Close Combat calculation formulas

[davidss]

Got this from a readme file of some program ... don't remember which one. I'm not sure of its accuracy ... but it is interesting.

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 approximately 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 poisoned, you make a 2D6 roll "under poison resistance").
For example, the base accuracy is the value to determine if a fully experienced gunner firing the first shot at anon-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 occurs. 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 calculation, 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 are 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]

[TheReal_Pak40]

Hence here are the chances to hit :
6m-40m : 90%
41m-100m : 48%
101m-300m : 17%
301m-1800m : 2%

Wow, if this is true then it explains why tanks can't hit $hit in this game. I assume this if for stationary targets. Are moving targets harder to hit in the game engine?

[Andrew Williams]

You will have to check the LSA data files for each weapon.

Also remember most CC maps are only approx 500m wide

[TheReal_Pak40]

Andrew, the size of the CC maps should not matter. The "to hit" % should reflect real life figures. I have a hard time believing that a tank gunner, (even in a Sherman) will hit only 48% of the time between 41m-100m with AP ammo. This is point blank for any tanker. Obviously the CC figures are dumbed down for playability or whatever reason. This also explains tanks have a hard time hitting the sides of buildings from relatively close range. This should be 99.9% chance to hit a house at 200m, but in CC is closer to 40%.

[SteveMcClaire]

These formula was true in older versions of CC. Note that the formulas are also dependent on the values in the data files, since the range bands are defined there.

For the new combat model in LSA ranges are closer to realistic, and the factors that affect the to-hit calculation are different.

[TheReal_Pak40]

OK, but in regards to area fire on buildings, I don't recall tanks having much of a problem hitting buildings in older versions(Atomic) of CC. Maybe my memory is faulty. Also, the shots arn't just missing the buildings, the shots are WAY off, as if the gun was depressed several degrees below the targeted building. It's as if the buildings are being treated like they are flat ground and therefore it's hard for the gunner to hit the exact spot.

Also, there seems to be no bracketing of fire. If the area fire order is left in place there really seems to be a random chance to hit rather than an increased chance to hit with subsequent shots. Many times I've seen the gunner hit near or the exact spot where I'm aiming only to have the next shot miss the building entirely by over 10 meters.

[davidss]

ORIGINAL: Steve McClaire

These formula was true in older versions of CC. Note that the formulas are also dependent on the values in the data files, since the range bands are defined there.

For the new combat model in LSA ranges are closer to realistic, and the factors that affect the to-hit calculation are different.

Hi Steve,
what is the probability of you explaining the new LSA model probability calculation in detail?

have been curious about this for a long time, but never asked

[SteveMcClaire]

Prior to LSA, base accuracy was generally quite high and almost every shot any soldier took was a hit of some sort. This was compensated for by jacking up the terrain protection values so that the terrain would protect the target from most hits unless the accuracy of the hit was high (what is called 'critical' or 'good' in the notes above).

The main change in LSA (and on into future versions) is that aiming is now the main factor in accuracy. Troops that are suppressed (or worse) will tend not to aim (or lose their aim if they come under fire) resulting in low chance to hit beyond point blank range. This means that shots actually miss now, and terrain protection values can be dialed back to realistic levels since it no longer has to compensate for unrealistic accuracy ratings.

Steve

[davidss]

Thanks Steve ... appreciate you taking time to answer

[davidss]

Also, just out of curiosity ...

1. Regarding: 2*255+1=511 ... is the one added (at the end) so that there will never be a zero outcome?
2. Do shots fired at a specific target become more accurate as more shots are fired? and if so ... do they remain accurate once they hit the target?
3. Does each shot of a burst get is own probability of hit/kill calculated ... or is the entire burst one calculation?

[SteveMcClaire]

ORIGINAL: davidss

Also, just out of curiosity ...

1. Regarding: 2*255+1=511 ... is the one added (at the end) so that there will never be a zero outcome?
2. Do shots fired at a specific target become more accurate as more shots are fired? and if so ... do they remain accurate once they hit the target?
3. Does each shot of a burst get is own probability of hit/kill calculated ... or is the entire burst one calculation?

Hi davidss,

1) You're correct -- the two random components are generated first, then the +1 is added, so the result will never be zero.

2) Yes and yes. As long as the shooter doesn't switch targets the bonus stays.

3) The entire burst is one calculation, and only the first round of the burst hits the target even if you do get roll a hit. The rest of the rounds are treated as misses that hit the same map tile, which gives them a random chance to hit soldiers or vehicles within that tile (including the original target). If there's a vehicle within the tile the misses will almost always hit the vehicle. Soldiers will be hit by misses only rarely, and the chance goes down further the lower the soldier's stance. All the rounds in a burst apply suppression to the tile, even if they hit nothing.

Steve

[davidss]

ORIGINAL: Steve McClaire

ORIGINAL: davidss

Also, just out of curiosity ...

1. Regarding: 2*255+1=511 ... is the one added (at the end) so that there will never be a zero outcome?
2. Do shots fired at a specific target become more accurate as more shots are fired? and if so ... do they remain accurate once they hit the target?
3. Does each shot of a burst get is own probability of hit/kill calculated ... or is the entire burst one calculation?

Hi davidss,

1) You're correct -- the two random components are generated first, then the +1 is added, so the result will never be zero.

2) Yes and yes. As long as the shooter doesn't switch targets the bonus stays.

3) The entire burst is one calculation, and only the first round of the burst hits the target even if you do get roll a hit. The rest of the rounds are treated as misses that hit the same map tile, which gives them a random chance to hit soldiers or vehicles within that tile (including the original target). If there's a vehicle within the tile the misses will almost always hit the vehicle. Soldiers will be hit by misses only rarely, and the chance goes down further the lower the soldier's stance. All the rounds in a burst apply suppression to the tile, even if they hit nothing.

Steve

Hi Steve, thanks for your answers.

Since I don't have the training and expertise to understand how all the 0's and 1's produce a computer simulation ... I'm seeing things from a limited perspective.
But, I've noticed some aspects of LSA don't seem to align with expected results.
This of course is a subjective opinion ... which may or may not be true, but perhaps subjective viewpoints can In some way help improve simulation.

The problem with making changes in weapons.txt file data (for example) based on a person's perception of the simulation ... is finding a method to prove that the changes reflect the desired effect. Although "in game" observations can show if changes are moving the right direction ... it nevertheless leaves a person wondering if a more concrete method is possible ... perhaps using some of the data the game runs.
I've been making changes to some of the weapons data in GJS/ LSA (for Operation Perch). And in doing so have stumbled upon some things which seem to contradict the data in the columns.
For example: when trying to lessen the effect of the MG42 ... it was found that making small but significant changes to base accuracy, range modifiers, and penetration potential made very little difference in game.
Therefore I took a big swing at just the penetration potential and reduced it by 45% ... going from a nine to a five. The end result being a toned down but still powerful MG, which doesn't seem as much out of balance with other weapons.
A similar finding with rifles .... their penetration potential was increased 50% and ranges increased for better accuracy, which combined seems to give them suppression/penetration effectiveness that would be expected when compared to other weapons.
This leads me to believe that the extra rounds in a burst that the MG42 delivers, somehow gives it an advantage that isn't proportional to its weapons.txt data ... when compared to other weapons. And similarly, the single shots of rifles don't deliver enough penetration/suppression as expected, unless the penetration values are increased.
GJS doesn't have windows and doors coded in buildings, but these mentioned observations also seem apparent outside of buildings.

So, my question is ... is there another way to measure a weapons effectiveness , that takes in to account the apparent extra advantage of automatic fire, especially with a large burst MG42?
Maybe it would then be possible to calculate the penetration values for different weapons based on their effectiveness in game ... rather than their real world ratings.

[SteveMcClaire]

I don't see anything you've described that doesn't match up with what I said about the LSA changes above?

The extra rounds an MG42 delivers gives it that many more chances of a miss hitting someone in the target tile. 8 rounds vs. 4 for most other MGs means the MG42 has about 2 x the chance for misses to randomly hit someone else in the target area.

Changing penetration values for small arms (things that hit soldiers) change the amount of terrain cover they can penetrate. If you reduce MG42 penetration to 5 it means there is a lot more types of terrain that now have a chance to stop the round and prevent it from hitting the target soldier.

The single shots of rifles don't usually hit, and one rifle shot is not terribly suppressive. So when you say "...the single shots of rifles don't deliver enough penetration/suppression as expected..." I think it is a question of expectation. If you want a game where riflemen are much more effective then upping penetration values so rifle bullets penetrate terrain cover more often is one way to do it. Keep in mind that the % hit chance quoted in the first post is /not/ correct for LSA. The chance to hit is lower in LSA and subsequent titles since aiming and soldier skill are more important factors than the inherent weapon accuracy from weapons.txt.

Steve


Keep

[davidss]

Hi Steve,
thanks for your reply.
Think I'll continue along the route of adjustment/observation, in order to match things closer to expectation.

Also,
1.Could your explain the "aim" part of the calculation please? (using a math formula, like in the first post)

2.When you say "soldier skill" ... do you mean the "experience" and/or "morale" columns, in the teams.txt file?

[SteveMcClaire]

ORIGINAL: davidss
1.Could your explain the "aim" part of the calculation please? (using a math formula, like in the first post)

Sure, but I will need to go back and review the code to supply that level of detail. If you don't hear from me over the holidays please ping me again.

2.When you say "soldier skill" ... do you mean the "experience" and/or "morale" columns, in the teams.txt file?

Experience.

Steve

[davidss]

ORIGINAL: davidss
1.Could your explain the "aim" part of the calculation please? (using a math formula, like in the first post)

ORIGINAL: Steve McClaire
Sure, but I will need to go back and review the code to supply that level of detail. If you don't hear from me over the holidays please ping me again.

ping [:)]
sorry, my ping is two years overdue [8|]

[SteveMcClaire]

Hi davidss,

After some digging in the code, the way 'aiming' works in LSA is quite simple: If a soldier doesn't aim at all, their hit chance is minimal when firing at anything beyond point blank range. Unaimed shots at point blank range have 1/2 accuracy. Everyone always aims unless they're prevented by suppression (suppressed, pinned, or cowered) or morale state (panicked.)

Steve

[davidss]

Hi Steve,
Thank you

[davidss]

Hi Steve,
If/when you hv time ...

I. Aiming:
1. So, a soldier firing a weapon is in one of two states ... either aiming or not aiming?
2. Do different suppression and morale states affect aiming in varying degrees, or each of those states just switch a soldier's state to not aiming?
3. And only data ranges affect variation of not aiming?

II. Accuracy bonus:
4. Please explain how the accuracy bonus works when a gunner is locked on a target and more than one shot is fired?
5. Does the bonus increase as more shots are fired, or just one bonus percentage amount for each shot fired after first shot?

III. Probability Calculation:
6. I'm interested in how the LSA probability result is calculated.
If possible, can you give a math example of combat, which includes aiming and bonus?
Combat example: a Sherman against a PzIV in hedge, distance of two hundred meters, one tank suppressed ... or something like that.

Thanks

[SteveMcClaire]

Correct - a soldier either aims or he does not. Suppression effects whether a soldier aims at all -- if they're suppressed there is a chance they won't take time to aim. If they're pinned there is a high chance they won't take time to aim.

I am not sure what you mean by "And only data ranges affect variation of not aiming?" Any soldier will aim unless they're in a position where they can't (firing blind) or are too rattled to risk it (suppressed or worse.)

The accuracy calculation starts with the weapon's accuracy, as given in weapons.txt, scaled for range.

This initial accuracy is reduced by any wounds or suppression the soldier is under, and increased if he's gone heroic or better.

The resulting accuracy is then reduced a percentage amount corresponding to the max possible experience rating minus the shooter's experience trait (or in the case of crewed weapons/vehicles the higher of the shooter or the spotter's experience trait.) So the lower the experience value, the higher the percentage reduction.

For weapons that get a subsequent shot bonus (any crewed or vehicle weapon) an experienced-level based bonus is then added back to the accuracy value for every shot fired after the first, up to the maximum possible accuracy.

The maximum possible accuracy for any shot is the weapon's accuracy using the given ammo and range, from weapons.txt. For the first shot at new target, the max possible accuracy is the weapon accuracy or the shooter's (or spotter's) experience rating, whichever is lower.

Note that this is only the attacker's accuracy calculation. The actual shot is resolved by the defender and the attacker making an opposed roll where the defender's cover, movement speed, etc. influence the final determination of hit/miss, and the quality of the hit.

That is about as accurate as I can be without spend an hour or two stepping through the code to make sure I have every calculation down. But it does give you the important points -- weapon accuracy and soldier experience are the main modifiers.

Steve