Combat Equation

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proline
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Combat Equation

Post by proline » Tue Mar 03, 2015 7:20 pm

Is there a good post anywhere that clearly explains the combat equation in full detail? I've done some searches and found bits and pieces but not a comprehensive explanation.

ThvN
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Re: Combat Equation

Post by ThvN » Fri Mar 06, 2015 10:03 pm

Hi, sorry for the late reply, but what exactly are you looking for? Some combat mechanics are completely or partially 'hidden' (RoF, trait bonuses), other factors are external, like the weather/terrain (ini caps). I'm trying to mod some unit stats so I have compiled a fair amount of data to better understand what is happening.

If you want to know how the hit/miss percentages are determined, these are hardcoded and are the result of the absolute difference between the total attack and defense values, there are two sets, one for direct attacks and one for artillery/level bombers. So HA=20 vs. GD=18 combat would have the same miss/suppressed/kill chances as a SA=9 vs. GD=7 (both a 2 point difference).

proline
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Re: Combat Equation

Post by proline » Sat Mar 07, 2015 6:07 pm

ThvN wrote:Hi, sorry for the late reply, but what exactly are you looking for? Some combat mechanics are completely or partially 'hidden' (RoF, trait bonuses), other factors are external, like the weather/terrain (ini caps). I'm trying to mod some unit stats so I have compiled a fair amount of data to better understand what is happening.

If you want to know how the hit/miss percentages are determined, these are hardcoded and are the result of the absolute difference between the total attack and defense values, there are two sets, one for direct attacks and one for artillery/level bombers. So HA=20 vs. GD=18 combat would have the same miss/suppressed/kill chances as a SA=9 vs. GD=7 (both a 2 point difference).
I'd like to have a complete explanation of everything that is going on, so that I can build a computer model to make thorough combat prediction (ie. see the probability distribution curve of possible damage outcomes, probability of close defense, etc.). For that I'd need to know about the basic combat mechanics (how attack, defense, initiative, and ROF are used), as well as stuff like terrain and weather effects.

What inspired me to do this was the previous discussion about the 109K vs the 190. I strongly suspect that the higher damage output of the 190 makes it more effective on the eastern front, particularly where enemy fighters are too weak to do much damage, even though it has lower initiative. I bet there are a lot of scenarios where two 190s can kill a sturmovik or other such bomber where it would take 3 hits from a 109, meaningly you need a lot less of the former. However, without a proper computer model this is just a hunch, not an evidence-based opinion.

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Re: Combat Equation

Post by ThvN » Sun Mar 08, 2015 1:53 pm

I'll try to collect some info for you later today, it might be helpful for some kind of strategy guide as well... I am not sure how some chances are calculated, but the to-hit tables I have will be helpful, as I've already used them to mod unit stats to calculate the average number of kills they would inflict.

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Re: Combat Equation

Post by ThvN » Mon Mar 09, 2015 1:42 am

The basics: at the bottom of the Combat Log there are those all-important numbers that show the chance of inflicting a miss (grey), a point of suppression (blue) or a kill (red). These are based on the ratio between the Effective Attack and Effective Defense. These 'Effective' Attack/Defense values are simply the result of the game applying all relevant modifiers to the basic stats of the units.

Note that these chances are independant of Initiative (Ini), Strength (Str), Rate of Fire (RoF), etc.
Those values influence only when, and how many times you can try to make a 'dice roll' with these Miss/Suppress/Kill chances. Having a very high kill chance per attack (or shot/dice roll, whatever you want to call it) still means little if the strength or initiative are too low to make effective use of a high kill chance.

Panzer Corps v1.22 - Combat Odds Table for direct attacks.
Disclaimer: may contain errors, after a while all numbers start to look alike and it's easy to miss one or two...

A-D = Attack minus Defense
Miss%, Supp% , Kill% are in percentages

Code: Select all

A-D	Miss%Supp%Kill%
>14	10	 9	81
 14	10	 9	81
 13	12	 9	79
 12	14	 9	77
 11	16	 9	75
 10	18	 9	73
  9	20	 9	71
  8	22	10	68
  7	24	10	66
  6	26	11	63
  5	28	11	61
  4	30	12	58
  3	35	12	53
  2	40	11	49
  1	45	11	44
  0	50	10	40
 -1	55	10	35
 -2	60	 9	31
 -3	65	 9	26
 -4	70	 8	22
 -5	72	 7	21
 -6	74	 7	19
 -7	76	 7	17
 -8	78	 7	15
 -9	80	 6	14
-10	82	 6	12
-11	84	 5	11
-12	86	 5	 9
-13	88	 4	 8
-14	90	 4	 6
-15	90	 4	 6
-16	90	 4	 6
-17	90	 4	 6
-18	90	 4	 6
-19	90	 4	 6
-20	90	 4 	 6
-21	90	 5	 5
-22 through -30 idem
-31	90	 6	 4
-32 through -40 idem
-41	90	 7	 3
<-41?	90	 7	 3


ThvN
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Re: Combat Equation

Post by ThvN » Mon Mar 09, 2015 1:44 am

Panzer Corps v1.22 - Combat Odds Table for indirect attacks (artillery & strategic bombers).

A-D = Attack minus Defense

Code: Select all

A-D	Miss%Supp%Kill%
>53	 ?	 ?	 ?
 53	10	25	65
 52	10	26	64
 51	10	27	63
 50	10	27	63
 49	10	28	62
 48	10	29	61
 47	10	30	60
 46	10	31	59
 45	10	32	58
 44	10	33	57
 43	10	34	56
 42	10	35	55
 41	10	36	54
 40	10	36	54
 39	10	37	53
 38	10	38	52
 37	10	39	51
 36	10	40	40
 35	10	41	49
 34	10	42	48
 33	10	43	47
 32	10	44	46
 31	10	45	45
 30	10	45	45
 29	10	46	44
 28	10	47	43
 27	10	48	42
 26	10	49	41
 25	10	50	40
 24	10	51	39
 23	10	52	38
 22	10	53	37
 21	10	54	36
 20	10	54	36
 19	10	55	35
 18	10	56	34
 17	10	57	33
 16	10	58	32
 15	10	59	31
 14	10	60	30
 13	12	59	29
 12	14	59	27
 11	16	58	26
 10	18	58	24
  9	20	57	23
  8	22	57	21
  7	24	56	20
  6	26	55	19
  5	28	54	18
  4	30	54	16
  3	35	51	14
  2	40	47	13
  1	45	44	11
  0	50	40	10
 -1	55	37	 8
 -2	60	33	 7
 -3	65	30	 5
 -4	70	26	 4
 -5	72	24	 4
 -6	74	23	 3
 -7	76	21	 3
 -8	78	20	 2
 -9	80	18	 2
-10	82	17	 1
-11	84	15	 1
-12	86	13	 1
-13	88	11	 1
-14	90	 9	 1
<-14	90	 9	 1

TSPC37730
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Re: Combat Equation

Post by TSPC37730 » Mon Mar 09, 2015 3:23 am

Thanks for publishing that ThvN. It definitely helps my understanding of the game mechanics & I will adjust fire accordingly.

proline
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Re: Combat Equation

Post by proline » Mon Mar 09, 2015 2:30 pm

Very enlightening so far! Keep in mind that as an iPad player, I've only seen combat logs on screenshots others post :( so this is all the more helpful to me.

So now that we know how kill probabilities are determined (basically just a function of A-D), the next question is how many rolls do you get? Seems like there are a lot of variables left to account for- terrain, initiative, entrenchment, mass attack, weather, strength, ambush/rugged defense, and RoF.

Tarrak
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Re: Combat Equation

Post by Tarrak » Mon Mar 09, 2015 6:05 pm

Assuming a rate of fire of 10, which the majority of all units have, you get one dice roll per one point of current, unsuppressed strength of the unit. A unit with a strength of 7 gets 7 dice rolls, a unit with strength of 13 would get 13.

If the unit in question got different RoF then the amount of dices is multiplied by the RoF divided by 10 and the outcome is always rounded down to an integer. A unit with RoF of 7 and strength of 10 would get 7 dice rolls (10*7/10=7). The same unit with strength of 13 would get 13*7/10=9.1 also 9 dice rolls.

proline
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Re: Combat Equation

Post by proline » Mon Mar 09, 2015 8:45 pm

Tarrak wrote:Assuming a rate of fire of 10, which the majority of all units have, you get one dice roll per one point of current, unsuppressed strength of the unit. A unit with a strength of 7 gets 7 dice rolls, a unit with strength of 13 would get 13.

If the unit in question got different RoF then the amount of dices is multiplied by the RoF divided by 10 and the outcome is always rounded down to an integer. A unit with RoF of 7 and strength of 10 would get 7 dice rolls (10*7/10=7). The same unit with strength of 13 would get 13*7/10=9.1 also 9 dice rolls.
OK, now let's discuss initiative. I read elsewhere that for each +1 of initiative you have, you get to do 20% of your shots before the enemy returns fire. Is this rounded down as well? Also, what is the initiative roll-off and how is that determined?

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Re: Combat Equation

Post by ThvN » Mon Mar 09, 2015 11:32 pm

I did some testing to see how the 20% shot advantage is rounded, and everything I see points to a rounding off to the nearest integer. Values of 0.5 and higher are rounded up, lower is rounded down.

So for example a 2-str unit with an advantage of 1 initiative point would fire with (20% of available shots) 0.2 x 2 = 0.4 , this is rounded down to zero advantage. This means the combat dice are rolled and effects are applied simultaneously. I saw one combat were the combatants virtually wiped out each other due to this. I tested this by modding the % percent advantage, some other unit stats and play out some combats and checking how many shots were taken before retailiation. So it is only observed indirectly, but still I'm fairly sure this is how it works.

At the start of the combat, the base initiative of the units has some factors added/subtracted. This results in the 'Effective initiative' that determines which % of shots are taken first by whom.

It is true that for each point of advantage, a unit gets to attack with 20% of its available shots before any retaliation can occur. So if a unit (10-strength) has a 2-point initiative advantage, it can make 40% = 4 of its attacks before the opponent can start shooting back. Any kills/suppression inflicted with those 4 shots can't retaliate anymore. So if you attack another 10-str unit with that 2-point initiative advantage, those first 4 shots are 'free', and if those inflict one kill and one point of suppression, the opponent can retaliate with just 8 attacks.

To be clear, the suppressed strength point will of course survive, but not participate in the combat anymore. Also, there is a mechanism that causes units to get additional suppression if they suffer kills. To quote Rudankort:
When a unit takes 1 kill, this also generates some suppression. The formula is (50-stars*10)%. This means that a green unit takes additional 0.5 points of suppression per every kill. This models the fact that green unit becomes disorganized and demoralized when taking damage. Veteran 5-star units take zero additional suppression because they are so tough they are immune to this effect. All the rest units lie in between these two extremes.
If no shot hits, the enemy can still use all its attacks. So it is important to not just have better initiative, but to be able to inflict some damage with those 'free' shots, otherwise the unit will still have to withstand the full force of the enemy attacks.

Initiative modifiers: Every unit has its initiative stat, but there are some big modifiers that can really alter the Effective Ini.

Experience bonus: is different between 1.14 and 1.20 rulesets (iPad 1.20 by default, PC gets to choose)

Newer rules have a .5 initiative bonus per star (100 exp) for infantry, tank, anti-tank and fighter classes. This is rounded to the nearest integer, so a 3-star fighter unit has 1.5 = 2 initiative bonus. The 1.14 rules have a fixed bonus for every class, it uses the lowest value of either: 1 point bonus per star/ 10% to the basic ini stat per star. So a 3-star unit with 6 basic ini will have either +3 / +1.8, so the game will give that unit a +2 experience bonus (it uses the lowest value, 1.8, and rounds that to the nearest integer).

Mass Attack Bonus: for each additional friendly unit able to directly attack the same enemy unit, the enemy initiative is lowered by 1.

So if you surround a Spitfire with three fighters, the first attacking fighter will see that the Spitfire has a -2 to its initiative, caused by the two additional fighters. After the first fighter has attacked, only two fighters are still capable of attacking, so during the second round the Spitfire will have -1 initiative.

No Fuel: If a unit has zero fuel (empty, red icon showing) it gets a -2 ini 'bonus'.

Hero bonus: a standard initiative hero gives +1 ini, custom heroes can be different (even negative).

Ambush/Rugged Defense: if a unit is ambushed (or has an 'Unexpected Encounter') its initiative is lowered to 0 (zero). Rugged defense chances are influenced by unit class, entrenchment and experience, I do not know the calculations involved.


Class-specific Initiative modifiers:

Radar bonus: for aerial combat, am air unit that is in spotting range of a friendly radar unit gets a +2 ini bonus.

AT vs. tank/recon: if an anti-tank unit is attacked by a tank or a recon unit, the AT unit will have +3 initiative.

Air vs. Ground: ground units that have an air attack stat, passive ( [x] ) or active, always fire first at attacking aircraft. In these combats the ground units' initiative is set to 99 and the air units' is set to 0.

Capital Ship vs. Capital Ship: if two capital ships have a combat, their ini stat is ignored and the attacker is set to 99 ini and the defender to 0 (zero). So be sure to shoot first.

Submarine attacks: if a submarine initiates a combat, its ini is set to 100.

Submarine defends: if a destroyer attacks a submarine, the sub's ini will be set to 0.

Note that all these extreme values are still modified with experience bonuses etc., although that obviously will not make a difference in the end. But the 100/99/0 initiatives here are still overruled by weather caps. In the case of air units vs. ground this is not noticable because there can't be any combat between those two due to the bad weather. Another thing about air vs. ground in cloudy weather is that the units involved only use half their strength points to attack each other. Air vs. air combat is unaffected during cloudy weather but becomes impossible during rain/snow/sandstorms.

Terrain/Weather modifiers

Terrain Cap: The game library show the Initiative Caps for different terrain types. For example, hills=5, this means any unit in combat on a hill hex will see its initiative lowered to 5. Combats are always fought in the hex of the defending unit.

Weather Cap: during rain/snow/sandstorms, initiave is capped to 1. (initiative cap for clear or cloudy weather is 99, by the way)

These last two 'overrule' everything, even heroes. So no matter how many bonuses you can apply, if you're fighting in a city or during bad weather it will all be reset to 1. Unfortunately, that is not all...

Random modifiers

Dice roll: After all of the above modifiers have been applied, the game adds a random +0, +1 or +2 to the result for each side.

In my opinion this random roll is the biggest contributor to the perceived inaccuracy of the combat predictor. If you are using a high-initiative unit with a +1 ini hero to try to dislodge a surrounded enemy unit with no fuel in a city during bad weather, so no matter what the ini will still be 1. But the game will sometimes, on top of that, roll a +0 for your side and a +2 for the enemy, which can drastically affect the outcome.

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Re: Combat Equation

Post by captainjack » Tue Mar 10, 2015 5:18 am

That's a good explanation.

I must admit that I don't like the Ini limits that overrule all hero and experience modifiers. I can't believe a 5* unit or a hero would lose all it's combat edge over a green unit just because it's snowing, foggy or heavily built up.

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Re: Combat Equation

Post by TSPC37730 » Tue Mar 10, 2015 2:00 pm

Thanks again ThvN for the helpful information. It's a big help in lifting the fog.

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Re: Combat Equation

Post by ThvN » Tue Mar 10, 2015 6:21 pm

I edited in some additional info that was still missing (submarine rules), and I managed to figure out how the initiative advantage % is probably rounded. I'll have a look at posting about strength/defense modifiers, as these are also only visible in the combat log.

proline
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Re: Combat Equation

Post by proline » Tue Mar 10, 2015 8:45 pm

ThvN wrote:I edited in some additional info that was still missing (submarine rules), and I managed to figure out how the initiative advantage % is probably rounded. I'll have a look at posting about strength/defense modifiers, as these are also only visible in the combat log.
Thanks for all the work! Is there any kind of initiative bonus for being the unit to initiate combat? Or do units do exactly the same on the attack as on the defensive?

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Re: Combat Equation

Post by ThvN » Tue Mar 10, 2015 9:01 pm

@proline: normally, the initiative is not influenced by who initiates combat. The only exceptions are the submarine/capital ship/ground-to-air combats, and the +3 ini for an AT unit when it is attacked by a tank/recon unit. Mass attack bonus also favours the attacker, but luckily surrounded units do not have their ini lowered in their own turn when they attack.

Attack/Defense modifiers

Heroes: they normally come in +1 through +3 attack or defense bonuses, some custom heroes are different. Bonuses are stacked, so two +2 attack heroes give +4 attack. Don't forget these bonuses are applied to all of the units attack/defense stats, like close defense and air attack!


Experience bonus: again, this is different between 1.14 and 1.20 rulesets (iPad uses 1.20 rules by default, PC gets to choose). The 1.14 rules have a fixed bonus for every class, it uses the lowest value of either: 1 point bonus per star/ 10% to the basic stat per star. So a 3-star unit with 6 basic attack will have either +3 / +1.8, so the game will give that unit a +2 experience bonus (it uses the lowest value, 1.8, and rounds that to the nearest integer).

In 1.20 , there are different sets of modifiers for each class/stat type. Table is below, first I will quote the comments in the file to help explain the values:
For each unit class, there are 8 columns specifying per-star bonus to attack, defense and initiative. Each value is the number of 1/100s, so 100 means 1, 50 means 0.5 and so on. After applying the bonus, the game rounds the result to the nearest integer. So 3.2 attack is rounded to 3, and 3.7 attack is rounded to 4.
SA= soft attack
HA= hard attack
AA= air attack
NA= naval attack
GD= ground defense
AD= air defense
CD= close defense

Code: Select all

Class		  Ini    SA	 HA	 AA	 NA	 GD	 AD	 CD
Infantry		50	100	 50	  0	  0	100	100	100
Tank			 50	100	100	  0	  0   100    50     0
Recon          0    50    50     0     0   100    50     0
Antitank		50	  0	200	  0	  0	100	 50	  0
Artillery		0	100	 50	  0	  0	100	 50	  0
Anti-air		 0	  0	  0	200	  0	100	 50	  0
Structure		0	100	100	100	100	100	100	100
Fighter		 50	  0	  0	200	  0	 50	100	  0
Tac bomber	  0	100	100	  0	 50	 50	100	  0
Strat bomber   0	100	100	  0   100   100   100	  0
Submarine		0	  0	  0	  0	100	100	100	100
Destroyer		0	  0	  0	  0	100	100	100	100
Capital ship	0	100	100	 50	100	100	100	100
Carrier		  0	  0	  0	  0	  0	100	100	100
Transport		0  	0	  0	  0	  0	  0	  0	  0 
Armour train	0	100	 50	  0	  0	100	 50	  0
River boat	  0	  0	  0	  0	100	100	100	100
For the transports, I put all types in a single line: land, sea, rail & air. These can be modded separately, but the stock values are all 0.


Entrenchment: For 1.20 each level of entrenchment adds to the defense, but this is calculated differently against different types of attack. When attacked by most unit types, each point of entrenchment gives +1 defense against that attack (a 100% defense bonus). If attacked by a ranged attack (artillery), each point counts double (200% defense bonus), so a unit with level 3 entrenchment would get +6 defense against ranged attacks (this last bonus does not apply when playing with 1.14 rules).
When attacked by infantry, the bonus is only 50%, so a unit with 2 entrenchment would get only +1 extra defense. This number seems to be always rounded down to the closest integer (for example, 5 entrenchment when attacked by infantry counts as +2 defense).

Note that higher experience and entrenchment also contribute indirectly to better combat results, because they both increase the chance of a rugged defense. Experience of the attacking units also matters, as that seems to decrease the chance. Combat engineers ignore the defense bonus of entrenchment and are not subject to a rugged defense. Two other specialized units have this same 'meng' trait, the Flammpanzer II and the Churchill Crocodile.


Miscellaneous bonuses:

During 'Ambushes/Rugged Defense/Unexpected Encounters', the unit that does the ambushing gets +4 defense (and the ambushed unit gets ini=0).

Target on river: when a unit is on a river hex (not frozen) and engages in combat, their opponent receives a +4 bonus to its attack and defense. Bridge engineers do not suffer this penalty.

Infantry vs. AT: if infantry attacks an antitank unit, the infantry get +2 attack.

AT vs. Infantry: if an antitank unit attacks infantry, the infantry get +2 defense.

Ground vs. Naval: if a ground unit attacks a ship, the ship gets a +8 defense bonus.

Low altitude attack: if a fighter or tac bomber unit attacks a ground target, its ground defense is lowered by 5 points during that combat.

During Snow/Rain/Sandstorm, units receive a +3 ground defense bonus when attacked by artillery.

Units in close terrain receive a +4 air defense bonus when attacked by air units.

Fort killer: units that have this trait get +5 attack when attacking structures (fortresses, strongpoints).
This trait is shared by:
Combat engineers - paratroopers - US Rangers
Flammpanzer II - Churchill Crocodile - Churchill AVRE - Crommwell CS
Stug IIIA & B - StuH42 - Brummbar
M40 da 75/18 - M43 da 105/25


Minefields are a bit tricky, normal units will only inflict a single kill with each combat on a minefield, artillery and infantry do normal damage (often a few kills per combat) and combat engineers and mine-clearing tanks can kill an entire minefield in a single round of combat (NOT if they are ambushed by the minefield!).

To be complete, there is also an optional range penalty for all ranged units, this can only be modded into the game and subtracts a fixed penalty per hex.

Phew! I hope I did not forget anything important. One thing I left out is strategic bombing to cause suppression, loss of fuel/ammo and possibly prestige. I'm not sure how those numbers are calculated, it has its own set of rules and a lot depends on the experience of the bomber.

proline
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Re: Combat Equation

Post by proline » Wed Mar 11, 2015 12:25 am

So what about when you attack from a river? Does the unit you attack get the same +4 attack / defense?

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Re: Combat Equation

Post by ThvN » Wed Mar 11, 2015 12:49 am

proline wrote:So what about when you attack from a river? Does the unit you attack get the same +4 attack / defense?
Yes, it does, sorry for the confusion. A unit that attacks another unit that is on a river hex gets this bonus, and (your example) if a unit attacks from a river hex the opponent gets the bonus as well, no matter on what kind of hex it sits.

Fun fact: if two units are both on a river hex and engage in combat, both sides will get the bonus.

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Re: Combat Equation

Post by JimmyC » Wed Mar 11, 2015 1:15 am

This is really useful, although some of the combat stats go over my head.

Particularly the miscellaneous bonuses section and entrenchment information is useful. I never new that entrenchment worked that way, even though i've been playing the game for the last 2.5 years! I just wish that there was some way to display the unit traits in-game.

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Re: Combat Equation

Post by captainjack » Wed Mar 11, 2015 3:35 am

I'm near certain that the British SE units also have fortkiller - given what they specialised in that makes sense.

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