

Therefore there is aways a 50:25:25 (or maybe 45:30:25) probability of your unit targetting a Unit, civilian, building respectively. So in bombarding a size 1 city with no buildings left you are already starting out with at best a 50% chance of success even before the actual odds of the battle are computed.

For the record one thing I forgot to mention at the start is that my tests are being run at Civ3 v1.29f. There should be no difference with PTW, but one never knows.

Good Tests I too knew of the 50%-25%-25% ratio but can't remember where I first saw it or what its support was (i.e., whether it was Firaxian comment or poster testing/sleuthing) -- it could have been long ago in cracker's thread suggesting improvements to the bombard process (which the "search" function no longer finds).

One other quirk to note - for both testing purposes and to dispel the myth of "secret capitol bonuses" that sometimes arises - I believe that bombarding a civ's capitol will skew expected results. At the preliminary 50-25-25 die roll, one would expect the "city improvement" target to come up 25% of the time. There would then be another die roll based upon the bombard unit's A value and the improvement's D value of 16. Defender wins produce a "failed." I am not certain how the game "chooses" which improvement is targeted, but they should all have a D of 16.

BUT, if the targeted inmprovement happens to be the Palace, the bombardment will always fail because the Palace cannot (apparently) be destroyed by bombardment. So keep in mind when running tests that if attacking a test city that is also a capitol, you will likely encounter slightly less than expected success due to the "Palace skew."

BTW - I think it was again cracker that identified this "skew."

Originally posted by etj4Eagle

Second test was bombing cities. This city had 60 warriors, 50 civilians (at D=2) and 17 buildings (D=2) w/ no defense bonuses. Each time I attacked till I destroyed 15 buildings. Out of 211 trials I hit the warrior 97 times, civilians 65 times, buildings 49 times and did not miss.

This gives the following percentages:
Unit: 46%
Civilian: 30.8%
Building: 25%

This does seem close to the 50:25:25 ratio. Though it would also seem to suggest that 45:30:25 is the correct U:C:B ratio.

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Both tests in PTW:

Test 1: With a weak bombard unit (catapult=4) attacking a fortified strong unit (mech inf fortified=24.3) in a size 1 city -- no buildings . Out of 250 tries it hits the unit 15 times. If the probability of attacking the unit is 46% then I would expect about 250*.46*4/(4+24.6)=16.08. Actual results=15 hits on the unit.

Test 2: However, when I added improvements (no wonders, palace or defense improvements) and citizens to the city, out of 200 tries I got only 7 hits on the unit. I would expect 200*.46*4/28.4, or about 13 hits. Using binomial distribution this result (7 of fewer hits out of 200) should happen only about 5% of the time. So I might have just stumbed into this 5%
phenomenon, or PTW is different, or is are the probabilities for selecting a target different when there are buildings in the town?

Test 3: same as test 2 except the defender is fortified warrior. Using a .46 probability of selecting the warrior, I expected 200 tries*.46*4/5.35=about 69 hits on the warrior but got only 50. According to Bernoulli trials this kind of distribution (50 or fewer out of 200) happens only .002 of the time.

For PTW at least, I don't think we have all the answers yet for bombarding cities. Since these "bombard selection" probabilities for a city are not in the editor all we have is emperical evidence.

I think we do agree on bombardment of units outside cities though, and that is progress!

One important detail about bombardment: if your bombardment hits a fortified unit outside a city, that hit un-fortifies the unit. A unit hit inside a city stays fortified!

Originally posted by TheNiceOne

This is the answer. I'm too busy at work to search for the details (can be found somewhere here at CFC), but when you bombard a city, there is first a random selection of target, either improvement, citizen or defener. IIRC, the chances are 25%, 25% and 50% (but I don't remember which of the three that has 50%).

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Maybe this thread:

http://forums.civfanatics.com/showthread.php?s=&threadid=21161

Hurricane's post says that Soren said the probability to hit a unit is 50%:

"I remember Soren mentioning that the percentages were roughly 50/25/25. For example, in your case (1 reg defender, 1 improvement, 3 pop point) the chance of hitting is not 20/20/60 as you suggest, but rather 50/25/25."

I think cracker's results indicate the % for selecting a unit is 48%, if you do the math, Hurricane's statement notwithstanding.

Soren may have said that, but I do not believe it's the way bombardment works in PTW today for land-based bombard units in cities that have buildings and more than 1 citizen.

Why don't my results agree with cracker's etj4eagle's, and Soren? Maybe I need to try bombers.

Originally posted by Catt

BUT, if the targeted inmprovement happens to be the Palace, the bombardment will always fail because the Palace cannot (apparently) be destroyed by bombardment. So keep in mind when running tests that if attacking a test city that is also a capitol, you will likely encounter slightly less than expected success due to the "Palace skew."

BTW - I think it was again cracker that identified this "skew."

Click to expand...

One note on my tests, I was not attacking the capital. To avoid any palace effects I had placed another city with the palace elsewhere in my test map. And all the buildings were regular city improvements.

I would be a bit surprised if the game tries to target the palace, as it doesn't target Great Wonders. Though maybe it does target small wonders (since they are raised when you take the city) or the palace (as it can be built buy any city at anytime).

One tricky thing about bombard tests: I have bombarded a city with 7 oridinary improvements down to 1, an aquaduct. The aquaduct cannot be destroyed! Is it because it's the only improvement or is the game hard-coded so that an aquaduct will never get hit?

sumthinelse: I have never seen an aqueduct destroyed - but I have seen a city of mine loose the last Temple it had. Also, you cannot sell aqueducts - so safe to say it is hardcoded you cannot destroy it (not saying you can't hit it)....


(but I guess you knew that).