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A simpler and easier way to work out some balances for combat games

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X3M
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I have worked on a new way of balancing a game through numbers. (Since I got notching else worthwhile to do) This is regarding how armor as subtraction works on damage value's. It doesn't matter if the game is a wargame, or some sort of RPG. The method works for both.

A lot of games are designed with armor being a subtraction. Not in the form of a percentage in a table. But in the form of just 1 number that is used to subtract from a damage value.
It can be done with fixed numbers attached to a body or equipment, but also in the form of dice rolls etc as a more advanced form of damage reduction.

While a simple damage reduction looks simple to players. 8 damage - 3 armor = 5 damage.
It will be very hard for game designers to determine the balance of a game.
Is the 8 damage worth 8? Worth 5? What about other weapons in the game? What about other armor value's in the game? How do they compare?

Play tests often show if something should be "rarer" or "more expensive" in terms of worth. But this process is slow. Some might want to have a head start by using some math. And work from there. The method will not bring perfect balance. But will get you to "practical" balance.

The key in this is that you don't design with an open world in mind. I did this a lot. And while I have 1 system that works. A simple damage reduction through armor subtraction never seemed to work properly. This means that you will not design with the intention of expanding the game "forever". The method will show you why you design the game with a fixed set in mind.

If any one is interested.
I will share the method though math examples.
Starting with some basics.
But also show the big impacts that some changes can have on a game.
Further, the unwritten rules that a designer (through math) needs to follow are important here.

X3M
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The one thing that I learned.

After rapidly pushing out numbers with my new excel file. I fairly quickly reached a conclusion.

Using the [subtract armor from damage] rule/mechanic. Is one of the worst out there.
That is, if you want to make a proper and fair RPS system. That is visible after working all the numbers.

This includes weapon multiplier and health modifications. To keep the game balanced.

What happened?

Let's look at the 4 corners of "any" RPS table.

This is what I see in general:
"weapon" versus [no armor] -- [armor]
"anti infantry" 80/100% -- 100/125%
"anti tank" 0/20% -- 100/80%

The anti tank weapons are mostly all rounders. I rarely see the factor go above 125% in effectiveness.

Anti infantry weapons are mostly almost as effective as the tank weapons, regarding fighting infantry.
Yet show hardly any damage against tanks.

1 -- 1
0 -- 1

The above would summarise the effect. And don't get me wrong. But while anti tank weapons are effective against anything. The are also just as effective against no armor. This means that using anti infantry weapons is a bad thing to do. Bottom line, all designs get anti tank weaponry. It is better to get tanks as well.

The sharpest RPS that I have seen so far will have as minimum factor of 1,2 between the anti tank firing on tanks or infantry. This means that for that little bit of difference, players will not go infantry, nor go anti infantry.

In the long run, choosing the wrong units of 20% difference would mean a factor of 27% extra losses.

(I don't understand how they managed to put this in Starcraft. It is almost as if they intended to have tier one being only useful in the first trimester of a game)

***

There is another system that might still provide use to armor being a subtraction. And that is simply putting a higher price tag on it. The catch is that all weapons are going to depend on this price tag as well.

I am going to work on that system later. I am familiar with it since I used it before. But not knowingly that the "fair" way would be a complete fai(r)lure.

let-off studios
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Damage Soak, Armour Types

I think I understand what you're saying here. What you're describing made me think of the Palladium Role Playing System. Regarding combat in that system (if I recall correctly), you would throw 1d20, and anything above a 4 is a hit. There were additional modifiers that made things interesting, and not so incredibly lethal.

ARMOUR TYPE VS. DAMAGE TYPE
There are some armours that are less effective against certain types of damage. Earlier this year, I recall commenting on someone's blog entry or whatever about weapon type versus armour type in AD&D from back in the day. But the old-skool Marvel Super Heroes also had armours that would resist or nullify certain types of damage (like radiation damage, or kinetic/physical damage), and not be effective against others. Maybe something like this is worth considering?

SOAK
This is one thing I've not seen much at all, but I think it bears consideration in your case. There's a measure of armour resistance a tank has that an infantry unit can't come close to.

As an example, imagine two soldiers: one in a leather jerkin and one in a suit of steel plate mail. Both armours will not only protect against different types of damage differently (as in weapon versus armour type, above), but also, will protect the wearer from more damage in general. In other words, the armour itself "soaks up" damage so that the wearer doesn't even have to worry about the integrity of the armour and/or suffering damage. In terms of the Palladium system, these armours will absorb/soak a certain amount of damage, and only that which makes it through causes damage to the wearer.

There were other issues about durability and fatigue/deterioration based on how much damage the armour had to soak, either per hit or over successive hits. Soak would be reduced over time after several strikes until repairs could be made to restore the armour's integrity.

Not sure how far you want to go down the rabbit hole about this, particularly if it's not an option you wish to consider. Hope it's a useful digression.

X3M
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Natural vs Syntetic

Well. I am starting to go pretty deep here. But it is all research in general. I have no other goal in mind.

I initially wanted to share some newfound knowledge. But I am also open to discussion.

I am curious about all the mechanics that people have come up with. Some are basic. Others are genious.

But have each of them considered a chance that there might be no rps at all in the system that they thought of.
That is what I learned with calculating the armor from damage subtraction mechanic.

Warcraft 2 is brilliant. It works the same way as simply subtracting armor from damage. And so does starcraft.

The difference is that warcraft 2 has also implemented a piercing damage. This is different per unit. And means that high armor can't defend against it. 6 basic minus 4 armor is 2 basic. 6 piercing is 6 piercing, period. That is a factor of 3 difference. In the 'target is armored' league.

Starcraft. As sad as it may sound. Relies on a damage table instead. Having the remaining damage being multiplied by a factor. 1 or 0.5 or 0.25 etc. This factor is a syntetic rps. Not a natural one.

Subtracting armor from damage is a natural one. That is why it interests me so much.

My "Projectile" has to begin with: A natural rps that is ridiculous strong already. And as most might recall. I added a syntetic one by simply telling players to add more damage when dealing with a certain type.

The natural rps was strong enough to create a factor of 6 slow down when the weapon or armor was a factor of 6 away in tiers. In other words. A factor of 6 against the armor league.

The armor subtraction has given me only a 50 percent slowdown. A mere factor of 1.5.
Which is only in the best of chosen situation.

This 1.5 works great in rts games with a lot of units. The survivor has like 1/3th of its army left. Especially with extra damage against certain targets. Hence was starcraft 2 born. But this is a combination between a weak natural rps and a strong syntetic one.

Overall. I am going to recheck several other games. Most are a combination of subtracting and a syntetic factor. But also the so called piercing damage. Whether by a simple number, a number different per unit or an overall percentage.
I am very interested to see AoE(2).

Just to see if it is natural or syntet8c.

X3M
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let-off studios wrote: There

let-off studios wrote:

There were other issues about durability and fatigue/deterioration based on how much damage the armour had to soak, either per hit or over successive hits. Soak would be reduced over time after several strikes until repairs could be made to restore the armour's integrity.

I know of several systems that use the durability of armor and its effect on damage.
Most of them are hard to translate to boardgames.

One example is that the armor can be shredded like in Xcom.

Another example is that armor and health are both damaged. If armor is 100 percent. It takes 100 percent. If the armor is only 80 percent. 20 percent goes to health.
This can be done in 2 ways. Either armor always gets damaged by the weapon. Thus the total damage increases. Or the damage is completely divided. Keeping damage constant.
But health goes down either way.

***

There is also one that only looks at the total health. Used so far I think, in only one video game. Here the damage is reduced if the health is higher. Eg. An unit does 4 damage on 40 health. But against 80 health, it only does 2 damage. A weapon with 8 damage will do 8 damage against both health.
When the 80 health is lower to eg 60. The 4 damage will start putting more damage on the unit. It will go up to 3. And later 4.
Due to balancing. The weaker weapon will be weak at first. But once the target is damaged enough. The 4 damage will be stronger.

X3M
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Artificial weight increase for armor

In a previous post, I talked about having artificial weight added to armor value's. And why this is better then trying to get a system that tells us how much each armor is worth.

I am not even going to compare the 2 systems here, since the other system is such a mess for so many reasons.

What I am going to do is tell you how to set up a system with artificial weight to armor.

Tips on keeping it easy
- It is best to have only 2 types of armor. 0 and a relative high number.
If you design with 3 types, it gets 3 times as hard to find a good system.
- The weight will be always increasing for each next tier of armor. Preferably the sum of all previous tiers plus a little extra. eg. tier 0;1 tier 1;1+3=4 tier 2;4+2=6. The reason is that we want to get the high tiers to increase in worth, or else the systems will not work.
As extra pointer, the weight will be in that exact order at infinite damage.
- A minimum damage is nesesary.
1 is the best option.
Starcraft has 0,5.
Warzone2100 has 33%.
Warcraft 2 has a variable minimum damage.
- The weighs are how much each hp is worth. eg. If you have a weight of 1, 2 and 6. The units will have their hp ratio in 6, 3 and 1.

Also, you design this for one dimension. Meaning all ground units. If you use other types like air. Then you need to add separate systems. This is more complex. And is not explained here.

***

Sometimes, you just have to get started. I often use Excel for my calculations. And I then manually search for what I want.

In the system that I design today;
I use 0 and 24 armor.

The weight for 0 is obviously 1. I call them infantry.
The weight for 24 armor, I have chosen 6. These are my tanks.

This means that all infantry units are going to have 6 times as much health then my tanks. If I design my tanks to be 6 times as costly. Then the infantry and tanks would be having equal health.

Any weapon ranging from 1 to 25 damage, will result in only 1 damage on the high tier armor. 26 and beyond will have the high tier of damage increase too.

Since the high tier is worth 6. This will start high compared to the primary damage, but keep constant. Thus it will become less worth after a while. And after 25 damage, it will increase very fast.

The Excel sheet

A:
This damage column will be 1, 2, 3, 4, etc to 120 or so.

B:
Column B will simply be A - 24. With a minimum of 1. This damage column will be 1, 1, 1, 1 etc to the row of 25. Then it will be 26, 27, 28 etc to 96 or so.

C:
Column C will simply be B multiplied by 6.
This damage column will be 6, 6, 6, 6 etc to the row of 25. Then it will be 12, 18, 24 etc. to 576 or so.

D and E
Column D will be A divided by C.
Column E will be C divided by A.
What we see here are the ratio's. And these 2 columns will be used to manually select what we like. We always look at the ratio's 1 or higher.

With some added rows, you can tweak with alternate weight factors and/or armor value's. eg. If we want to change the weight 6 to 8 or the armor from 24 to 25. We can easily do this at the top. It requires you to have more knowledge of Excel. Feel free to ask me how to do this.

***

1 damage sucks!

Let us look at the very fist damage, that would be 1.

At 1 damage, the ratio is 6. The only other ratio 6 would be.... it's not there!!!
As mentioned before, at infinite damage, we can have the ratio that we have set. Seeing as how we had chosen 6, this is where we need infinite damage for.

There are many arguments as why we don't go for infinite damage. But there are possibilities. However, do we even need that other ratio 6?

What we need are twins that are each others opposites.
1 damage has a 1 to 6 ratio. But so has infinity. Both are in favour for dealing with tanks!. That's right, the very first damages are anti tank due to all the math involved.

You hardly see this in any game. But I have used it for my mod!

***

Where to start?

We have much more options beyond 25 damage than we have between 1 and 25. So we will be looking at the lower range first. And then look for their cousins in the higher ranges. What we look for are the ratio's that are exactly the same, but cancel each other out. 1 to 3 and then 3 to 1, 2 to 1 then 1 to 2 etc.
Looking for nice round numbers is an easy task in excel, IF you have added column D and E.

Damage 2 is where it all starts!
2 damage yields 1 damage on the high tier armor.
Thus we have a weapon that is worth 2 on infantry and 6 on tanks.

-->The ratio is 3<--

By skimming through the list, we need to see if there is a ratio of 3 for either the infantry or the tanks.

I have found 2 of them; at 18 damage and at 48 damage.
18 still yields 1 for tanks. We have a worth of 18 and 6 in favour for killing infantry.
48 yields 24 for tanks. We have a worth of 48 and 144 in favour for killing tanks.

Designer rules of Balancing

We now have 1 weapon in favour for killing infantry and 2 in favour for killing tanks. It is advised to make sure that there are equal units in terms of damage on each side. Or else the practical damage shifts of pretty fast.

Since the ratio is equal for all three weapons. This is self balancing!!! It is very nice to see, players simply pushing out twice as much anti infantry weapons then anti tank weapons, on the basis of ratio 3.

But you can help them in this.
How to do this?

With 2, 18 and 48 damage. It doesn't mean they are worth that much. As said before, the damage on the high tier is worth 6. To have a good balance, we need to see how much worth they are.
They yield 2+6=8, 18+6=24 and 48+144=192 as "costs".

When you apply these costs to the weapons, wheter it is by unit costs or a different cool-down/ROF. It will balance itself automatically in that 2 to 1 composition. But to make sure that players will use the anti infantry more often (twice as much) without having much of trouble figuring this out.

Simply have 2 unit designs that use the same weapon and armor. The differences can be in speed, health, ROF and range of the weaponry.

***

When will it end?

From a math point regarding combat leftovers. It is often wise to choose ratio's that are linked. 1, 2 and 4.
Or 1, 1.5, 2, 3 and 6.

Factors between 1 and 1.5 are often not noticed at all. End results of leftovers of armies are between 0 and 33%. This doesn't feel like a victory.

For the next example, I am going to use the ratio's 1, 2 and 4.

So, what do I find in my list?

Ratio 1:
6 damage, yields 1(=6), worth 12, all rounder, used 1 to 4 times

Ratio 2:
3 damage, yields 1(=6), worth 9, anti tank
12 damage, yields 1(=6), worth 18, anti infantry, used twice unless one of the other ratio 2 weapons is scrapped.
36 damage, yields 12(=72), worth 108, anti tank

Ratio 4:
24 damage, yields 1(=6), worth 30, antiĀ² infantry, used 1 to 2 times
72 damage, yields 48(=288), worth 360, antiĀ² tank, used equally much as the 24 damage.

The damages used on a row: 3, 6, 12, 24, 36 and 72.
Their costs in a row: 9, 12, 18, 30, 108 and 360.

We can have 6 to 12 weapons in the game. With only 2 armor types, we can have 12 to 24 units in the game. That is relatively much for most RTS these days!
But we are sure:
-The game is balanced.
-The factors are nice round.
-Battle outcomes give noticeable differences.

***

Silly if it is used in your board game?
So I have given a list of damages.
Some anti tank damages are below the 24 armor mark.
This means that there is a minority of damages where players subtract 24 armor from. Why even include it?

It is for this reason that most games use a damage table instead of subtracting armor.
If we want to make the subtracting more useful. We need to scrap damages that are below 24 and anti tank. And their opposite twin.

In this case, it would be 3 damage and one of the 12 damage designs. But come on! How many times do you see a fast firing anti tank weapon?
[Auto-Cannon Tank from KKnD]
[Auto-Cannon Turret from Warzone2100]
[Laser Turret from Tiberian Sun]
[Disintegrators from Tiberian Wars]
Hmmmm, more often than you think. :)

Either way, using percentage's is what most designers go with these days.
Even board games will have a table of damage X/Z instead of letting players do the calculations of X-Y=Z.
Most often due to the reason of using numbers closer to each other then 3 and 72.

If you want to get nice round ratio's in existing games through a mod. Like Warcraft 2 or Starcraft[1]. Then this is the system that you need.

The only reason to use this system in a new game would be to give the players some sort of aesthetic feeling of the tank is "armored".

X3M
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Make things simple for players, also + or x ?

Subtracting low armor value's is non done these days in board games. Having small squads of different damages and armor. Already asks for a tedious task of checking each possibility, that is, IF players want to do strategies.

Not only that, but I have seen design after design that uses subtracting low armor from damage. To have almost no RPS. It often comes in the soft counter department. Except for 1 match up, that immediately will shift the entire balance of the game to "we are not going to use these units any more".

Soft RPS is great in big war and RTS games. But for board games and RPG's, we need some harder RPS.

***

Keep it simple

How to get better RPS, and without the hassle of subtracting high armor value's?

Simply tell the players how much damage each weapon does against each armor type.

eg.
The laser tank does 8 damage.
16 against biological units.
12 against small units.
20 against small biological units.

Or...
The laser tank rolls 2 dice.
4 against biological units.
3 against small units.
5 against small biological units.

Keep it strong

What is important here to do?
If you want a head start in designing with balance. You need to keep nice round numbers as ratio's, with the lowest number being 1, 2 or 3.
This way, your RPS will be at least of medium scale and worthwhile consideration by players. Even if you use these only in later tiers of the game.

Why nice round numbers? This will make it easier for both designer and player to work with.

But it is important for the designer to know how the balance works. So in the back ground, keep a plan of ratio's.

Add them up

eg. of a simple yet effective system:
3, 2, 1, Anti infantry
2, 2, 2, All rounder
1, 2, 3, Anti tank

The first tier will probably have a couple of all rounder units.
The second tier will change this into anti infantry and anti tank.
But what is even more important is that when you add up the damages. You can tell that each damage type and armor type are worth equally.

Factor them up?

eg2. of a simple effective system with 1 "flaw":
4, 2, 1, Anti infantry
2, 2, 2, All rounder
1, 2, 4, Anti tank

Believe it or not, but this system is balanced as well. It is much more suitable for 1 on 1 battle's though. Having a mistake in either direction dealing the same punishment of a factor of 2.
But having this system will also be useful for larger scales. Multiplying each factor will yield a result of 8. But when simply adding them up will give 7 or 6. It is noteworthy that the all rounder does 6 and the medium level of armor takes 6. This means 2 things: one, it is still balanced. Two, your medium units and weapons will be slowing down the game by a small margin. But they will be more suitable for meat or fodder units.

Why only consider using the +?
There are 0 damages possible. ground to air is such an example. If you use this as a factor, you get 0 for the whole weapon.

Both adding and factoring up
There are games that use both systems and look at the average value's. These games often have 1 on 1 fights to start with and end up having bigger battle's. But they also make use of certain blocking units like concrete walls. In those cases, it is good to know both situations.

I am not a fan of averaging them up. I rather look at the situation from beginning to end of a combat. A wall doesn't go down in the middle of the battle, it could take a short or long time too! And this is only noteworthy through looking at the added up value's.

***

What is a weak system?

When we look at the systems provided. We can see that these mirror in their diagonals. When mirroring them in the horizontal or vertical plane, the sum will automatically be compensated. These are hints of true balance.

A weak system lacks in these mirroring effects.

Not balanced, yet?
Of course, there are systems out there that are not balanced to start with. They still might be practical balanced if players don't have any other choice than to use some units of the imbalanced system.

But if they have a choice. Those imbalanced units will either not be used. Or the only ones to be used.
You need to counter this imbalance. And this is easier then you think.... not.

eg. of a system that is imbalanced at first sight:
6, 3, 1, Anti infantry
1, 3, 2, Anti vehicle
1, 2, 3, Anti tank

The diagonal mirroring is a mess.

Adding up leaves us with
10, 6, 6 for the weapons.
And
8, 8, 6 for the armor types.

That is:
10 to 8 for infantry.
6 to 8 for vehicles. And
6 to 6 for tanks.

Infantry seem to be more durable by a factor of 1.25 on average.
Vehicles on the other hand will be dying faster by a factor of 1.33.
Tanks are properly balanced here in terms of receiving and inflicting damage.

The total margin are 67% for the weapons and 33% for the armor types!

How to balance this? That I do not know.
What I do know is that each armor type does have a greatest weakness ready in this system. So a simple practical balance has been met.

I only know a path to increase the practical balance by simply applying the factors 6 and 10 for the weapons. And 6 and 8 for the armor types.

I know it isn't perfect. And there is even one more step to get closer to balance. But it requires you to redefine the weight factors of either the damages, or the armor types.

Maybe with a loop...

***

I wonder if any one reads this. Also, what would you like to know regarding RPS, wargames or anything mathematically speaking?

Experimental Designs
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This may not be something

This may not be something you're looking for but I done a simplified formula of weapons being specialized for anti-armor and anti-personnel.

For starters I went with a basic "effectiveness" stat for all weapons that more or less abstracted factors such as the weapon crew/gunner experience and the weapon's accuracy. You roll this plus 2D6 versus another model's target value with modifiers included.

Then account certain factors such as vehicle armor or the survival level of infantry squads and subtract the overall effect from the first roll.

For example if your EFS is a 5 versus a target factor of 11 and you roll a 7 on 2D6 your overall effect is 1.

If the same weapon has an impact level of 4 and the target's armor is 2 then your overall effect is 3. Alternatively if the impact level is 4 versus an armor of 8 then your overall effect is -3 which is practically an ineffective attack.

Then you roll for damage thresholds. From the previous example if your effect is 3 and the model's damage threshold is 9 you roll 2D6 + 3 and if you roll equal to or above 9 then the model is disabled or destroyed.

X3M
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You have given something good to talk about.

A simplified basic attack. With an extra against either personnel or armored units. Always is a good start.

This will also make it easy for players to discern the difference between the 2.

eg. A basic roll of 2, with an extra roll if facing eg. personnel. Is easy to grasp and easy to work with.

Since you are talking about dice rolls. Which are natural in board games. You need to know that when you add 1 more dice, the chances will go up differently than when the given dice amount. This will make balancing harder. And believe me when I say that you work with insane numbers here if you are using subtracting.

On the other hand, if you use numbers for attack and defence that are close together or even overlap. Then you might get a decent RPS system.

To make sure you know what chances each battle gives, use www.anydice.com to see the differences.

I could work out some example's with RPS like systems and dice if you like.

Or.

If you give much more detail on your rules. (here or a pm) I could check situations that can occur in your game. As long as these are 1 on 1 battle's. Things are simple enough for me to check.

X3M
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Do I have discovered something new?!

Yes I have.

I am not going to put much maths here. But the finding sure teaches me why balancing games is so hard.

But there is also light at the end of this tunnel.

Ok, the key word here is 'Conjecture'.
https://en.wikipedia.org/wiki/Conjecture

This is basic what I have been doing.
I set up some rules to determine the balance. Did so. But it required a loop.
I looped a lot. Loopyloopyloopy etc. Loopholes too. Loopy tunes!

Any way.
You can't calculate the balance of certain games. RPS is one of those balances if you do an off set in your RPS.
As said before, when you make sure that each damage type is equally strong as the opposed armor type. The system is automatically balanced.

When I started to loop the correction factors on "unbalanced" systems. I slowly ended up with the same type of balanced system. However, the results where correction factors on those damage and armor types.

These correction factors, can be different for the armor types than for the damage types. Especially when you have more or less damage types than armor types.

But above all. The correction factors between damage types. OR between armor types. These are the same as what you started with.

The only thing that remains for the loop calculating is the difference between all damage systems combined, compared to all armor systems combined.
There is no easy way to get this difference, except for the constant looping.

The difference that you get... Well, that is how much balance your game has. Most of them are at most 10% off. And this off set is actually that your game runs faster or slower then expected.

You know what to do to get the result.
You can't calculate this, only follow steps.
Henceforth the Conjecture.

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