Sorry about being slow to get this up - work is interfering with my "research."
I attached an Excel file with most of the trials I've done on attacks of bombers/stealth bombers on SAM/MSAM. I think I've got the SAM defense figured out, but the MSAM I haven't quite pinned down yet . . . I've found AA combat to not be quite as straightforward as the regular ground combat.
I noticed as you did that only about 4-5 anti-air units attempt to intercept an attacking aircraft, but haven't figured the exact number, yet.
I also noticed that setting the anti-air value for MSAMs to 1,000 resulted in a 100% aircraft kill rate, so I reasoned that the anti-air value must influence the probability of intercepting an aircraft. Also, even though AA combat is "all or nothing" (aircraft are destroyed, never damaged), I noticed that altering the hitpoints of the air and AA units altered outcomes. So, I reasoned that air combat likely had two stages: the aircraft must first be "intercepted," then the units combat to determine if the aircraft gets destroyed.
I made the assumption that the units fight a "normal" C3C combat using the anti-air defense as the attack value and the air combat defense as the defense value and that if the air unit loses the combat, it is destroyed. Of course, the expected outcome of such combat can be easily calculated. When the conditional probability of an aircraft kill given an interception is known, the probability of interception can be easily estimated given the overall aircraft kill rate. Trials with a variety of different combinations of hit points and air combat defense values but the same AA defense all yielded similar estimates of the probability of interception for regular and stealth bombers. Thus, I concluded that the probability of interception was solely a function of the AA value.
When I varied the AA values for attacking bombers and stealth bombers from 1 to 1,000, I found that the estimated probability of interception followed a predictable but non-linear form relative to AA values (see charts). It looks like some kind of inverse function. When you plot the AA values on a log scale, the curves take the nice sigmoid shapes of a logistic regression. I kind of doubt the C3C programmers are as into logistic regressions as I am; so, even though I can reasonably predict the probability of interception, I don't think I've hit on the data generating function, yet. Also, the minimum probability of interception appears bounded at ~0.2. The curves for the bomber and stealth bomber appear to have the same origin and ending, but the stealth bomber appears to have a lower probability of interception across the range of AA values even though values are quite similar around AA values used in C3C (2-8).
The SAM AA mechanics appear simple. I think there is an invariant probability of interception for bombers (50%) and stealth bombers (5%). Aircraft hit points don't seem to affect outcomes, and I think the aircraft and the SAM "fight" a single round of combat, and the aircraft is destroyed if it loses.
I hope this agrees with what you've already found out or nudges you along in your quest for knowledge. I made some guesses on the MSAM mechanics to save time on simulations, so let me know if you think I'm on the wrong track. I'm also assuming that the fighters function in the same way as the corresponding bombers. Give me a holler if anything doesn't make sense; I spend too much time hobnobbing with statisticians to make much sense to most people.
In addition to nailing down the MSAM function, I still have many unanswered questions . . .
Can AA attack>1x in the same turn?
What about MSAM's stacked with a SAM?
Does intercepting an aircraft cause abortion of the bombing run, even if the aircraft "wins" the combat?
Can an aircraft be attacked by >1 AA unit in the same attack?
Why does the stealth fighter have an air attack value?
If you haven't tackled these, I might be able to find time to chip away at a couple.
Looking forward to the stand alone calculator with ground and air combat.
