Reviewing my latest model
Hi FrEDa,
I hope my calculations are up-to-date too, but right now I wouldn't bet any money on it.
I went back and checked my latest model against as much data as possible. These numbers ought to work for all kinds of units and situations, not just GD = 0 or any other special case.
To clarify, because I think I'm working from different assumptions than you are:
P(hit) = 0.924
GD base = 0.767
I assume the same two-stage process as in AA fire, with one change, that a maximum of ONE point of GD can be used against each successful hit. So the process goes:
(a) At random, pick one unit from one side and allow it to fire on one unit from the other side.
(b) Compute firing unit's current SA allowing for strength and effectivity. Compute target unit's current GD rating allowing for same.
(c) For each full point of SA in the firing unit make one "did we hit?" check with 92.4 % probability of hitting.
(d) For each hit on the target unit, if there are still GD points unused, make one "was the hit nullified?" check with 76.7 % probability of nullifying the hit.
(e) For each hit not nullified, apply damage according to this distribution:
0.075 -- 33.3 % chance
0.150 -- 33.3 % chance
0.225 -- 33.3 % chance
Confirming the model against Mikel's observations
Mikel provided us with four different sets of test data. In one set of tests he got the GDeff value up high enough to completely stop all hits, but the results were perverse because they benefited the wrong side. In another set, he tested with smaller bonuses to GD base. I used that set of data to derive the values in this model. Finally, he also tested with day-long fights between units with high ratings, and 10-hour fights for units with low ratings. Let's look at those and see how my model fits.
If you have two 30/30 units fighting, in each hour you should get:
30 x 0.924 = 27.72 hits
27.72 x 0.767 = 21.26 of those hits nullified, leaving 6.46 that get through
For each of 6.46 hits, average of 0.150 % damage to target, total 0.97 % per hour.
If you look back to page 1 of this thread, you'll see that Mikel did a series of 30/30 trials and got losses of 16 to 22 % per day, average 19 %. If you allow for the fact that unit strengths would decline as damage accumulated, my model says 0.85 x 0.97 x 24 = 19.8 % per day.
For the trials that Mikel did with 30/60 or 30/120, we would expect the damage to be almost the same. The only case where the points above 30 would matter would be if one unit fought two, so that the extra GD points could be used against a second enemy. Mikel didn't do any tests of this kind.
Meanwhile if you look at Mikel's 1/1 trials, we would expect the one SA to hit 9.32 times in 10 hours, and then to be nullified 7.15 times, leaving 2.17 hits per 10 hours. Actual hits in 10 hours: 2.08. And in Mikel's 2/1 trials, we would expect 2.17 hits per 10 hours from the first SA point plus 9.32 from the second, total 11.49, and again this agrees with Mikel's observations.
So this model fits, within the limits of random error, with everything Mikel has given us. We still can't explain (a) how the wrong side gets the benefit of ground_def_eff bonuses, or (b) why sometimes hits get through what should be a 100 % shield. But otherwise the model is consistent.
Side comment
Now to be clear, this model as it stands at the present moment doesn't agree in any coherent way with the 10 % rollover text you see in the actual game, or the 66.7 % mentioned in the manual, and it doesn't agree especially well with Mikel's early 1/3rd rule either, although it does agree that there will be a minimum amount of damage suffered at all times.
However, I think we just have to set that aside. Not agreeing with the manual or with rollover text really doesn't prove anything. I've been tempted to look for some hidden agreement a number of times and it has never worked out.
