RTS, is it even possible to balance?

[X3M]

A lot of math in this thread.

 

Although I don't have much time now. I will try to re- awaken this thread.

I did the following classes test for checking the usability of my units:

 

Each statistics can have a very low, or very high number. So you double classes with each statistics that gets tested.

Armor/Health

Damage

Range

Speed

 

This means there are 16 "basic" unit designs.

 

I also used my formula to determine the prices. I used extreme values to almost reach the minimum and maximum prices. As mentioned before:

 

Ah, you know what, I post the formula here:

 

€ = Stats = Size

Stats is used as Build Time

€ * X asks a Size reduction: Size / X²

Stats = (Armour + (Multiplier * Damage)) * (Range + Speed + 6) / 10

Health = 6 * Armour² / 2500

Max Damage, is per dice/multiplier on target = Armour² /2500 or Damage² / 2500

 

And thus I discovered 1 major glitch. 1 particular type of unit that has almost no value in combat, and is way to expensive.

Perhaps you can guess which one (and 2 more) it is (are).

 

For the testing, I used 50 and 500 for the Armour/Damage value's. Comparable with infantry and tanks with armour that of a mammoth tank. So the firepower as well. The 500 damage however can also be viewed as 10 times 50. Meaning it is anti infantry.

And I used 2 and 12 for the Range/Speed value's. Comparable to normal range and that of the SSM or V2 launcher. Speed, normal tank speed or something like the Recon Bike.

---

 

The 16 unit designs:

Whereas A=Armour, D=Damage, S=Speed, R=Range

 

..A    D    S    R      €    Unit

.50   50    2    2    100    A

.50   50    2   12    200    B

.50   50   12    2    200    C

.50   50   12   12    300    D

.50  500    2    2    550    E

.50  500    2   12   1100    F

.50  500   12    2   1100    G

.50  500   12   12   1650    H

500   50    2    2    550    I

500   50    2   12   1100    J

500   50   12    2   1100    K

500   50   12   12   1650    L

500  500    2    2   1000    M

500  500    2   12   2000    N

500  500   12    2   2000    O

500  500   12   12   3000    P

 

 

 

Now the question remains. For what would you use these units? Every unit will serve a purpose and is useful in some way. If there is no usefulness, the formula that is used, fails.

 

A

Is a typical basic unit. Weak in any aspect, yet strong through numbers. It can serve as cannon fodder, or support for finishing of enemy infantry. So a Dual Basic.

B

Is the same unit as A. Yet has insane Range. Due to this range, the duality is removed. And this unit now simply serves as Support.

C

Is the same unit as A. Yet has insane Speed. Due to this speed, the duality is removed. However, due to the other statistics, you would only use this unit for Hit and Run tactics on the enemy base.

D

Is a combination of B and C. Both Range and Speed are insane. Due to this, this unit is perfectly to do Hit and Run tactics on the enemy units. It would be one of my favourites.

E through H

These units all are some sort of Support. This due to their insane damage value. Yet E can still be used as meat against cannon fodder, if there are other more expensive units to be protected. F is Support only just like B. G has the same usefulness as C. And H is the same as D. If you are going for a "cheap" OP unit, H is your choice.

M through P

These 4 are again the same as A through D. However, they are the expensive variant.

 

The other 4, I through L

These 4 have almost no damage. But they have a lot of armour. Therefore they should act as Meat units. Of course they still can act like A through D. However...

The only problem is. Why pay twice the amount for armour for a ranged unit, while the damage is almost non existent. I do understand that long ranged units are safe. So the high armour is only useful if such a unit is trapped. But twice the costs on armour is not needed. If you are going to use meat. Then the one without range can act as such. So you pay for something that you don't use. And to top it off, you pay it twice.

 

And this is where my formula fails. An extreme version would be:

 

..A    D    S    R      €    Unit

.50    0    0  594   3000    X

 

So basically an infantry level wall with Insane³ Range. This is clearly a fail. And if it is possible to have a clearly fail. Then there are hidden fails as well. So, my formula needs to be changed. But into what? This question is continued in the other thread for my board game. Clearly, Range is not allowed to touch Armour with a factor. No matter what the Range is. The costs should only be €30, not a one hundred fold.

 

Summarized: I did not use a perfect formula for a balanced RTS. FAIL!!

[X3M]

I noticed that I never posted the new and improved results.

The 16 unit designs:

Whereas A=Armour, D=Damage, S=Speed, R=Range

 

..A    D    S    R  old-€  new-€    Unit

.50   50    2    2    100    100    A

.50   50    2   12    200    200    B

.50   50   12    2    200    200    C

.50   50   12   12    300    300    D

.50  500    2    2    550    550    E

.50  500    2   12   1100   1550    F

.50  500   12    2   1100    650    G

.50  500   12   12   1650   1650    H

500   50    2    2    550    550    I

500   50    2   12   1100    650    J

500   50   12    2   1100   1550    K

500   50   12   12   1650   1650    L

500  500    2    2   1000   1000    M

500  500    2   12   2000   2000    N

500  500   12    2   2000   2000    O

500  500   12   12   3000   3000    P

 

 

Summarized: SUCCES!!!

And to top it of. Fast units also have a reduced hit chance when targeted while moving.

2 has a 69% chance of being hit while moving, but 12 has only 11% chance of being hit while moving.

 

F:

People will keep using that one.

G:

Really great in hit and run tactics now.

J:

A marvellous toy of annoyance.

K:

The least useful, unless you need emergency meat somewhere where you expect an attack very soon. Then this one is the only option.

 

 

I've been thinking in quite the opposite direction, do you think it could be possible, since its a boardgame and you can implement whatever rules you want, to make a really more realistic combat model? With limited ammo, different attacks for different targets etc.? I guess that the most troublesome part in this approach is actually the calculation of hits and misses, since accuracy is going to be a serious issue (relative positions of the attacker and the target, projectile type, wind etc. etc.; but on the bright side, all of that can be calculated reliable with the "huge load of math" as you put it :)).

I never answered this, did I? Sorry for that.

 

- Limited ammo?

Yes, that is possible. Although, very tricky and I never really thought about it.

 

First degree approach is having all the units carry the same amount of possible damage. Meaning if one unit has a value of 50 and another one has 500. That the first one can have 10 ammo, while the second has only 1 ammo. Further more, this is expandable to any factor.

 

Second degree: However, if you want to have units with more ammo or less ammo in comparison. Then there should be a tweak in balance comparison as well. I am not aware of the approach of this. But a possibility would be a "total possible damage". Where one unit with 30 x 50 ammo would have 1500 points and another unit with 5 x 500 ammo would have 2500 points. Thus 67% more expensive.

 

The question then remains, how much is this system part of the damage system? is it a 50-50% for normal weapons? Is limiting ammo to 0, giving the result of 50% worth of damage? What about unlimited ammo?  This is a trick question for me. And a lot of games have both systems in one. Having ammunition of 0 should return a € 0 for weaponry. Having ammunition of 1 time something/something should return € 100% for weaponry. Is it up to the designer where to place the basic Damage/Ammunition ratio? Just like the Health/Damage ratio? Then the designer can decide on a "normal" game where both ratio's have the same number. Thus having just enough ammo for killing your own kind. Or having 2 or 3 times the clips? That simply results in overkill. If the design only allows 99% or less, there is always a retreat for refilling. This could give pause to players constantly. A bit to much retreating and players find the game boring.

 

However, training troops would result in cheaper ammunition refill if you think about it.

 

- Different attacks for different targets. (Mammoth Tank Assembled, C&C3)

Yes, this is simple. ..With long time consuming math. I ensure you

However, you need to keep in mind that an unit can shoot both, or just 1 target at a time. There are different factors in play for that.

There are 3 main choices in this.

 

Lets assume there are 3 possible targets, Normal units are specialized in dealing with 1 of them.

 

Choice 1:

Having an unit that can shoot all (2) different projectiles at the same time at 2 different targets, simply means all projectiles count 100% in costs. The unit is simply much weaker in normal chaotic combat, dealing with 3 different targets. But a good support unit for "noobs" as long as another unit takes the damage.

Dealing with the 2 desired targets, and your unit wins anyway. Also keeping in mind that if all projectiles go to one of the two, the damage is on target, but slightly less effective.

Dealing with just 1 desired target, and your unit already has a chance of losing. If there are no desired targets, your unit fails even more so then the specialized units.

If the targets are in different dimensions, whereas 100% of 0% damage is in play. Players need to think extra carefully about using these units. However, if both ground and air are there, then both can be targeted. The unit simply can't focus all shots on one target.

 

Choice 2:

Ok, now for the, can shoot only 1 target with 1 type of projectiles at 1 time. While having 2 types of projectiles. Thus the Mammoth from RA1.

Each round of firing, the damage is considerably less. However, not less then 50% in a 2 types of projectiles.

I do not like these units. Nor the balance behind them. That's why I did not write down rules for them. Nor do I use them in my game.

But if I have to explain these in balancing terms?

I guess I could say that even if this unit could hit the ground with 2 different weapons, disabling one and activating another should lead to calculating the total damage against any target. And compare this with when both weapons can shoot at the same time.

 

Let's say the targets are 50 (1), 150 (9) or 300 (36).

The weapons are 6 x 50 and 1 x 300. Obviously the total worth normally would be 600.

But since only 1 weapon is activated at the same time. We need to observe the total amount of possible damage (in a game with infinite possibilities of targets this is not possible)

 

Against 50, we have 300, against 300 we too have 300. But what to use against 150?

In my game we have an armor of 9 for 150, thus 6/9 with 6x50 or 9/9 with 1x300. Obviously the 1x300 is used. Thus even though the weapon is less effective in the long run. The worth is 150 points for the mid section? (Using the wrong weapon is only 100 points) While the other 2 are 300 points each. Thus a total of 750 points.

 

How does this compare with the worth € 600 weapon?

It is 350 points for the first, 250 points for the second and 350 points for the third. A total of 950 points.

 

If € 600 is worth 950 points. Then the other unit with 750 points is only worth € 474. (€ 237 for each weapon instead of € 300, which is cheaper, right?) So a cheaper unit relatively speaking, is actually more expensive. Since only 1 weapon is used each time. The problem lies within the fact that this unit pays for the most optimal weapon. Which is good and helps. But fails in chaotic combat. No sweat there, it is balanced. But is it useful for players?

 

It ain't useful if you want to expand a game with more types. If another type comes along, lets say 600 armor aka 144. Then the points immediately become different.

For the € 600 there is an addition of 175, a total of 1125.

And for the other one we have the most optimal choice is 1x300, thus 150 more points. Thus a total of 900.

The new price would become 900/1125 of € 600 = € 480. That is 6 more. Thus this unit would become more expansive after an expansion pack.

 

The main things that I don't like about these units is that

A) mistakes in weapon choice can be made during game play and

B) the balancing is harder since weird prices come along and

C) my game is expandable into infinity.

 

Choice 3: Back to C&C3.

While other units can only hit ground or air. This unit can hit ground or air with the same projectile. There are more choices compared to the basic units. Thus a bit more of a more expensive weapon. It also depends on the number of choices that a game has. With only ground or air. The bonus might be big, but never is allowed to surpass the square root of 2. Thus the bonus an unit during combat has is 42%, but in a chaotic combat, it is 42% for the enemy. Since players then tend to get chaotic battles instead to prevent this abuse. Another square root could be applied. Leaving only a difference of 19%. So if mister Recon Bike could not hit air, then it's worth would be roughly around $ 500 instead of $ 600. Keep in mind, the factor to this depends on the number of dimensions a game can have. To be close to only 2 in my game, I use 33% costs instead of 42%. Yet another 33% is added every other dimension. With 4 dimensions, the weapon is times 2 in costs. Never allowing myself to surpass 4 dimensions.

 

Just like choice 2 never would allow me to add more types. But dimensions are limited and types are not. Thus choice 3 is made, choice 2 is not.

 

-Hits and misses

Obvious. Yes.

Of course the most exceptional rule is the one that I have for targeting moving objects. The faster they are, the harder to hit.

However, calculating this with only dice. Results in some sort of overkill on slow moving objects and over miss on fast moving objects.

However, no matter what kind of unit it is. Once standing still, it is 100% hit.

Forests and other obstructions influence projectiles as well. Where hiding in a forest gives the same bonus as hiding behind a forest. But this is downsized with 50% once a player decides to attack from a forest. The missing part is only for the other player that shoots into the forest.

Calculating all of this is not an issue. A chance of 5/6th means the worth of the weapon is 5/6th. Thus a weapon of 300, simply costs 250.

And the risk part makes a part of the game.

[X3M]

Wow, more than a year ago. This topic.

 

Any way. I had some discussions with someone who designed a real RTS.

Regarding balance.

 

He too had troubles in balancing. But went with trial and error.

The result was still pretty neat.

 

I got a copy of his game. And shared it with my cousin. It is in java. And I await a response.

 

---

 

With the talk going back and forth. We got to some new conclusions.

Where actually, only 1 method requires math and 1 method requires play testing. These are mostly though experiments considering the level of skill of players. And the experience of designers over the past 20 years.

 

Just some tricks to add to the game. To see it more balanced.

 

Here we go:

 

1a

Encourage players to keep some resources stand by to become any thing. With RPS going on. You loose your R against P. But you know you need to get S. The fight has to go slow enough for players to see what the enemy has. They can build new units back in their base and know how much they need. So they will not waste it all on the new right unit. Just enough to win a battle. The more skill a player has, the more efficient this flows. But somehow, it balances itself out because "normal" players always build the right counters. And can't overcome initial fights since both players are behind the facts by 1 step.

1b

Scouting should not be permanent. Fog of war balances the game because it maintains for players to be behind by 1 step. Of course this means that scouting itself should be balanced.

 

2

Increase health for ALL units if you feel that one unit is a bit too effective. Often you get into a chain reaction of modifying unit, after unit. And you could go in circles with this if your testing is incorrect. It seems that having an overall health increase automatically balances towards what you had envisioned. If that doesn't help, increase all health once again. Of course you can't go on with this. If having 200% or more health doesn't help you. Go back to 100% and simply adjust that one unit instead.

 

3

Indirectly increasing health by allowing units to take cover. And of course having the smaller units a better job at this. You can use other units that are meat or that can be entered. You can also use walls. Structures too.

 

4

Going the other way for all units with health. But not really health. No, instead you increase damage on those specialist units. But not just for against 1 type of unit. You need a specialist that is able to destroy another type instantly. A sniper against infantry. A bunker buster against bunkers. A tank killer rocket for dealing with tanks. A laser that deals with light armoured units. An EMP blast against 1 air unit. In fact, you design your game to have RPS, not just a soft version, but also a hard version at the same time.

 

5

The well known math trick is known by many designers. But also hated by many designers. After having set your first statistics. You pick your weakest unit. And compare it to all your other units in numbers. Do not apply a differentiation in damage on types. Just basic damage is what you need. Also you take in account how many units a player will have on average. Now fill in the formula for each unit:

 

Td = (H-1)*N*D + 0,5*(N*N+N)*D.

 

Where Td is your total damage score.

H is literally hit points of the unit.

N is the number of units.

D is the damage of the units.

 

If you apply cooldown or rof, you need to use DPS instead: And subtract the H for both units by 1.

 

Both units will supply you with a Td. Now you will calculate the following:

€ factor = Root of ( "Td current unit"/ "Td of the weakest unit")

 

If you need help with the formula for your recalculating. Call me.

The thing that designers hate is that root part. It always gives crappy numbers.

 

6

Cheaper units, should be healed way faster. Most RTS fail in this. And the strong unit heals just as fast as a weak unit. This is incorrect since the weaker units also die faster?

 

7

Damage is linear to health. OMG, this one is that obvious one. Although, in board games it is hard to implement. Most RTS could benefit from this. If implemented right.

It is also the first thought trick ever implemented to RTS. And we all know which game.

[X3M]

6 years later...

In the meantime I matured more in math regarding RTS games. And to sumarize, most of them have to do with infinities and limit interactions.

The 3 main pillars are:
- Chain reaction weapnry. Where every hit could trigger another chance to do more damage. O-game is a very good example in this. Where a chance of 50% for each increase of 1 would result in an average of 2 damage on the infinite scale.
- The same as the chain reaction. But the chance for the projectile to go through a section of the terrain in combination with infinite range. Would eventually result in an average range. Where a chance of 5/6th per region would result in an average range of 5 regions.
- Considering cooldown/charging or ROF or, yes even a weird salvo can now be balanced by math. Burst, Salvo and Charged weapons now go together. This calculation makes use of the set Health/Damage ratio.

There is a clear difference between theoratical balance and practical balance.
Practical balance includes effects of the terrain, the combination of units and the skill of players. Sometimes the set of designed units might secretly shift the Health/Damage ratio as well, this happens when there is no mirror design.
There is math to it all.... Except the skills of players. And thus my final verdict is that balancing a RTS game starts with theoratical balance and has to proceed into practical balance by having a team test the game.

If you want to know more about a subject. Feel free to ask. I know this will not really happen. But I am happy I solved a couple of mysteries in the RTS genre.

[X3M]

Another 4 years later.

Working on something for a RTS tought me even more. Alas, that project is dead or a scam.

2 years ago, I finished a research of 2 years. Where the health to damage ratio had to vary for the individual unit designs. The conclusion is that games like Starcraft and their design choices started to emerge. While most argue that Starcraft might have been a stack of lucky accidents. I do see a patern in the numbers. I even got a formula for it now.

I wanted to use this new knowledge in an upcomming game. Together with some other calculation mechanics that are unique to RTS in general. It would have been refreshing for the players for sure. Alas...dead or a scam.

Perhaps... someone is interested.

I just wanted to share this with the remaining visitors of this forum.

[X3M]

I see people pop up. Making their own RTS.
Then calling it quits again because their playtests fail.

 

I don't see it anywhere. The "root"-factor.
It is a god tier way of theoratically balancing a RTS game.
Anyone interested in me explaining this?
 

[Fey]

22 hours ago, X3M said:

I don't see it anywhere. The "root"-factor.
It is a god tier way of theoratically balancing a RTS game.
Anyone interested in me explaining this?

lay it on us, brother 👀

[X3M]

Very well. If there are any questions, feel free to ask.
This balance theory looks at the fact that in RTS, players can attack those with the lowest ratio of body points to weapon points.
And that synergy between 2 different designs, is not an option for the players.

First I explain without the balance.

First some basics. When you design an unit. The design consists of value's that belong to a body. And value's that belong to a weapon.
I am not going into detail of all the value's that can be in a RTS game. But the most important ones, for explaining this, would be:

Body: Health
Weapon: Damage

That is all we need for understanding this. We are not going to look at movement speed, attack range, size or other stuff. Just the 2 mentioned above.
Of course we need to shoot an X times with Damage before we get to Health.

The cost of Body is Health.
The cost of Weapon is X * Damage.

Most designers initially add the 2 together.
What you get is that a well balanced design had 50% Body and 50% Weapon points.
50%+50%=100%

In case of the above, lets say we have 72 health and X=12 with 6 damage.
The cost here is 144.

If we now design a support unit. One that deals more damage. We could design the following:
36 health and 9 damage. The cost...? Would still be 144.
But while this unit deals 50% more damage on anything. It is much weaker compared to the balanced design.
It has only 50% health.

What do we get when we look at a 1v1?
72 health / 9 damage = 8 hits
36 health / 6 damage = 6 hits

The balanced design here, has 33% more durability.

***

This is all fine if you have a game with the rules that one unit blocks projectiles for another. You see this in games like Warzone 2100 (Yes, it happens, look it up )
And designing like that would be ok.

Because you get this synergy: The tank would have 108 health and deal only 3 damage.

2 Normal vs a tank and a support:

Normal: 72 + 72 health.
Tank + Support: 108 + 36 health.

Both sides deal 12 damage before one of the 2 dies.
If there is no micro, except for one player putting the healthiest one in front.
72/12=6 hits
108-72=36.
Now, the normal are down to 1. And can deal only 6 damage.
72/12 =6 hits.
36/6 = 6 hits. Clearly the tank takes the bullets here.

And voila, the support unit is still at full health after this exchange.

***

What happens in RTS?

The player with the normal units first focus on the support unit.
72/12= 6 hits.
36/12= 3 hits.
Clearly we remove the support unit here.
And the normal units take only 12 x3=36 damage.
36/3= 12 hits.
108/12= 9 hits.
Clearly we now also remove the tank unit.
And the normal units take only 3 x9=27 damage.
The normal units here have 9 health remaining on one, and the other is at full health.

This is the reason why most support units have more attack range. Because you need to move further into the army in order to destroy them.
A RTS that I think fails here would be The Frozen Throne. Where the support units have weaker armor, compared to Warcraft 3.
But also, the rocket soldier in C&C td seems to be much weaker. And is not used that much in direct combat at all. It melts vs most tanks.

***

The root factor?

If we look at the cost calculation. We can balance tanks and support units with normal units with one simple calculation.
Instead of body + weapon. We do 2 * sqrt ( body * weapon )
We get for the normal: 2 * sqrt ( 72 * 72 ) = 144
We get for the support: 2 * sqrt ( 36 * 108 ) = ~125 (ok, not the most perfect number, but my time was short)
But if we keep the health the same and increase the weapon or damage value. We get:
2 * sqrt ( 36 * 144 ) = 144
And for that 144 in weapon value, we have a 12 in damage value.

A normal has 72 health, divided by that 12 = 6 hits.
A support has 36 health, divided by that 6 = 6 hits.

The support and normal are equal now.
And the same goes for the tank. The tank would keep the 3 damage, but have 144 health.
144 / 6 = 24 hits.
72 / 3 = 24 hits.

And a tank vs support?
144 / 12 = 12 hits.
36 / 3 = 12 hits.

When a tank or support face a normal, the battle takes longer.
But when a tank or support faces each other, the battle takes the same time.
Of course, a tank vs a tank is super slow. And a support vs a support is super fast.

Ok, so, to finish this formula. Let's design a wall then, the ultimate tank in a game.
How much health should it get?
The formula breaks here. Because we have 0 damage.

2 * sqrt ( ? * 0 ) = 0

It depends on the game how much micro players can apply. Thus, how fast would a player attack the support units first, before taking on the tank units?
What a good design does is:
a * (body + weapon) + b * (2 * sqrt ( body * weapon ) ) / ( a+b)

You can see the results in KKnD for this one.
As for the walls, they are not free anymore. But support units and tank units are now more balanced compared to the normal units. And depending on how much micro the players can use. You can shift the bar between a and b. If you use Excel for this, it can be an easy factor at the top of the list.

My favorite a and b are: 1+1 and 1+5.
With the 1+5 I have walls being 12 times more durable than their soldier counterparts. In a sense, I have 600 for body, 0 for weapon, costs is 100.
A rifleman has 50 for body, 50 for weapon, costs is 100.
A support type of rifleman has 30 for body, 80 for weapon, costs is 100. -20 on the body for a +30 on the weapon is a good exchange already.
And once you add in attack range and movement speed. You can make the support units even more effective or better said, immune to micro managament effects.

Either make support units slower, thus more durable. Or faster, can hit and run. And you get this RPS between units, based on the root factor, movement speed and attack range. This RPS is a natural one.

If there are any questions, feel free to ask.
I understand if it is a bit too much to get in one go. So, as soon as you get a question. It is better to answer that one first. Before you continue the read.
 

[X3M]

Right, I guess in simpler/different terms?

When you have the body value's and weapon value's added up. There is an optimal balance at a 50%+50%=100% value.

But when you start shifting the percentages. To either meat or support.

The overal effectivness of 1 unit will drop. Compared to the most optimal design.

You can see this by simply multiplying the value's of the body and weapon.
50 * 50 = 2500
40 * 60 = 2400
30 * 70 = 2100
20 * 80 = 1600
10 * 90 = 900
0 * 100 = 0
The productvalue is what matters in combat. And the lower it gets, the less this unit is effective.

If you apply the root factor for calculating the costs. You get:
2* sqrt( body * weapon )
2* sqrt( 25 * 100 ) = 100 and the producvalue will then be:
25 * 100 = 2500. Which brings it back to the maximum possible effectivness.

Of course, we cannot have infinities. Thus we need to add a bit of the normal calculation.

1:1 portions
( body + weapon + 2 * sqrt( body * weapon ) ) /2
With 30%+75%. We get:
( 30 + 75 + 2 * sqrt( 30 * 75 ) ) /2 = 100.
And the productvalue is 30 * 75 = 2250. This is now 90%.

1:5 portions
( body + weapon + 10 * sqrt( body * weapon ) ) /6
With 30%+80%. We get:
( 30 + 80 + 10 * sqrt( 30 * 80 ) ) /6 = 100.
And the productvalue is 30 * 80 = 2400. This is now 96%.

While previously we had 2100 or even 1600, which equals to only 84% or 64%.

[Fey]

it sounds a bit too basic to really work out ^^ there are so many other factors to consider in a unit's power. maybe as a starting principle, but certainly not as the core of balance decisions and whatnot

do you have some kind of example to showcase the success of this method?  a practical example, not... not more math

[X3M]

5 hours ago, Fey said:

it sounds a bit too basic to really work out ^^ there are so many other factors to consider in a unit's power. maybe as a starting principle, but certainly not as the core of balance decisions and whatnot

do you have some kind of example to showcase the success of this method?  a practical example, not... not more math

It is not the core. It is the giftpackage that finishes it. 
In order to understand it. I explained it with the 2 most basic value's.

As practical example. Where I got this idea from would be KKnD.
KKnD is the best example. Here you can tell which units act as tanks and which as support. These tanks often move forward too.
The AI shoots at the units that are the closest. The player can get an advantage here by aiming for easy soft targets that normally give dps.
The units that are tanky, compared to their damage:
Survivors have the Anaconda Tank and ATV. But also the Swat, these infantry are relatively cheap, but very durable in small forces combat.
The Mutants have the Monster Truck, which just so happens to be 99,9% balanced to the ATV. And the Mastodon is the equivalent of the Anaconda Tank. They excel in their durability. And their infantry version would be the shotgunner.
While the game has a lot of assymetry. The functional uses of the units are almost always, the same.

My boardgame was another example. But that project slowly died due to creeping.
As for other RTS. You can tell the absense of this root factor in C&C td.

As for the core for balance. The H/D ratio, is THE key number for the weight factors of the movement speed, attack range, salvo (or dps, but cooldown and charging included).
Map design also adds weight to the attack range.
Body has the health, movement speed and other body related value's.
Weapon has the attack range and salvo.

As for the whole game balance. You have a basic formula. Based on the H/D ratio. Then you wrap it up with the root factor.
Getting advanced?
If you wonder if your H/D ratio changes due to having more or less support combat units. You could recalculate this one. And recalculate the entire list, assuming all units are used equally.
A little macro. And you end up with a mathimatically balanced list. Still theory. Playtests will show how much players truly use certain units.

Now for the fun part. Upgrade the list with the weight factors on how often the units are build. If they weight more. Their influence on the H/D ratio will weight more as well.
Recalculate the entire list again.

I believe that C&C3 didn't use the root factor to begin with. But I suspect they did use a matrix balance on multiplayer results.
C&C3 also has an important factor...Size, thus the combat density sometimes matters when large armies are used.

And another factor that matters with low unit counts. Would be the fodder/tank ratio. 

[X3M]

The post from Posted August 4, 2013 contains a mistake in the calculations. While it was used for a board game. It doesn't work that way. I never corrected that one. A few extra modifications on these, and you can use most of them for RTS as well. I see some on the internet. Assuming that they differ due to different game mechanics in their RTS.

Most common used formula's in my department

Main balance formula:
Stats = a * ( Body + Weapon ) + b * ( 2* sqrt( Body * Weapon ) ) / ( a+b )

Initial H/D ratio. You simply pick a number that indicates how many turns or seconds a basic ammount of damage is needed for destroying a basic ammount of health:
= HDratio

Normally:
Cost = Stats = Size

Used for stacking cover mechanics. The SumSize gives different proportions to units that take cover inside things:
SumSize = Body + Weapon

Used for hiding cover mechanics. The Size of a design can also decide on the combat density of an army. Smaller means a higher density:
%Cost = %Stats / sqrt( %Size )
Basicly, if the size is only 25% of what it is supposed to be. The costs will double. I left the %Stats in there, it is always 100% stats, so you can replace it with a 1.

Please note that the Armor mechanic works completely different in every RTS game. In some, its subtraction. In others, it is part of a RPS system. Here it is part of a "RPS system" and receives a weight percentage:
Body = %Armor * Health * %BodyAttributes * ( Speed + HDratio ) / HDratio

Map design can be of influence on movement and projectile movement. Most modifications are withing the Attributes. But there is always a fixed factor between the Body and Weapon calculation:
= Rf
Personally, I always use 1.5 here. But the average number in RTS is actually sqrt( 2 ).

%Damage is the mirror of %Armor:
Weapon = %Damage * Damage * %WeaponAttributes * ( Rf * Range + HDratio ) HDratio

Some designs can move AND attack at the same time:
Weapon = %Damage * Damage * %WeaponAttributes * ( Speed + Rf * Range + HDratio ) HDratio

Instead of simple Damage, you can also add in a SalvoFactor or DPS number in the Weapon formula above. However, the SalvoFactor is a sum of the moments that damage is dealt. And each moment has its own weight:
SalvoFactor = Sum of all DamageMoments
DamageMoment = (( HDratio / ( HDratio + 1 ) ) ^Moment ) / HDratio

Salvo's can contain smaller salvo's. With each smaller salvo having its own moment weight.
A simple example; if you pick a HDratio of 5 seconds. And the weapon shoots every second. With the first moment at exactly 1 second. The second moment at exactly 2 seconds, etc. The SalvoFactor will be 1. If you however start at 0 seconds immediately, your SalvoFactor will be 1.2. And to balance this, the damage should be 5/6th.
A HDratio of 5 is actually very short. The fun starts when you consider a higher cooldown. So you fire every 5 seconds after the first one being on 0 seconds? The SalvoFactor here will be 0.33438. In a sense, this design may deal roughly 3 times more damage in order to be balanced again.

In my boardgame, splash damage works different than in RTS games. In RTS games, there are several ways. But the main rule is that it is a yes/no mechanic, depending on the targets choices. This means that an explosion causing splash damage, will get an 50% extra weight for each additional possible target. In most RTS, smaller units can receive more damage this way. In rarer occasions, there is a maximum ammount of targets that actually get hit in the explosion. This is based on the fact that certain units absorb the damage, like in real life. This factor is often put in the %WeaponAttributes:
%WeaponAttributes = 1 + 0.5 * NumberOfPossibleTargets

If the game allows lower damage value's, further away from the centre of the explosion:
%WeaponAttributes = 1 + 0.5 * %Exploson * NumberOfPossibleTargets + 0.5 * %Exploson2 * NumberOfPossibleTargets2 + ...

[Fey]

I dunno, mate. maybe it's just cuz I'm a hands-on learner, but I've played KKND and this still sounds both overcomplicated and oversimplified at the same time... there are so many more factors that define a unit's strengths or weaknesses

there was one concept you brought up that's particularly comprehensible to me though 😛

14 hours ago, X3M said:

While the game has a lot of assymetry. The functional uses of the units are almost always, the same.

how I tried to balance the Summers' Solstice campaign was through units' roles, or functions as you put it, as opposed to on an individual basis. so even if we've got some new stuff here or there, they fall into certain categories and their strengths and weaknesses are representative of the category they belong to

like Shock Raiders, for instance. fast, high damage, low durability. excels over open terrain, swarming targets. bad in head-on frontal assault. very similar to Quads, Raiders, Flame Tanks, other stuff like that

even that example accounts for movement speed, effective weapon range, and other stuff like that too though. not just health and damage

a lot of theory falls apart in practice, I've found. you know what they say: in theory, there's no difference between theory and practice. in practice, there most certainly is a difference 😆

Edited 13 hours ago by Fey

[X3M]

True. I remember 3 moments where I had to adjust my calculations as well.

1. The formula all above in this topic has movement speed and attack range on the same side. That is wrong. Because 0 damage with infinite attack range would make the unit infinite expensive. And a lot of formula's on the internet do the same. Why was it there in the first place? Many thought that a longer attack range would add to the durability of an unit. While true, it is movement speed that truely adds to durability, simply by moving away.

2. Attack range on equal grounds as movement speed? That didn't stay too long. Many games showed that the attack range is taking place on a 2d field. While movement is 1d. What I mean is that if you have a terrain. And you want to reach your target. Using movement, would need you to move to every spot possible on the map in case of the most crowded map with impassable terrain. As for attack range, a simple direct trajectory is the case in 99.9% of the RTS games. This means that the average terrain creates a factor between the movement and attack range. You only notice the effect of long range weapons if the designers did it wrong. I noticed this in Red Alert 2 with the Prism Tanks, but also the sniper and the GI inside a IFV.

3. The size of units. The combat density is one that is done wrong more than other value's. And this includes a limit on units as well. I started to look into this a lot more when I was making Starcraft/Broodwar maps with an altered RPS. The Siege Tanks in there are actually super small and packed together. Especially when I applied my own rules. According to my calculations, the Siege Tanks would cost 800, while marines cost 100. First, I thought it was the cumulative versus squared rule. But I quickly could rule this out. I discovered that due to the size effects, eventually I had to ram up the cost to 1200. This is over 10 years ago by now.

As for theory and practise.
I never said that you make it with theory alone.
There are still aspects like:
- Player Skills
Slow/fast, dumb/smart, where do you place your balance?
- Resource managment
Testing on money maps, show the best results
- Visuals
How much can players see? Highest attack range, like in Warcraft 2? Or lowest tier attack range, like in Warzone2100?
What about fog of war?
- Special designs/Unique functions
Some units, you need only 1 or 2 of. Maybe 3. Or a dedicated squad. If you build too little or too much of them, they don't serve their function anymore.

Quote

like Shock Raiders, for instance. fast, high damage, low durability. excels over open terrain, swarming targets. bad in head-on frontal assault. very similar to Quads, Raiders, Flame Tanks, other stuff like that

Sounds like the Flame ATV from KKnD  But, the buggy/bike from the C&C games is similar.

Which are great example for the 3 practical balances regarding the Flame ATV:
A player needs to be smart. As for being fast, not sure, maybe?
Resource managment in the map has to be relatively low. The unit is cost efficient, but only at a small number. Spamming has no use due to short range attacks.
Visuals is not a key here.
1 can do the job. But if the enemy defends properly, Build like 4 to 6. No more. Or use 2 squads of 4. It depends on the map layout and defence structures. Their purpose? Find unquarded enemy structures. Preferably the resource managment of the enemy.

As for the Buggy/Bike:
A player needs to be fast.
Resource managment requires the player to have decent defences as well. where it matters. As for attacking, a nice mix of buggies and bikes is what matters.
Visuals is key here. There is a lot of FoW in C&C3. While in C&C td the vision for the player is simply small. You attack all over the place.
In C&C td, 6 bikes. Or you spam them. In C&C3 you spam them anyways. The buggies are there for being fodder and dealing with some infantry if needed. But also to create even more chaos for the enemy. You poke all over the place. Until you get the upper hand and snowball your way into the enemy.

In KKnD it is more of a tactical move, part of a grander strategy.
In C&C3, clearly it is RTS all the way with that tactic. The player simply needs to see for when it needs to switch tactics at the right time.

[Fey]

1200 resources in Starcraft for Siege Tanks? 💀 ik range is, like, the most powerful stat, but doesn't that just mean you gotta mess with how the economy works so the player's income can keep up with that kinda inflated price?

3 hours ago, X3M said:

Player Skills
Slow/fast, dumb/smart, where do you place your balance?

my father likes to play on easy mode just to blow stuff up, and aarmaageedoon says my missions are "too easy" even with multiple restarts 😆 can't please everybody

I'm not the worst at d2k, and my focus is on mission or campaign design - player versus AI - so my process is testing crap on hard mode / fastest game speed, then scaling it down for normal and easy modes. it matters for the maximum difficulty since players on hard are looking for a challenge. it should be both fair and engaging. normal and easy, those are where some theoretical scaling should suffice to nail the target difficulty as long as hard mode is done up nicely

the metric I look to primarily for determining if a mission is balanced how I want it is how long it takes me to complete it, including compared to its neighboring or counterpart missions. players will inevitably have a variety of experiences, but how closely in time it takes for me, knowing them in and out and optimizing for them, to complete them does a lot to illustrate the sum of whatever balance decisions I made for them already

that doesn't mean I don't consider how things might work out in a hypothetical multiplayer game though. I passed an MP compatible version of my stuff over to the boys, and some unexpected metagaming came out of it, like... walls and concrete were useable. lol

3 hours ago, X3M said:

Resource managment
Testing on money maps, show the best results

micro potential is a big deal in determining units' viability. take Blink micro for Stalkers in SC2 for example. you can have a unit with relatively weak stats, but with good player control, it dominates. over here in d2k, in ArkDebut, the Keravnos Laser Tank's shield system has revealed some interesting interactions already and suggests great micro potential. needs more testing. there are innumerable complex interactions in RTS, even in a simple one like d2k. makes theoretical balance pretty messy when the rubber hits the road

wym money maps? like, macro-heavy, macro missions? there are a lot of differences between how macro and micro missions need to be designed and how a player will use units just thanks to that fundamental difference. or do you mean how the resources are painted on macro missions? at some point we get more into mission design theory as opposed to unit balance theory 😛 different things

Edited 14 minutes ago by Fey