Has anyone figured out the AA formula yet?

[korn469]

I'm getting ready to mod air units soon and I was wondering if anyone had figured out what the exact AA formula was yet? It'd be a big help to me if somebody had.

[Risa]

I have run a small test as below:
6 stacks of AA units (2 stacks of Moderm SAM, 4 stacks of Flak, each stack has 20 units) as target, 6 stacks of various bombers (20 per stack) bombard their target, then count casualty of each stacks of bombers. All units have 5 hp.

Stack 1: Weak Stealth Bomber (0/2/1, bombard 12/0/3, stealth) vs. Modern SAM (AA 4);
Stack 2: Bomber (0/2/1, bombard 12/0/3) vs. Modern SAM;
Stack 3: Strong Bomber (0/4/1, bombard 12/0/3) vs Flak (AA 2);
Stack 4: Weak Bomber (0/1/1, bombard 12/0/3) vs Flak;
Stack 5: Bomber vs Flak;
Stack 6: Fighter (4/2/1, bombard 3/0/1) vs Flak.

I have run 10 times of the test, and the result (numbers of remaining bombers) is as follow:
Stack 1: 8,13,8,8,8,7,13,7,10,12
Stack 2: 10,10,9,12,13,12,9,13,8,7
Stack 3: 16,15,16,16,16,15,18,15,18,16
Stack 4: 6,10,10,10,12,10,9,9,5,13
Stack 5: 12,18,16,16,8,13,13,13,17,10
Stack 6: 12,11,8,12,9,14,12,16,14,14
Survival rates of each stack are 47%, 51.5%, 80.5%, 47%, 68%, 61%.

Assuming AA units only shoot down planes that bombard its tile, here are some observations:
1) Stealth isn't a factor in AA formula.
2) Possible formula is:
shot down rate = AA value / (AA value + 2 * aircraft defense value)

However, it may be more complicated than I thought. I tried Stack 7: Weak Bomber vs. Modern SAM, got following result: 5,3,5,4,3,4,3,4,3,5, survival rate is only 19.5%, differs too much from expected 33%.

[Catt]

I started doing some testing but it is so monotonous as to be almost unbearable . It is monotonous because stacking AA units in one square seems to increase the interception chances -- which means to get a good jump on the formula you need a test scenario with only one AA unit per tile -- lots of clicking to build up sufficient trials.

In my very preliminary exploration, it also seems that the attacking air unit's defense value plays a role. This surprised me a bit since I've never seen an air unit take damage but survive -- it is either intercepted and shot down, or not intercepted and not injured.

Maybe I'll go back to it at some point, but I "stood down" several days back after enduring about an hour of boredom.

Catt

[Catt]

Cross-posted with Risa.

Now that I see Risa's test results, I think I can confirm that the AA / (AA + 2*Defense) is not the working formula. My tests utilized 368 individual bombers bombing individual tiles, each occupied by a flak unit.

Test 1: Standard bomber with "2" defense; flak modified to have AA value set as "1." Of 368 bombers, 349 survived and 19 were shot down. Shoot down rate was 5.163% though on limited trials.

Test 2: Standard bomber with "2" defense; flak modified to have AA value of "4." 290 bombers survivie; 78 dead. Shoot down rate is 21.196% (closely linear with changed AA values).

Test 3: Modified bomber with defense of "30." Modified flak with AA of "4." 364 bombers survive; 4 dead. Shoot down rate is 1.087%.

I was so bored at the end of 3 interations that I never actually looked at the data and started exploring possible formulas. Just glancing at the very limited trials, I suppose it is conceivable that the rate is AA / (Def * 10) [EDIT: Ooops! Not even close to correlating to Risa's results, although the stack effect may be at work. End Edit].

Catt

[Risa]

Oh that is BAD news. If number of AA units in one tile is also a factor in the formula, it would be near impossible to find out even a not-so-exact one!

Having that in mind, I changed my test scenario by splitting one Flak stack to two, each with 10 Flaks. Here's result of one stack of Bombers bombing two small stacks of Flaks: 16,18,13,11,14,15,17,9,16,11, survival rate is 70%. No big difference.

Perhaps I should try even smaller stack.

[korn469]

from what i read in a chat

the AA number goes against the attacking air unit's defense number, and it does indeed increase as more AA units are in the stack

i may create an AA test scenario

[Risa]

Now 4 stacks of 5 Flaks in each:
15,15,16,14,14,16,10,13,12,14, survival rate is 69.5%. Still no big difference. I'll test 10 stacks of 2 Flaks in each tonight.

BTW, these result means Flak is not much useful. Fighters are far better than them.

[Catt]

I tested fighters a long time ago (civ vanilla), and stacking fighters in a city did not increase the chances of interception, it just increased the number of potential interceptions per turn to equal the number of fighters. That function was changed at some point, because in PTW (and Conquests), stacking fighters actually increases the interception rate. For flak, I did a quick test with 50 unmodded flak in a tile, and 5 unmodded bombers. Bombarding the stack produced 3 or 4 lost bombers in each of the four or five reloads -- a significantly higher loss rate than I experienced attacking tiles with one flak and one bomber for each engagement.

I am hopeful that someone who deciphers the one vs. one forumla can easily extrapolate to a number of AA defenders.

Catt

[Risa]

OK, now is 10 stacks of 2 Flaks in each, and finally we can see some difference:
14,18,18,18,17,19,18,19,18,16,survival rate is 87.5%.

And here is bomber vs 2 stacks of 10 Modern SAM in each: 7,10,10,6,8,9,10,9,11,11, survival rate is 45.5%.

[korn469]

ok from Catt's results it looks like the formula for a single stack is

(air unit's defense/AA rating)/10

[steven8r]

Originally posted by Catt
....I've never seen an air unit take damage but survive...
Catt

Catt, I've seen many times my fighters' health meter go down after shooting-down bombers. Several times, I've had to take the fighters off of Air Superiority and fortify them for a turn to regain lost hp's (the town had an Airport--otherwise it's just 1 hp per turn). If the fighter gets too low on hp's, the Bomber will shoot it down--I've seen this a couple of times too.

======================================

So far in C3C, I've not had any cities bombed by Bombers, however, I have seen several AI Bombers shot-down over other AI cities.

Just a totally unscientific observation: It seems that more AA units in a tile = better success rate for shooting down enemy plans.

[korn469]

steven8r

fighters vs. other air units does result in a hitpoint loss, whereas with AA units (either land or sea) it results in a simple yes or no situation where the air unit is either intercepted and killed or not

[steven8r]

Ah, thanks for the clarification Korn.

[Catt]

Originally posted by korn469
ok from Catt's results it looks like the formula for a single stack is

(air unit's defense/AA rating)/10

Actually, my speculation is [AA Rating] / [Air Defense * 10], but that is based on very limited trials.

Catt

[alexman]

Would that mean that you have a 100% chance of success with AA = 10*AD? That should be an easy enough test... or not!