Understanding combat resolution

[bbasgen]

The manual and the strategy guides leave, it seems, two critical pieces of combat resolution a mystery:

1. How is attack damage distributed between org and strength?
2. What is the chance of not being hit?

Regarding #1, according to the Strategy Supplement Guide, consider that units retreat at org 1, and typically take 8 to 12% damage by that time. It isn't clear if the strength damage taken is an even distribution, but if we make the assumption that 10% damage is an average, here are some thoughts.

Let's take a target with a 50% organization. To achieve victory, we need to remove 49% of that organization, and presumably remove ~ 10 strength. This would seem to mean that 59 total damage will be required. While it may not be clear when damage to strength versus organization occurs, this gives us a general idea of damage required to win. It is implied by the strategy guide that the actual number is random to some degree, such that we may only need to cause 8 strength damage sometimes, and other times 12.

Regarding #2, this is particularly interesting because while we have something called "defensive effectiveness", it only identifies the capacity to have a chance at defending. It doesn't identify what that chance actually is.

Is the defending "chance" an objective value? Is it effected by anything in game, such as doctrines or unit type? Is it cumulative in any way? We know it isn't 100%, and it is likely 50% or greater. It seems hard to empirically identify without an answer to #1 above, and it seems likely that it could be a relatively fixed range (e.g. ranging from 80% to 90% chance to defend per shot, based an a die roll).

More questions than answers at this point, but I'm hopeful we can figure these things out.

 

[dhelmet99]

The defensiveness (and toughness for the attacker) values relative to the attack values definitely has an influence, as per the manual. From L4.1:

Once eligibility (“allowance”) has been determined, those
units fire at their targets. The target then has a chance to
avoid being hit. Defending Divisions use their Defensiveness
value, multiplied by their Defence Effectiveness. Attacking
Divisions use their Toughness value, multiplied by their
Defence Effectiveness. Similar to the way the resulting Attack
values determine for how many rounds a Division can fire, the
resulting Defensiveness or Toughness values allow a Division
to avoid that number of shots from enemy Divisions during
a single Firing Phase. So if a defending Division’s modified
Defensiveness is 6.3, it may avoid being hit by the first six
shots aimed at it, while any additional shots would hit.

The manual is not clear about how much org vs strength is damaged. I doubt Paradox will release info this close to the game mechanics.

 

[bbasgen]

The target then has a chance to
avoid being hit.... it may avoid being hit by the first six
shots aimed at it, while any additional shots would hit.

Emphasis added. The question is: what is that chance?

It is important because, at the end of the day, all the attack, defense, etc values don't mean a heck of alot when you don't know how they are actually used in the equation. We can, of course, rate them purely relativisticly for pragmatic purposes, we just can't determine definitive effectiveness, etc.

 

[dhelmet99]

Very true. I would love to know this as well. I've been trying to quantify the division design problem (http://forum.paradoxplaza.com/forum/showthread.php?t=420352), but in the end it's about winning battles and therefore about how much the division stats effect this. Judging from some of the calculations that we're able to see I would expect the actual formulas to be pretty simple. Damn. Now you're tempting me to set-up some test battles and try to reverse-engineer the whole combat system the way I did for the stacking penalty. I've already spent almost as much time analyzing the game as I have playing it!

 

[bbasgen]

Very true. I would love to know this as well. I've been trying to quantify the division design problem (http://forum.paradoxplaza.com/forum/showthread.php?t=420352), but in the end it's about winning battles and therefore about how much the division stats effect this. Judging from some of the calculations that we're able to see I would expect the actual formulas to be pretty simple.

Great work you've done on quantifying division design, btw. I agree about the formula, it doesn't look like it would be too complex.

Damn. Now you're tempting me to set-up some test battles and try to reverse-engineer the whole combat system the way I did for the stacking penalty. I've already spent almost as much time analyzing the game as I have playing it!

Ah yes, my plan is coming together nicely. What have you been doing to create a good sandbox for testing?

 

[EntropyAvatar]

T
[*]What is the chance of not being hit?

IIRC, in defines.lua, there are two values which seem to suggest that the chance of avoid a hit if you have some defense left is 0.8 while the chance of avoiding a hit if you have no defense left is 0.6.

I changed these to 0.85 and 0.5, but I'm not entirely sure I'm interpreting them correctly.

 

[EntropyAvatar]

Now you're tempting me to set-up some test battles and try to reverse-engineer the whole combat system the way I did for the stacking penalty.

What were your conclusions about the stacking penalty? Because one of the values I saw in defines made it seem like a division-based stacking penalty.

 

[Jorgen_CAB]

I think that is slightly more complicated actually. What the manual refer to are that the efficiency are multiplies with the units defence/toughness and Softe/Hard attack. That is a unit that has a soft attack of 10 and an efficiency of 50% would be able to fire 5 shots in a round. A unit with a defence of 8 and an efficiency of 150% has a "chance" to withstand up to twelve shots. It is the chance that is ORG or strength loss we have no clue about when the unit get to defend. I would say that is is about 10% chance for a Strength loss and 90% for an ORG loss. But I really have no clue.
It also seems as if the longer the combat last the higher the strength loss will be in total even if ORG loss are the same, so time in combat equals more chance of a Strength loss, but I'm not so sure about that either, just a gut feeling.

 

[Jorgen_CAB]

What were your conclusions about the stacking penalty? Because one of the values I saw in defines made it seem like a division-based stacking penalty.

Stacking penalty are per brigade and it is 1%, though I don't know exactly how many free you get. I do know that either Army/Army Group or Theater leader will have an effect on this.

 

[dhelmet99]

What were your conclusions about the stacking penalty? Because one of the values I saw in defines made it seem like a division-based stacking penalty.

The testing I did was not conclusive. I went into the 1939 scenario as Germany and removed ALL of the leaders at all command levels for the troops facing Poland and then got into a bunch of fights and looked at the reported stacking penalty in the combat screen for a range of brigade numbers. The stacking penalty kicked in at 5% for 13 brigades in a single province (I only did single province testing), and increased roughly linearly according to the following formula:

Penalty = 1.8 * (# of brigades - 10)

Obviously the formula should only be applied past 13 brigades. I was confused in that the results were not perfectly linear, as they should have been since I removed the leaders (and the resulting coordination bonus). I'll test if the number of brigades makes a difference tonight. The manual claims it is the number of brigades, but there's no guarantee it's correct and there was that annoying variance in the data.

 

[bbasgen]

soft attack of 10 and an efficiency of 50% would be able to fire 5 shots in a round. A unit with a defence of 8 and an efficiency of 150% has a "chance" to withstand up to twelve shots.

Correct.

It is the chance that is ORG or strength loss we have no clue about when the unit get to defend.

The chance the manual refers to is the chance of any damage being taken. Once damage is taken, then it is a matter of whether or not org and/or strength is lost.

 

[bbasgen]

IIRC, in defines.lua, there are two values which seem to suggest that the chance of avoid a hit if you have some defense left is 0.8 while the chance of avoiding a hit if you have no defense left is 0.6.

Interesting find. 80% seems reasonable, yet I'm not sure about that 60%. The manual says:"So if a defending Division’s modified Defensiveness is 6.3, it may avoid being hit by the first six shots aimed at it, while any additional shots would hit."

I read this to say that after the capacity for defense is used up, all shots will hit and cause damage. The manual could be stating it wrong, of course.

 

[dhelmet99]

It turns out that the stacking penalty is determined by division and not brigade. I'll be posting a new thread soon with tables and graphs to definitively prove it. I also found that it only depends on the divisions engaged in combat and not the number of divisions in the province. This also contradicts the info in the manual.

 

[bbasgen]

Okay, I've got some empirical data to share:

Czech: 1 infantry division (3 brigades). Level 2 infantry. Attack efficiency is 77%. 7.8 base soft attack = 6.00 effective attack.
Hungary: 1 infantry division (2 brigades). Level 1 infantry. Defensive efficiency is 119%. 10.66 base defensiveness = 12.68 effective defense. Started with 23.25 org and 70.3 strength.

Battle test 1 time: 290 hours (e.g. almost two weeks)
Battle test 2 time: 297 hours
Battle test 3 time: 290 hours

The battle always ended when the Hungarians reached 1.0 organization. Strength loss did vary, but only within 0.3. The average strength at the end of the battle was 62.0. Thus a total of 22.25 org was lost, and 8.3 strength. This would seem to equate to 30.35 total damage taken by the Hungarians.

What does this mean?

First, the battle lasted 290 rounds, and in every round the Czech's got to take 6 shots, and the Hungarians always had that "chance" to defend. Let's assume entropy avatar found the correct value for chance at 80%. Each round (e.g. hour) that means that 1.2 shots will hit, or put another way, in five rounds 6 shots hit. The trouble is, this would mean 348 shots hit over a 290 hour period.

This would almost make sense if each shot caused only 0.1 damage. To make the numbers, the chance would have to be 82.5% -- which is feasible if entropyavatar found the right number and the game has a 2.5% modifier on it. In this light, it would have been 1.05 shots per hour, for 304.5 damage divided by 10 is 30.45.

More testing is needed in different circumstances to confirm or debunk this hypothesis.

 

[EntropyAvatar]

Keep in mind that during the night hours you won't get as many shots.

 

[dertechie]

As though you didn't have enough variables to play with, there's a few more in the defines file

	LAND_COMBAT_ORG_DICE_SIZE = 3,
	LAND_COMBAT_STR_DICE_SIZE = 2,
	LAND_COMBAT_STR_ARMOR_ON_SOFT_DICE_SIZE = 2,
	LAND_COMBAT_ORG_ARMOR_ON_SOFT_DICE_SIZE = 5,
	LAND_COMBAT_STR_DAMAGE_MODIFIER = 0.15,
	LAND_COMBAT_ORG_DAMAGE_MODIFIER = 1.0,

 

[bbasgen]

Keep in mind that during the night hours you won't get as many shots.

Interesting point. In theory that will account for --- 50% of the total battle time. I'll have to watch that for next time.

I did watch to make sure weather did not change the effectiveness during the course of the battle.

 

[bbasgen]

	LAND_COMBAT_ORG_DICE_SIZE = 3,
	LAND_COMBAT_STR_DICE_SIZE = 2,
	LAND_COMBAT_STR_ARMOR_ON_SOFT_DICE_SIZE = 2,
	LAND_COMBAT_ORG_ARMOR_ON_SOFT_DICE_SIZE = 5,
	LAND_COMBAT_STR_DAMAGE_MODIFIER = 0.15,
	LAND_COMBAT_ORG_DAMAGE_MODIFIER = 1.0,

Perfect. Interesting data. Not sure what dice size means. We could guess that the "die" is a fixed number -- let's say 6. This would seem to indicate that Armor is more likely to cause damage to the org of soft targets.

The strength damage modifier makes sense -- every shot does seem to cause some strength damage. The org damage is interesting. Entropy's point about the night will help, but not by a factor of ten (more like a 25% overall reduction).

 

[unmerged(52476)]

The modifiers are all called "dice_size", so my guess would rather be that with a dice size of 3 you can do 1-to-3 damage on a successful hit.

But that's of course only speculation as well.

 

[Phelan]

Did you think they changed the combat resolution from HOI2 to HOI3 in a drastic way, or can we assume, that they have taken over as much as possible form HOI 2?