Combat calculation

[SSLConf_pewp3w]

Okay, so this has been bugging me. It seems like PC2 has taken a page from order of battle, insofar that you do less damage to units that have little strength left. This is especially annoying with air units. I check how much damage all of my units combined would do and it comes out to 10 without the mass attacks. I then start the attacks and it turns out that the second and third attack do one less damage that it showed originally. This usually leads to enemy air units retreating and returning a turn later with full health. I checked the log but could not find anything. Is there any explanation or am I just having bad luck?

Or just a recent example. My tank would do 6 damage to a 7 strength unit. So I call in my air force to bomb the unit down to 6 so I can trigger an overrun. After the air attack my tank just calculates with 5 damage. Why is that?

[MickMannock]

Okay, so this has been bugging me. It seems like PC2 has taken a page from order of battle, insofar that you do less damage to units that have little strength left. This is especially annoying with air units. I check how much damage all of my units combined would do and it comes out to 10 without the mass attacks. I then start the attacks and it turns out that the second and third attack do one less damage that it showed originally. This usually leads to enemy air units retreating and returning a turn later with full health. I checked the log but could not find anything. Is there any explanation or am I just having bad luck?

Or just a recent example. My tank would do 6 damage to a 7 strength unit. So I call in my air force to bomb the unit down to 6 so I can trigger an overrun. After the air attack my tank just calculates with 5 damage. Why is that?

Regarding air combat, I totally understand what you are saying. I'm also having a frustrating time trying to kill off airplanes. It gets extra difficult as I find that I can't have that many fighter planes anyway, due to the limited core slots. I've found that having AA units shooting at the enemy airplanes first, before I send in my fighters help a bit. But the AA units gets used on very limited situations, so I'm not sure if it's worth the core slots they are consuming (I currently use 2 x 20mm flak guns).

[Rudankort]

Here is a slightly modified post from the beta forum:

This phenomenon is not entirely intentional, there is no special rule in place or anything, but it is a direct consequence of how this kind of a game works. It might be unintuitive on the first glance, but if you think about it, it will actually make sense.

Imagine that you attack a 10 strength unit and kill 5 points on average. Real results will be distrbuted equally around 5, you will get a lot of 6s and 4s, some 7s and 3s and so on. Prediction in this case will be 5.

Now imagine that you attack a 5 strength unit and also kill 5 on average. Often your attack will kill 5, slightly less often 4, occasionally 3 etc. But you will never kill more than five. It is impossible because the target does not have more than 5 points. So when you average out all possible combat results, you will get a number less than 5 as well. Note that you will not see this effect all the time, but only when expected kills are similar to unit's health.

This is how it always works in this kind of a game. It has nothing to do with "finishing crippled units is more difficult" special rule - if you have enough firepower, you will squash such units in a single attack. The logic which I described above applies the same way to Panzer Corps, to the old Panzer Generals and I think to many other games too. The only difference between Panzer Corps 2 and previous games is that it tries to provide a more accurate prediction. I actually did lots of tests (like 100000 repeats of every combat), averaged the result, compared it to prediction, and when there was a difference, I fixed it. I did it because in Panzer Corps 2 prediction is no longer just a prediction, but an integral part of all combat results at the default 50% randomness, so I felt it needed to be as accurate as possible.

[MickMannock]

Here is a slightly modified post from the beta forum:

This phenomenon is not entirely intentional, there is no special rule in place or anything, but it is a direct consequence of how this kind of a game works. It might be unintuitive on the first glance, but if you think about it, it will actually make sense.

Imagine that you attack a 10 strength unit and kill 5 points on average. Real results will be distrbuted equally around 5, you will get a lot of 6s and 4s, some 7s and 3s and so on. Prediction in this case will be 5.

Now imagine that you attack a 5 strength unit and also kill 5 on average. Often your attack will kill 5, slightly less often 4, occasionally 3 etc. But you will never kill more than five. It is impossible because the target does not have more than 5 points. So when you average out all possible combat results, you will get a number less than 5 as well. Note that you will not see this effect all the time, but only when expected kills are similar to unit's health.

This is how it always works in this kind of a game. It has nothing to do with "finishing crippled units is more difficult" special rule - if you have enough firepower, you will squash such units in a single attack. The logic which I described above applies the same way to Panzer Corps, to the old Panzer Generals and I think to many other games too. The only difference between Panzer Corps 2 and previous games is that it tries to provide a more accurate prediction. I actually did lots of tests (like 100000 repeats of every combat), averaged the result, compared it to prediction, and when there was a difference, I fixed it. I did it because in Panzer Corps 2 prediction is no longer just a prediction, but an integral part of all combat results at the default 50% randomness, so I felt it needed to be as accurate as possible.

Well, I was comparing to my experience with Panzer General/Panzer Corps and I have no numbers on this of course, it's just a feeling. But if I take the Poland and Norway scenarios as an example (where your 109's are up against biplanes), as far as I can remember, I was always able to bring a biplane down with two 109's. In Panzer Corps 2, there's no chance to bring a biplane down with two 109's and in several cases it doesn't even help bringing a third plane along (Bf110). And that feels kind of jarring, especially as I can't have as many planes in my core as I could in PG/PC (well, I can have more planes, but then I need to sacrifice a lot of other stuff).

I'm not saying this is wrong, I'm just saying it feels weird and unusual, as I'm just not used to this happening. I'll probably adjust after I've gotten a few hundrerds of hours of the game under my belt.

[Rudankort]

Well, I was comparing to my experience with Panzer General/Panzer Corps and I have no numbers on this of course, it's just a feeling. But if I take the Poland and Norway scenarios as an example (where your 109's are up against biplanes), as far as I can remember, I was always able to bring a biplane down with two 109's. In Panzer Corps 2, there's no chance to bring a biplane down with two 109's and in several cases it doesn't even help bringing a third plane along (Bf110). And that feels kind of jarring, especially as I can't have as many planes in my core as I could in PG/PC (well, I can have more planes, but then I need to sacrifice a lot of other stuff).

Well, it's a different question. If this particular plane is underperforming, then it's stats might need adjustment.

[MickMannock]

Well, it's a different question. If this particular plane is underperforming, then it's stats might need adjustment.

It's just my initial observation (both now and during the beta), but given that the 109 was the premier fighter plane in Europe in 1939/40 (next to the Spitfire), I think it should be comparatively stronger than your different biplanes, the Potez 630-series, Bristol Blenheim, etc.

[nexusno2000]

Well, it's a different question. If this particular plane is underperforming, then it's stats might need adjustment.

It's just my initial observation (both now and during the beta), but given that the 109 was the premier fighter plane in Europe in 1939/40 (next to the Spitfire), I think it should be comparatively stronger than your different biplanes, the Potez 630-series, Bristol Blenheim, etc.

My best guess why it's stated that way: balancing for multiplayer.

[SSLConf_pewp3w]

Here is a slightly modified post from the beta forum:

This phenomenon is not entirely intentional, there is no special rule in place or anything, but it is a direct consequence of how this kind of a game works. It might be unintuitive on the first glance, but if you think about it, it will actually make sense.

Imagine that you attack a 10 strength unit and kill 5 points on average. Real results will be distrbuted equally around 5, you will get a lot of 6s and 4s, some 7s and 3s and so on. Prediction in this case will be 5.

Now imagine that you attack a 5 strength unit and also kill 5 on average. Often your attack will kill 5, slightly less often 4, occasionally 3 etc. But you will never kill more than five. It is impossible because the target does not have more than 5 points. So when you average out all possible combat results, you will get a number less than 5 as well. Note that you will not see this effect all the time, but only when expected kills are similar to unit's health.

This is how it always works in this kind of a game. It has nothing to do with "finishing crippled units is more difficult" special rule - if you have enough firepower, you will squash such units in a single attack. The logic which I described above applies the same way to Panzer Corps, to the old Panzer Generals and I think to many other games too. The only difference between Panzer Corps 2 and previous games is that it tries to provide a more accurate prediction. I actually did lots of tests (like 100000 repeats of every combat), averaged the result, compared it to prediction, and when there was a difference, I fixed it. I did it because in Panzer Corps 2 prediction is no longer just a prediction, but an integral part of all combat results at the default 50% randomness, so I felt it needed to be as accurate as possible.

That makes total sense and I hadn't thought about that, but it is not what I mean. I will see if I can get a screenshot when I'll play later, but basically it means the following. Before I attack an enemy plane, I will check with all of my fighters how much damage they will do and if it will be enough to destroy the plane. Now for example the enemy plane has 10 strength left. I check with my first plane: It will deal 5 damage. I check with my second plane, it will also deal 5 damage. Now I move both planes in, attack with the first one and deal 5 damage. Then I select the second plane, hover over the enemy plane and for some reason it shows only 4 predicted damage now.

[Rudankort]

That makes total sense and I hadn't thought about that, but it is not what I mean. I will see if I can get a screenshot when I'll play later, but basically it means the following. Before I attack an enemy plane, I will check with all of my fighters how much damage they will do and if it will be enough to destroy the plane. Now for example the enemy plane has 10 strength left. I check with my first plane: It will deal 5 damage. I check with my second plane, it will also deal 5 damage. Now I move both planes in, attack with the first one and deal 5 damage. Then I select the second plane, hover over the enemy plane and for some reason it shows only 4 predicted damage now.

This is exactly what I'm saying. Statistically, given exactly the same parameters (accuracy, attack strength etc.), the number of kills WILL depend on how many enemies there are. So you cannot use prediction made when there are 10 enemies, and extrapolate it to situation when there are only 5 left.

[panzeh]

Well, it's a different question. If this particular plane is underperforming, then it's stats might need adjustment.

It's just my initial observation (both now and during the beta), but given that the 109 was the premier fighter plane in Europe in 1939/40 (next to the Spitfire), I think it should be comparatively stronger than your different biplanes, the Potez 630-series, Bristol Blenheim, etc.

I've played through the whole campaign and i never really found my fighters being anything but superior to their opposition except at Dunkirk with spitifres.

[MickMannock]

Well, it's a different question. If this particular plane is underperforming, then it's stats might need adjustment.

It's just my initial observation (both now and during the beta), but given that the 109 was the premier fighter plane in Europe in 1939/40 (next to the Spitfire), I think it should be comparatively stronger than your different biplanes, the Potez 630-series, Bristol Blenheim, etc.

I've played through the whole campaign and i never really found my fighters being anything but superior to their opposition except at Dunkirk with spitifres.

I was comparing to the power of the 109E in PG/PC. Is this what you are refering to also? Cause I'm not saying the 109E is a lesser fighter plane compared to the other fighters it's up against in 39/40 (the Spitfire being the notable exception of course).

[SSLConf_pewp3w]

That makes total sense and I hadn't thought about that, but it is not what I mean. I will see if I can get a screenshot when I'll play later, but basically it means the following. Before I attack an enemy plane, I will check with all of my fighters how much damage they will do and if it will be enough to destroy the plane. Now for example the enemy plane has 10 strength left. I check with my first plane: It will deal 5 damage. I check with my second plane, it will also deal 5 damage. Now I move both planes in, attack with the first one and deal 5 damage. Then I select the second plane, hover over the enemy plane and for some reason it shows only 4 predicted damage now.

This is exactly what I'm saying. Statistically, given exactly the same parameters (accuracy, attack strength etc.), the number of kills WILL depend on how many enemies there are. So you cannot use prediction made when there are 10 enemies, and extrapolate it to situation when there are only 5 left.

Ah, alright. I think now I understand. I wonder why I never had this problem in PC1 or at least never realized it

[Rudankort]

Ah, alright. I think now I understand. I wonder why I never had this problem in PC1 or at least never realized it

Like I said, Panzer Corps used a simplified prediction algorithm, so it would probably show you the same prediction for 5 and 10 enemies. But if you actually made a big number of tests, you would notice the difference in average outcome. In any case, it just means that you need to bring in slightly more firepower.

[turn4441]

I'm also confused with this as the 'logic' Rudankort describes is NOT the way it worked in PC1. As he describes it, a 10 strength unit attacking a 5 strength unit will have a hit chance probability curve that is truncated/maxed at 5 kills as the defender can only lose 5 units. However, in PC1, a 10 strength unit with a 50% kill chance when attacking a 5 strength unit, had 10 chances to roll a 'killing' shot and, therefore, the probability curve centered at 5, due to the fact that the attacker had 10 shots, not because the defender only had 5 strength. The attack could be anywhere from 0 (no killing shots) to 10 (all killing shots). Killing rolls numbering over 5 were allowed, but couldn't cause more damage than the 5 strength of the attacked unit. The defenders strength determined the max number killed while the attacking unit determined the number of kills (and potentially, non-counted overkill). See the pictures below showing a second attack (following a previous Bf109 attack) from a 10 strength Bf109 on a 5 strength Polish biplane from the first scenario of GC39 which shows the attacker getting 6 'kill' shots out of 10 on a 53% kill probability and 7 'kill' shots out of 10. Also, the pre-attack probabilities did not decline after the first attack due to the lower strength of the defender. Also, the combat modifiers/calculations didn't change no matter how much damage the first attack did, the attack values remained the same, predicting 5 kills for both attacks. Obviously, it would predict fewer if less survived the first attack, but it did not give a lower number for the second attack as described above. If a similar attacker is allowed a maximum of 5 'kill' shots in PC2 despite having 10 attacks, then this is very much different than PC1 and more like the OOB idea of being harder to chase down and finish lower strength units.

[turn4441]

After looking at some of the Combat Logs from PC2, it does appear that it will only roll as many times as necessary to get the max kills. For example, a 10 strength plane attacking with a 50% kill rate against a 2 strength plane may roll 10 times, if necessary, but will more likely only roll 3-5 times and will stop once it gets 2 'hits' with 'killing' rolls. However, the 50% random is then applied to only the two kills so, indeed, it will not be above 2 (as it could have been in PC1) but will be 2 or less. In PC1, the randomization was applied (unseen) to the individual rolls and all rolls were conducted, unless you played chess mode in which you received the predicted results without any rolls at all. So, given the above example, in PC1, you could roll anywhere from 0-10 post-random kills against the 2 strength plane while in PC2 you can only roll 0-2 kills which is then randomized, so 2 is the max and it is much more likely that you will not be able to finish a weak opponent than it was in PC1.

On a side note, while the new Combat Details is detailed, it was much easier to quickly decipher in PC1 given the tabular format. Now, it often requires scrolling more than one screen and is not so quickly obvious as you can't compare the antagonists side by side. That being said, I do like having previous combat results listed in order on the left side so you can look back more than just the most recent combat.

One other thing, I found it curious while testing this that if you save and repeat the same attack multiple times, you will always get the exact same dice rolls in PC2. Maybe so you don't get results you like better (but then all you need do is change the attack order)? If you reload PC1 and do the same attack over and over, you will get different rolls. Seems strange the random number generator wouldn't reseed when reloading.

[Rudankort]

However, in PC1, a 10 strength unit with a 50% kill chance when attacking a 5 strength unit, had 10 chances to roll a 'killing' shot and, therefore, the probability curve centered at 5, due to the fact that the attacker had 10 shots, not because the defender only had 5 strength.

That's the thing. We are talking about outcome, not about shots, and so how many shots the attacker has is irrelevant. You cannot kill more than 5, period, and so probability curve cannot be centered on 5, 5 is maximum.

You have made two tests, but it's not nearly enough. Ideally, you need a huge number. But here is my result with 10:
https://www.dropbox.com/sh/yvs4rumc9vtk ... 2j0Ra?dl=0

First six tests were 5, but then I got 2, 3, 5 again and 4. If we calculate average result, it will be:
(5*7 + 2 + 3 + 4)/10 = 4.4

So all of a sudden, 4 would be a more precise prediction than 5.

This is not a proof. This is an illustration. But I have extensively tested it and I can say with confidence that on a large number of tests predictions made by Panzer Corps 2 are more precise than predictions made by Panzer Corps. And this is the only real difference.

Yes, Panzer Corps 2 stops rolling dice when full enemy strength is killed, but it does not matter because the enemy is dead anyway. Damage done is not different in this case with PzC and PzC2 algorithms. It's just a little optimization which allows the program to avoid unnecessary work.

[turn4441]

Rudankort, I apologize, as I know you are busy with many things, but I wanted to clarify things and will try to be brief. I see what you're saying, I agree and was not trying to malign the calculations/testing involved. I'm aware that 2 examples does not a statistical distribution make and only showed those two pics as an example that you could have more killing rolls than defender strength points in PC1.

That being said, my logic was correct. However, it proceeded from an flawed premise. I incorrectly thought (or didn't look down far enough as I haven't played much and am used to the old combat log) that the outcome result (2-0 above) was being randomized by 50% (on default settings), and, if it could not be higher than 2, was only using the right side of a probability curve and, therefore, would have a bias on the low side. I now see my mistake is that it is 50% of the real outcome (as you mentioned & determined by the RNG) combined with 50% of the predicted outcome. Therefore, if the predicted and real outcomes are both 2-0, you should get a 2-0 and if real is 0-0, you should get a combined 1-0. In the latter case, I assume you would never get a 0-0, 1-1, 1-2, 0-2, 2-1 or 2-2 as 50% or each could only give a 1-0 result.

So, in summary, 0 random setting is chess, 100 is full random and any other percentage gives some result between the two. Is this correct now?

Again, I do really like the turn by turn history in the combat results.

[Gwaylare]

The problem here is that PC and PC2 shows different things. In PC we were used to see the expectancy value of hits (the old PC hits) in the combat prediction. It was the same in short and detailed prediction. As Rudankort explained we now have the expectancy value of kills.
As long as our targets strength is at least as high as the number of shots we fire, this is exactly the same. Once we have more shots than strength, the expectancy value of hits is larger than the expectancy value of kills.

Here an easy to calculate expample: Our unit has 2 shots with 50% chance to kill and our target has strength 1.

The possibities are
miss, miss
miss, hit
hit ,miss
hit, hit

The expectancy value of his is 1, because there are 4 hits out of 4 possibilities. This was displayed in PC.

Now we are doing the same with PC2 kills.

miss, miss
miss, kill
kill, already dead
kill, already dead

The expectancy value now is 3 kills out of 4 possibilities, so it is 3/4, ok this rounded to 1 as well, but is different for larger numbers. This is displayed in PC2.


What we did in PC was adding the expectancy value of hits of several units to get a picture, if they all togehter are able to kill a target. You can do this with PC2 prediction as well, because as long a strength of target is high enough both calculations are the same. The problem is it was wrong in PC already and now this flaw is getting obvious. A sum of 10 predicted hit is not a 100% chance to kill a strength 10 unit. I have learned to use a sum of 11 or 12 to kill a unit and even this is still not a 100% chance.

Best regards
Gwaylare

[Gwaylare]

Like I said, Panzer Corps used a simplified prediction algorithm, so it would probably show you the same prediction for 5 and 10 enemies. But if you actually made a big number of tests, you would notice the difference in average outcome. In any case, it just means that you need to bring in slightly more firepower.

With all you said about your calculations, I totally agree. As a prediction this is more precise than the short prediction we had in PC. The problem we have at the moment is a missing detailed prediction.

With the RNG setting of 50% I realized that with one of the first patches the calculation changed and you use decimal values instead of rounded integers. This does improve the result a lot, because those rounded values before gave a dominant impact to the result. As an example a prediction of 1 kill was 1 kill sure, because using 50% of your prediction, is rounded to 1 kill already.
Before the patch the patch a calculates prediction of 0.53 was rounded up to 1, meaning we will get a kill, even if RNG will give us no kill: (1 (prediction) + 0 RNG ) / 2 = 0.5 rounded up to 1 kill.
So now the prediction of 0.53 is not rounded anymore (just for displaying reasons), so calculation is 0.53 (prediction) + 0 kill / 2 = 0.265 rounded down to 0. That is much better and a great improvement for the 50% RNG mechanism.

For multiplayer we are using chess mode, there we still lack an improvement like this. So a prediction of 0.53 is rounded up to 1 kill, while 0.48 is rounded down. So an minimal improvement like adding a scout to a combat may give an additional kill or may do nothing at all. This feels a little bit odd. Together with RNG an action like adding a scout to a combat will always improve your chances, but never will have no effect. This leeds to some strange situations:

• Till the prediction of kills an attackings unit gets in return is lower than 0.5 you will get a kill yourself.

• If the prediction is lower than 0.5 you have absolutly no chance to inflict damage, even to a fully surpressed and surrounded tank

• There are situations, were splitting up a unit does inflict more damage (artillery or aircraft). With a prediction of 3.4 you do 3 damage, while splitting up the unit you will have a prediction of 1.7 and will inflict 2 damage twice.

I could add several points to this list. All are small effects, but they make feel the mechanism a little bit odd, because rounding values has to much effect on the result.

Here a two proposals to improve the situation:

1) If you like to stay without any random effects in chess mode multiply the hitpoints of units with 10. 100 for a tank and 150 for infantry. While taking damage inflict together with a prediction of 3.4 total of 34 damage. For combat calculation round hitponts to get combat strength, 74 hitpoints will get strength 7 for combat calculation. For displaying reasons you can show rounded strength values as well, better is to show real hitpoints instead. Overall you will shift rounding results by one decimal place. This will be much smoother than what we have now.

2) If you can deal with a little bit of RNG in chess mode, than overwrite your function to round combat results by an RNG based funtion. Just interpret any decimal places needed to be rounded as a chance to roll a die. So 2.51 will be 51% chance to get a 3 and a 49% chance to get a 2. Then any effect to improve your chances will really have an effect. In the prediction you can show this as 2.5 or as "2 - 3", may be 2.2 as "2 < 3" and 2.8 as "2 > 3".

Overall by changing RNG to a more intuitive and reliable concept, you do get other problems instead. So may be just try to roll even more dice. For a unit wit strength 10 roll 1000 or even 10000 dices and use an average value. This will give a much smoother result, but it is still an RNG.

Best regards
Gwaylare

[Rudankort]

Here a two proposals to improve the situation:

1) If you like to stay without any random effects in chess mode multiply the hitpoints of units with 10. 100 for a tank and 150 for infantry. While taking damage inflict together with a prediction of 3.4 total of 34 damage. For combat calculation round hitponts to get combat strength, 74 hitpoints will get strength 7 for combat calculation. For displaying reasons you can show rounded strength values as well, better is to show real hitpoints instead. Overall you will shift rounding results by one decimal place. This will be much smoother than what we have now.

2) If you can deal with a little bit of RNG in chess mode, than overwrite your function to round combat results by an RNG based funtion. Just interpret any decimal places needed to be rounded as a chance to roll a die. So 2.51 will be 51% chance to get a 3 and a 49% chance to get a 2. Then any effect to improve your chances will really have an effect. In the prediction you can show this as 2.5 or as "2 - 3", may be 2.2 as "2 < 3" and 2.8 as "2 > 3".

Zero randomness is advertised as "what you see on prediction is what you get", and this is how many players actually want it, so I don't think it's an option to make it random in any way. However, going to "everything is 100 instead of 10" is an interesting idea which potentially could be done as an option. Have you tried it (just open a scenario in the editor, and mass-make all units 100 in Configure Units mode)? Does it give a good enough result?

Overall by changing RNG to a more intuitive and reliable concept, you do get other problems instead. So may be just try to roll even more dice. For a unit wit strength 10 roll 1000 or even 10000 dices and use an average value. This will give a much smoother result, but it is still an RNG.

Rolling 1000 and especially 10000 dices will generate something very similar to prediction. In fact, by mixing in prediction to "true random" result, I think we achieve a very similar effect, except you can very precisely control how strong you want this effect of "randomness reduction" to be. I have not used this approach in any previous games, but I think that in terms of controlling randomness it is actually very powerful, although it does create some oddities.

BTW, note that we WILL allow to set any randomness you want in MP scenarios, once Advanced Options is unlocked. Zero will only remain as the default.