Combat calculations: the kill probability

[Martin_Goliath]

Maybe this has already been discussed elsewhere, but anyway: I got curious about how the kill probabilities in combats are determined. The combat log ('L' hotkey) does a fine job explaining the effective attack and defence strengths used in a combat, but how those numbers lead to the displayed percentages for miss, suppression and kill remains obscure. Trying to understand this better, I did some book-keeping by writing down numbers from the combat log of some hundred combats of various types. This is what came out of the exercise:

First, the key number for a specific combat is the difference A-D between effective attack (A) and effective defence (D). In other words, a 2:1 attack uses the same probabilites as a 3:2 or 4:3 attack. (This was a bit confusing for me, since the board games I played used the quotient A/D, so that a 2:1 attack used the same probabilites as a 4:2 or 8:4 attack.)

By playing around with the numbers I think I have found relations for the miss (M), suppression (S) and kill (K) percentages. The calculation of K differs for direct and indirect attacks (artillery and level bombers do indirect attacks), while M is calculated the same way for all attack types. In what follows, let x = A-D be the difference. Then

* When -4 <= x <= 4:
M = 50 - 5*x
Kd = 40 + 4.5*x
Ki = 10 + 1.5*x

* When -14 <= x <= -4:
M = 62 - 2*x
Kd = 22 + 1.5*(x+4)
Ki = 4 + 0.25*(x+4)

* When 4 <= x <= 14:
M = 38 - 2*x
Kd = 58 + 2.5*(x-4)
Ki =16 + 1.5*(x-4)

* When x <= -14
M = 90
Kd = 7 + 0.125*(x+14)
Ki = 1.5 + 0.125*(x+14)

* When 14 <= x:
M = 10
Kd = ?? + ??*(x-14) (no data available)
Ki = 31 + 0.9*(x-14)

M-values always come out as integers, while any decimals in K-values are dropped.

Given M and K, suppression is given by S = 100 - M - K.

Formulae for M are pretty solid, while the ones for K are my guesses based on simplicity. They are not 100%, but fine-tuning might correct that. Also, K's are shaky for x>14 and x<-14, where data was scarce.

A few examples:

Tank with A=5 attacks infantry with D=6:
x = -1
M = 55%
K = Kd = 35%
S = 10%

Artillery with A=13 attacks infantry with D=6:
x = 7
M = 24%
K = Ki = 20%
S = 56%

My 2 öre...
Martin

[starbird]

This cannot be right, for you did not take initiative into account.
More I have played, more I come to realize that initiative may be the most important attribute of melee units in Panzer.
For instance, when you attack a Mustang, usually you will find yourself probability-wise facing more losses than attacking a Thunderbolt with the same Me 262.
However, a Mustang is inferior in both attack and defence to a Thunderbolt.
And you didn't mention rate of fire either.

[Martin_Goliath]

This cannot be right, for you did not take initiative into account.
More I have played, more I come to realize that initiative may be the most important attribute of melee units in Panzer.
For instance, when you attack a Mustang, usually you will find yourself probability-wise facing more losses than attacking a Thunderbolt with the same Me 262.
However, a Mustang is inferior in both attack and defence to a Thunderbolt.
And you didn't mention rate of fire either.

My post didn't address the complete combat calculation as such, but only the probabilites used when shots are fired. As you say, initiative is of fundamental importance for combat outcome. Since the unit with largest initiative shoots first, it may be able to suppress some of the enemies, effectively reducing the number of shots the enemy gets against you. Likewise, rate of fire affects the number of shots fired. However, each shot fired use the kill percentages I tried to understand in the post above.

Speaking of initiative, having the better initiative often more than compensates for poor kill probability. Check out the combat log - it really opened my eyes for the game mechanics in PC!

[starbird]

Oh, sorry, now I see what you meant. I thought you were talking about expectations since you emphasized on "before shots".

[starbird]

Very interesting. I believe you are right, the numbers fit my impressions.
I didn't pay much attention to probabilities for I can see them directly and have an idea.
I am dying to know about how initiative comes into work though.
I knew it's not linear, and around a difference of 4, there is also a critical point.
How about you?

[Martin_Goliath]

Very interesting. I believe you are right, the numbers fit my impressions.
I didn't pay much attention to probabilities for I can see them directly and have an idea.
I am dying to know about how initiative comes into work though.
I knew it's not linear, and around a difference of 4, there is also a critical point.
How about you?

My impression is that the most important effect is the reduction of the number of shots the opponent gets at you. I read somewhere that for each initiative point in excess of the opponent, 20% of the enemies you kill will not shoot back. So, if you have an initiative excess of 4 and manage to kill off 5 points of the enemy, 80% of those - that is 4 - will not shoot back. Huge advantage!

I am only beginning to learn all effects that modify initiative, like terrain, mass attack etc...

[Kerensky]

Mmmmmmm.... theorycrafting. Yum yum.

[DreadWing]

Taken from PG 2 Manual, so this may not be 100% accurate for PC:

Initiative is an estimate of a unit’s ability to react quickly in combat. Initiative is determined by the equipment used in battle, the terrain upon which the battle takes place, and the experience of the units. It is also adjusted by a random factor, to help simulate the uncertainty of battle. The higher the unit’s initiative, the better, since the unit with the higher initiative takes reduced damage. If a tactical surprise or rugged defense occurs, the attacker’s initiative is zero.

Taken from PC Manual:

Initiative is a complex measure of unit’s gun range, optics, manoeuvrability and training, which indicates how much damage the unit can do before the enemy has a chance to shoot back. The bigger your initiative advantage, the more strength you can kill/suppress before the enemy counterattacks you, and so the less effective this counterattack will be.

[Martin_Goliath]

Taken from PG 2 Manual, so this may not be 100% accurate for PC:

Initiative is an estimate of a unit’s ability to react quickly in combat. Initiative is determined by the equipment used in battle, the terrain upon which the battle takes place, and the experience of the units. It is also adjusted by a random factor, to help simulate the uncertainty of battle. The higher the unit’s initiative, the better, since the unit with the higher initiative takes reduced damage. If a tactical surprise or rugged defense occurs, the attacker’s initiative is zero.

Taken from PC Manual:

Initiative is a complex measure of unit’s gun range, optics, manoeuvrability and training, which indicates how much damage the unit can do before the enemy has a chance to shoot back. The bigger your initiative advantage, the more strength you can kill/suppress before the enemy counterattacks you, and so the less effective this counterattack will be.

More about initiative. Here's where I picked up the "20% less return shots per initiative advantage" mentioned above: http://www.matrixgames.com/forums/tm.asp?m=2872579

[Iscaran]

Initiative is very important for fights.

The side with the higher initiative will fire first. Since many combats usually go with a lot of hits (kills or suppressed) the side which fires first usually "wins" the combat overall.

Although there is still the random dice rolls for the kills even AFTER the probabilities are calculated (dice rolls 1-100).

For intitiative another "non" random dice roll is done (I think the dice roll is actually done on the previous turn before klick next turn, therefore it is "saved" for the following turn - a compromise done as an "anti-cheating" measure for Multiplayer as it looks).

Now the initiative dice roll can be +2,+1,0,-1,-2.
I think Experience also gets +1 per star - since that is valid for both sides only the experience difference is of importance though.

With that in mind it means that if you have a +5 initiative advantage (for example 10 vs 5) you should ALWAYS fire first as long as you are looking at equally experienced units. This is making the combat much more predictable, though you still have the randomness of "kill/suppression hits" (dice rolls 1-100 vs probabilities dependant on the defense / Attack values of the units).


EDIT: What is your definition of 2:1 attack or 3:2 attack ? Are you referring to the actual unit "strenght" ?

I think the unit strenght is only used for the "number" of dice rolls vs the probability odds. For example a strength 5 unit gets 5 dice rolls vs the probability odds.

The odds themselves only depend on the effective Att/ Effective Def values.

[Martin_Goliath]

Now the initiative dice roll can be +2,+1,0,-1,-2.

Thanks for clarifying that!

EDIT: What is your definition of 2:1 attack or 3:2 attack ? Are you referring to the actual unit "strenght" ?

With "2:1 attack" I mean effective attack value 2 vs effective defence value 1, etc.

I think the unit strenght is only used for the "number" of dice rolls vs the probability odds. For example a strength 5 unit gets 5 dice rolls vs the probability odds.

Yes, that seems to be the case.

The odds themselves only depend on the effective Att/ Effective Def values.

Yes, and if my conclusion is right, it is actually only their difference that enters into it (A minus D).

[Horseman]

When the game shows you the odds, initiative is alos a factor...thats why when you do mass attacks the odds get better (well sometimes)

[Martin_Goliath]

When the game shows you the odds, initiative is alos a factor...thats why when you do mass attacks the odds get better (well sometimes)

Yes, and I suppose that is because the combat prediction takes suppression into account, which is affected by initiative. The effective attack value and hence the one-shot probabilities remain the same irregardless of the level of mass attack. But the lower number of return shots when mass attacking makes all the difference.

[fenglicao]

Can someone comfirm if Goliath's formulas are correct?

So is it somewhat different from the old Panzer General for the Kill/Miss/Suppression calculation?

Also is it true that every 3 kills also generate 1 suppression?

[Kerensky]

So is it somewhat different from the old Panzer General for the Kill/Miss/Suppression calculation?

Also is it true that every 3 kills also generate 1 suppression?

No, kills and suppression are generated on a separate basis, this is especially prominent for units with suppression attack models such as artillery.

[TheGrayMouser]

So is it somewhat different from the old Panzer General for the Kill/Miss/Suppression calculation?

Also is it true that every 3 kills also generate 1 suppression?

No, kills and suppression are generated on a separate basis, this is especially prominent for units with suppression attack models such as artillery.

YES ! ( and NO )
It appears the # of kills can cause Additonal supression:

quote from Rudenkort:

"
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. "

which was part of this thread:
viewtopic.php?t=28199&postdays=0&postorder=asc&start=40

[fenglicao]

The combat logs always show a higher suppression than the dice roll outcome. For instance, just checked one, 14 strength tank attacks 15 strength inf, 20% miss, 9% suppress, and 71% kill, dice roll shows 10 red numbers, 1 blue, 3 white, so it should be 10 kills and 1 suppression, but the result is 10 kills and 5 suppression. Another one, 14 str artillery attacks 15 str inf, 18% miss, 58% suppress, and 24% kill, dice roll shows 7 red, 5 blue, and 2 white, so it should be 7 kill snd 5 suppression, but the result is 7 kill, 7 suppression. None of the defenders had any prior suppression.
Sorry I can't figure out how to post the combat log images here.

And, can Goliath's formula be confirmed by a developer or someone?

[fenglicao]

whoops, GrayMouser just answered my question, thanks.

Just hope someone can post/confirm the actually miss/suppress/kill % formula.

[Molve]

Just hope someone can post/confirm the actually miss/suppress/kill % formula.

The more pressing issue, from my point of view, is to hope someone can change/rein in the actual combat formulas...

[Martin_Goliath]

Just hope someone can post/confirm the actually miss/suppress/kill % formula.

Yes, it would be great if someone in the dev team could drop a hint on this!

As mentioned above, the miss percentage is quite solid. The kill percentages are what I found best fitted all the combats I cared to check against.