AA combat formula

alexman · January 14, 2004, 10:37

The real strength of each AA unit is 1/10th of the value shown in the editor. So Flak has a strength of 0.2.
Each AA unit in the tile being bombarded takes a shot against the defense of the bombarding air unit. The chance of shooting down the air unit is A/(A+D), as with all other forms of combat in Civ3. Remember, A is 10 times less than what is in the editor for the AA unit.
The maximum number of AA units that are given a chance to shoot down the plane is 4. Any AA units above 4 are ignored.

So, for example, if you want the formula for the probability of N units with a strength of A shooting down a plane with defense of D, here it is:

1 - (D / (D+A))^min(N,4)

Jaybe · January 14, 2004, 11:13

alexman, basically how did you determine this (code examination, experimentation, ...)??

alexman · January 14, 2004, 11:29

Experiment. Debug mode with reveal map. Gave the AI 320 bombers all within range of my only city, and a number of flak units to myself. Contacted AI and declared war. After his turn, I hit F3 to see his remaining bombers. Change stats of bombers and flak, and repeat. It doesn't take long if you switch off all animations.

Arrian · January 14, 2004, 11:47

Thanks, alexman.

-Arrian

Capt Dizle · January 14, 2004, 12:11

This is one of my pet peeves, that we have to depend on folks like alexman to tell us how the game works. It ought to be revealed by Firaxis. Another case of developer's ego.

Great work. Kudos.

Catt · January 14, 2004, 12:39

Nice job, alexman

Catt

asleepathewheel · January 14, 2004, 12:41

cool

Cookie Monster · January 14, 2004, 12:46

So stationing more than 4 AA units in a city is a waste?

alexman · January 14, 2004, 12:47

Unless some of them die during the bombing.

MattPilot · January 14, 2004, 13:25

help me out here please, ..

A = attack value

D = Defense value (modifiers applied? say stock defense of 6 + 50% city + 50% fortified = Defense of 12 - did i get that right ?)

So plugging in the numbers for the flak, with above defense modifiers & assuming 20 bombers, i'd get:

1 - (12 / (12 + 0.2))^min(20,4)

1 - (0.9836)^min(20,4)

now, i'm stuck on the exponent part. help me out with the 'min' part & why there are 2 numbers posing as an 'ordered pair' ?
How would i go about solving that?

vmxa1 · January 14, 2004, 13:31

Well now I know why my AA defenses were stinking the place up.

I agree with jimmytrick, this type of stuff should be documented. I don't mind if they had put it in the strat guide and made us pay, but it should be published. I understand it cost money to publish manuals, but what about readme docs. They could be hosted by the game sites and not cost them anything. The work is probably already done, as this information must be available to the devs.

alexman · January 14, 2004, 13:34

D is the defense value of the bombarding air unit (2 for a bomber). No modifiers apply. A is the AA strength of the AA unit (0.2 for flak). N is the number of AA units, not the number of air units.

min(N,4) = N, if N less or equal to 4
min(N,4) = 4, if N greater than 4

Hope this helps...

Risa · January 14, 2004, 13:42

Splendid work!

asleepathewheel · January 14, 2004, 14:25

Quote:

Originally posted by jimmytrick
This is one of my pet peeves, that we have to depend on folks like alexman to tell us how the game works. It ought to be revealed by Firaxis. Another case of developer's ego.

I agree that it should be revealed, but then would Alexman get as much enjoyment out of the game?

Firaxis has always had this problem, even when BR was running the show, just look at the pod bloomings or pollution or whatever it was. Years, IIRC, before someone dissected that mystery. I would throw up another recent strat game (insert joke here), MoO3 as an example of the players having no clue as to the mechanics which greatly sabotaged the game's success (there were problems far beyond that though

)

MattPilot · January 14, 2004, 15:09

ah, oki thanks alexman - i feel stupid now that i asked

anyway, if i did my math right, then a bomber with a defense value of 2, would have the following chance to get shot down:

(**edit see alexman's data**)

alexman · January 14, 2004, 15:13

More like:
1 AA unit: 9%
2 AA units: 17%
3 AA units: 25%
4 AA units: 32%

Assuming the AA unit is a flak.

MattPilot · January 14, 2004, 15:14

btw, another question:

Does every AA get to 'try' to shoot down every plane, or does it become inactive after it shot down one plane?

Assuming i have 4 AA units in a city, and the enemy sends over 100 bombers in one turn. Say I shoot down the first 4 bombers, do the remaining 96 bombers have free passage or are they still subject to the AA?

Just like the Arty, once it did a defensive bombardment, it won't shoot again in that turn.

vmxa1 · January 14, 2004, 15:28

I have seen 3 and even 4 bombers shot down and the city only had Sam and 1 mobile sam.

alexman · January 14, 2004, 15:31

Unlike fighter airplanes, AA units get one chance to shoot down each bomber (unless they get killed by the lethal bombardment, of course)

Sarxis · January 14, 2004, 15:54

Quote:

Originally posted by vmxa1
...this type of stuff should be documented. I don't mind if they had put it in the strat guide and made us pay, but it should be published.

But then what would alexman do with his spare time? He'd go mad I say... MAaAaAdDd!!!

Thanx for this info alexman. Gives us real strategy with our AA.

MattPilot · January 14, 2004, 16:09

ah your right alexman, i'm sorry, stupid me forgot an additional bracket

which messed it up.

Kuciwalker · January 14, 2004, 16:29

How does Stealth affect this?

alexman · January 14, 2004, 16:52

No effect, but stealth units have a higher defense than bombers, so they are shot down less often.

vmxa1 · January 14, 2004, 17:44

And they have longer range.

MattPilot · January 14, 2004, 17:49

And they look cooler.

Fatwreck · January 14, 2004, 18:06

this is really great, thanks alexman

planetfall · January 14, 2004, 18:07

Quote:

Originally posted by alexman
Change stats of bombers and flak, and repeat. It doesn't take long if you switch off all animations.

How do you change stats? I thought every time you make an editor change you had to generate a new map or load a common scenario and editor changes do not effect saved games.

== PF

steven8r · January 14, 2004, 18:56

Alexman the Corruption King, now the AA Tsar.

Huzzah.

Thanks for the info Alexman.

Steven

PrinceBimz · January 15, 2004, 02:41

Quote:

Originally posted by alexman

The real strength of each AA unit is 1/10th of the value shown in the editor. So Flak has a strength of 0.2.
Each AA unit in the tile being bombarded takes a shot against the defense of the bombarding air unit. The chance of shooting down the air unit is A/(A+D), as with all other forms of combat in Civ3. Remember, A is 10 times less than what is in the editor for the AA unit.
The maximum number of AA units that are given a chance to shoot down the plane is 4. Any AA units above 4 are ignored.

So, for example, if you want the formula for the probability of N units with a strength of A shooting down a plane with defense of D, here it is:

1 - (D / (D+A))^min(N,4)

Good to know that any amount over 4 is ignored. Its good it does this and its how it should be. It keeps someone from stacking an area full of AA and shooting down every attacking plane. Nice job alexman!

MrWhereItsAt · January 15, 2004, 05:08

Thank God you discovered this alexman - if someone else had it would likely have been described in a far more complex manner! You always seem to have a knack of making things perfectly easy to understand, as well as figuring them out in the first place, so cheers for that.

BTW were there any uncertainties in your results at all? No slightly odd results? Everything is explained perfectly by your forrmula.

That would be the experimental physicist in me.