Close Combat calculation formulas
The results following an action are based on probabilities. I'll try here to sum-up the known facts about probability calculations.
The 1-511 rolls :
Many probabilities rates are based on 1-511 rolls (chances to hit probabilities, jamming probabilities ...)
Why 511 ? 511=255*2+1. For the ones who have played board RPG, it is like the 2D6+1 rolls in Dungeon&Dragon for example. Here it is a 2D255+1. 255 is the byte size.
The probability to make a given value from 0 to 255 is the same for every value. but if you add two of these values, you obtain values which probabilities are not the same. (it has approximatly a bell curve profile).
"Tests" :
When you want to know if you have hit or if your weapon is jammed, the program makes a 2D255+1 roll which must be under a given value. (just as in D&D, if you want to know if you have been poisonned, you make a 2D6 roll "under poison resistance").
For example, the base accurracy is the value to determine if a fully experienced gunner firing the first shot at a non-moving target at point blank range hits. (cf. CC2 FAQ, answer 87) The "base accuracy" value for many AT guns is about 400. It implies you must obtain a 2D255+1 inferior to 400 to hit. (in such condition, in the game, it is often inferior-moving targets ...).
Chances profiles of the 1-511 rolls :
Just try a little experiment : look at the results you can obtain adding the result of 2 dice : you obtain a 2-12 value. But in fact the chance to have a 6 is superior to the one to have a 2 or 12. The profile is about a bell curve.
Here is the probability profile of a 1-511 roll :
An event with a value of 511 always occures. For example the "No jam no break" value (weapons file) for the weapon Melee is 511. "No jam" occurs 100% of the time.
Chances to hit :
Then we can take exploit that : let us study the probability to hit. (calculs are based on what is said in the CC2 FAQ).
Base Accuracy :
I quote : Base Accuracy is the chance to hit if you had a fully experienced gunner firing the first shot at a non-moving target at point blank range.
Example : for a value 398, the chance to hit is 90%.
Accuracy at Close, Medium and Long ranges:
I quote : The accuracy drops for each range category the target is at from the firer (Close, Medium, and Long). It's an involved function, so I won't go into the details of the calulation, but basically, your chance to hit goes to 5/8 of Base at close, 3/8 at medium and 1/8 at long. Remember this is on a bell curve, so whacking 1/8 of the chance off is a major drop in the chance to hit.
The ranges is given for each gun and each ammo in the weapons file. For example : for a Sherman 75 (AP round), you fire at Point Blank (PB) if the attacker is not beyond 40m, Close : 100m, Medium : 300m, Long till 1800m. (beyond 1800m, proba should be zero).
According to the FAQ, here are the hit chance values for the different ranges :
6m-40m : 398
41m-100m : 249 (=398*5/8)
101m-300m : 149 (=398*3/5)
301m-1800m : 50 (=398*1/5)
Hence here are the chances to hit :
6m-40m : 90%
41m-100m : 48%
101m-300m : 17%
301m-1800m : 2%
...at best...
Chances to kill:
Hitting a target is not sufficent : you must destroy it ! Let us deal with the chances to kill :
I quote th FAQ :
The % chance [to kill] is calculated as follows if the attack is less than the defense:
[Attack is the kill rating at the given range, defense is the armor value at the given fire angle. (side low, bottom, high rear, front side low, etc... there are 21 fire angles for the Hull, 21 others for the turret !)]
(7 * (attack - defense) + attack) / (attack + defense)
or as follows if the attack is greater or equal to the defense:
(2 * (attack - defense) + attack) / (attack + defense)
An example :
So a bazooka vs a Tiger front turret would be (7 * (100 - 101) + 100) / (100 + 101) or 46% chance. Vs the Tiger's hull, it would be (7 * (100 - 115) + 100) / (100 + 115) or less than 0% which would require a critical hit.
It's interesting to note that if your are not firing directly at the front turret of the Tiger, you can't reasonably kill it with a bazooka. The front/side rating for the Tiger is 148 and 138 for turret/hull resp. Thus, if you want to kill a Tiger without a side shot, the Tiger will most likely be shooting at you. For a side shot, its 80 and 60 so the chances go to 77% and greater than 100% respectively.
But there different types of hits, which depends upon two other 1-511 rolls :
Here is how a hit is determined. Each attack is measured in a chance to hit (1 to 511) [attack roll, the lesser it is the best for the attacker (gun)] and chance to be protected or behind cover (1 to 511) [defense roll, the less it is the best for the defender (target)]. These are 2d 255 + 1 = 1 to 511 on a bell curve rolls. If the defense roll is greater than the cover rating, it is a "hit".If the defense roll is less than or equal to the cover rating, it is an area hit.If the defense roll is less than or equal to the cover rating, it is an area hit. If the attack roll is less than 1/4 the needed to hit [the value we spoke about above], it is a critical hit, if it is less than 1/2 the needed to hit, it is a good hit, else it is a poor hit.
A critical hit gets resolved at 2 x kill rating and defender gets no protection from terrain.
A good hit gets resolved at normal kill rating and defender gets no protection from terrain.
A poor hit gets resolved at normal kill rating and defender gets full protection from terrain.
An area hit gets resolved at (kill rating - protection from terrain) and defender gets full protection from terrain.
Because it is resolved on a bell curve, a To Hit at 50% (256) does *not* get a critical hit 12% of the time. 1/4 of 256 is 64, and on a 1-511 bell curve, this is acheived only about 3% of the time.[just look at the curve above] If your to hit gets up to 80% (350), the chance for a critical goes to about 5% [the same way, chances to do a poor hit increases if the chance to hit decreases]. Also, as you can see, a weapon with high penetration value and poor to hit can still do fairly well as long as the protective value of the terrain is less than the penetration value of the weapon. When you are firing at someone in a building, you almost have to have such a weapon to hurt them as the chances of getting a Good or Critical hit are very small.
If there is no terrain protection, and let us suppose that the target have been hit. (the accuracy value was for example 300, the chances to hit were about 65%). The defense roll is always superior to the terrain protection since there is no protection.
1/4 of 300 is 75, 1/2 of 300 is 150.
We have a "hit", but which hit ? On the curve above, we see that we have the following probabilities to do the different hit types :
critical : about 4% (75)
good : about 17% (150)
poor : 100-17-4=79% (more than 150)
There is no terrain protection, so here good and poor hits have the same result, so :
normal kill rate, normal armor protection : 96% chance.
double kill rate, normal protection : 4% chance.
If my chance to hit would have been lesser than 300 (let us take 100), my chances to hit would have been reduced (about 8%), but my chance to do a good or critical hit would have decreased also :
1/4 of 100 is 25 : chance to do less is under 2% (critical hit)
1/2 of 100 is 50 : chance to do less is about 3% (good hit)
chances to do more than 50 is about 95%.(poor hit)
My opinion is that in the interface, the critical and good hits are reported as "direct hit" and "hit", and the poor or area hit as "area hit". You can see that at great distances, when you hit, the hits are often reported as "area hits".
Important : this part is not sure, it is my theory. I may be wrong, but it describes good what I saw in CC2. I may be wrong, and if you have any comments, please email me at: hadacef9@cti.Ecp.Fr.
Kill ratings
Let us interprete this figures with cool diagrams, for AT guns vs armored vehicules.
For many (if not all) AT guns, the base accuracy is equal to 400. Then we can calculate (independantly from the chance to hit calculation), the chances to make the different hit types at each range (with a fully experienced gunner, on a static target, at first sight, and with no terrain protection) :
PB : accuracy is base accuracy (400)
critical hits : 8% (100)
good hits : 30% (200)
poor hits : 62% (100%-8%-30%)
Close : accuracy is about 400*5/8=250
critical hits : 3% (62)
good hits : 12% (125)
poor hits : 85%
Medium : accuracy is about 400*3/8=150
critical hits : 1or2 % (37)
good hits : 4% (75)
poor hits : 95%
Long : accuracy is about 400*1/8=50
critical hits : less than 1% (12)
good hits : less than 2% (25)
poor hits : more than 98%
Then we can do penetration diagrams since we know that :
-at PB, there 8% chance that the hit is at 2*kill rating
-at close range, 3% ...
Then the kill computation is made with the following formula :
I quote the FAQ :
[The kill rating is :]
(7 * (attack - defense) + attack) / (attack + defense)
or as follows if the attack is greater or equal to the defense:
(2 * (attack - defense) + attack) / (attack + defense)
So a bazooka vs a Tiger front turret would be (7 * (100 - 101) + 100) / (100 + 101) or 46% chance. Vs the Tiger's hull, it would be (7 * (100 - 115) + 100) / (100 + 115) or less than 0% which would require a critical hit.
It's interesting to note that if your are not firing directly at the front turret of the Tiger, you can't reasonably kill it with a bazooka. The front/side rating for the Tiger is 148 and 138 for turret/hull resp. Thus, if you want to kill a Tiger without a side shot, the Tiger will most likely be shooting at you. For a side shot, its 80 and 60 so the chances go to 77% and greater than 100% respectively.
Let us take another example : US gun 75L40 (AP round) of a sherman against Tiger Front Side Hull (armor value : 138) : here are the basic kill ratings of the 75L40 at the different ranges :
PB : 133 (doubled : 266)
Close : 115 (doubled : 250)
Medium : 80 (doubled : 160)
Long : 60 (doubled : 120)
At PB :
Here is the formula [see above] to calculate the probability to kill : 133 is inferior to 138. There is no terrain protection. Hence the formula is :
(7*(133-138)+133)/(133+138)=36% : a good or poor hit has 36% chance to kill.
Here is the formula [see above] to calculate the probability to kill with a critical hit : 2*133 is superior to 138. The terrain protection has no effect (plus there is no). Hence the formula is :
(2*(2*133-138)+2*133)/(2*133+138)=288% : a good or poor hit has 100% chance to kill.
The final chance to kill if you hit at PB is thus :
92%*36%+8%*100%=42.2%.
The Sherman 75 has 42.2% to kill the tiger at this fire angle, if it has the chance to hit the tiger.
[In fact there is also a chance to hit the Tiger Front Side Turret Armor which is better armored (149) instead of the hull part, so it is a bit more complicated and the tiger also have a 88L56 gun, good luck gunner, you'll be a hero]