# Balancing Unit Levels

#### rulerofiron99

Level 25
So I'm making a map with lots of different unit levels over a potentially long game, and in the interest of balance, I like to be able to tell exactly how strong a group of creeps is using a spreadsheet.

Ideally I'd like to have a level 2 be as strong as two level 1s, a level 3 be as strong as two level 2s, etc.
This way the gold reward can also be accurate: (2^(level-1))*base

Some googling on the matter suggested that a unit's value, or "impact" as this article called it, can be defined as
impact = damage output * survivability

In terms of this map, that's a simple DPS * Effective HP (hp * armour bonus * abilities e.g. evasion)

So using this formula, a Footman with 840 HP and unaltered damage and armour is exactly twice as good as a regular footman with 420 HP.
IF the stronger footman was to fight two regular footman in sequence, he should die precisely as he kills the second footman, which would mean that the above formula is true.

HOWEVER

Units don't just line up to die one by one. Battles are dynamic things (not to go into things like range, movement speed and collision size), so in reality, in the above example of the two footman types, the stronger footman will die precisely when he kills the first of the two footmen.
So the impact = dps * survivability equation does not hold true in this form and under these conditions.

Determining each unit's "true" level empirically would be a nightmare, so I'm asking if anyone knows of a more accurate equation?

Basically I'm looking for the fragmentation equation, if anyone's heard of that (read it in a blogpost by a former Blizzard dev, failed to bookmark it, and can't find it)

Thanks

EDIT: Did some more testing using the impact = dps * ehp equation
Unit A: 10 dps * 100 hp = 1000 impact
vs Unit B: 10 dps * 200 hp = 2000 impact
Result: Unit A better (lose 1/2 units)

Unit A: 10 dps * 100 hp = 1000 impact
vs Unit B: 15 dps * 200 hp = 3000 impact
Result: Units equal (Unit A won with one attack worth of hp remaining)

Unit A: 10 dps * 100 hp = 1000 impact
vs Unit B: 10 dps * 300 hp = 3000 impact
Result: Units equal (Unit B won with one attack worth of hp remaining)

So in this test, for a unit to be exactly as strong as two units of the previous level, its impact has to be 3 times that of the lower level units.

#### edo494

Level 23
just a tip
maybe it is better to calculate how much hits unit can survive then multiplying dps with its life
I may try to do some formulas but I dont have time right now

#### rulerofiron99

Level 25
How many hits from which unit type? Using its own damage as a "hit" counter wouldn't suit my needs, since I have units balanced to be heavy ranged hitters, and other units designed to be sturdy front-line tanks.

Or do you mean like a standard unit for each level?

#### defskull

Level 33
So basically you want to create units in your map, to be like in base 2 order ?
(1, 2, 4, 8, 16)
1 * 2 = 2
2 * 2 = 4
2 * 3 = 8

Assume that Unit A/B has 100 HP (attack speed is the same - base on a same unit, just copy paste in Object Editor).

But Unit A has 10 Damage while Unit B has 20 Damage.

When you want to create Unit C, its Damage would be... ? Yes, 40 (20 * 20).

But first you gotta define as in what aspect does "Unit C > Unit B > UnitA".

Like;
- Damage
- Attack Speed
- Armor
- Movement Speed (this does not affect "battle" in Warcraft III, but still..)
- HP
- MP
- many more

You gotta define those first (in what aspect, they are "improved" compared to the unit's level before them).
But the base technique would be base 2.

Since if you compare Unit A (1) with Unit B/C/D
- It would take 2 Unit A to be the "same" level as Unit B.
- It would take 4 Unit A to be the "same" level as Unit C.
- It would take 8 Unit A to be the "same" level as Unit D.

#### rulerofiron99

Level 25
I'd like a single number to describe it, if at all possible.

For player units, I evaluate their worth by comparing DPS and EHP separately and comparing it with similar units - ie comparing tanks with tanks and archers with archers.

#### edo494

Level 23
well, lets say unit has 100 ehp and 500 dps but like 10 seconds attack speed and is going to fight unit with 50 dps 1 second attack speed, 100 ehp and 5% evasion, if the second unit evades first attack it will rape the first unit until it gets chance to hit him second time but the second unit has ehp*dps 10 times lower theb the first unit

#### rulerofiron99

Level 25
well, lets say unit has 100 ehp and 500 dps but like 10 seconds attack speed and is going to fight unit with 50 dps 1 second attack speed, 100 ehp and 5% evasion, if the second unit evades first attack it will rape the first unit until it gets chance to hit him second time but the second unit has ehp*dps 10 times lower theb the first unit

There won't be any outliers like that.

The map in question is Region (link in my sig), your armies cannot be micro='d. It's a management game about cold, hard stats, unit counters and formations.

I try to make every unit balanced differently and accurately to its gold value. Legion TD did balance the lazy way - each unit's DPS is exactly 10% of its hit points.

#### Elfansoer

Level 4
So using this formula, a Footman with 840 HP and unaltered damage and armour is exactly twice as good as a regular footman with 420 HP.
IF the stronger footman was to fight two regular footman in sequence, he should die precisely as he kills the second footman, which would mean that the above formula is true.

HOWEVER

Units don't just line up to die one by one. Battles are dynamic things (not to go into things like range, movement speed and collision size), so in reality, in the above example of the two footman types, the stronger footman will die precisely when he kills the first of the two footmen.

Personally I think about that, is they're depending on what situations. One strong footman (S) vs 2 regular footman (R)? There's 2 answer.

1. If they're fight in sequences, it's 50-50 possibilities that S or R will win, since he has twice of maxlife, with the same dps.
(So, It's like S=[2hp, 1atk] vs. R=[2hp, 1 atk,], because 2 R's life equal to 1 S's, meanwhile their attacks remains same)

2. If they're fight on parallel, it'll OBVIOUSLY that R will win, because the R is attacking twice damage
(And it's like S=[2hp, 1 atk] vs. R=[2hp, 2 atk], because 2 R's life equal to 1 S's, and 2 R's attack is double than S's)

So, I think Unit's value:
//Impact = DPS*Life//
Is not totally false, and not totally true, too.
(When it's one-on-one, yeah, it's true. when it's one-on-group? Who knows?)

And for myself, a unit's value is depends on its "Durability", which I defined as how much he can take down enemies on how much enemies's averagelife and averagedps.
(Durability = n*[L*D])
n = total enemies he take at once
L = average life of enemies he take at once
D = average dps of enemies he take at once

Well, that's just my opinion, and feel free to disagree with it... I'm just a newbie...
(Don't be mad at me, ruleroffire!!!)

*EDIT
On S vs. 2R, which S's life is 3 times R's, it would be R's wins:
([3hp*1atk] vs [2hp*2atk])

And The "Durability" isn't counted with abilities, armor, etc. Just pure strength. Maybe you can add it.

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#### rulerofiron99

Level 25
Thanks for the input.

I don't quite understand what you mean by "total enemies he can take at once", or the values for L and D.

Personally I think about that, is they're depending on what situations. One strong footman (S) vs 2 regular footman (R)? There's 2 answer.

In this map, two players that fight both spawn their entire armies at the start of the battle, and the battle ends when one army is destroyed. So generally it's situation 2, where they fight together. That is what my focus is.

#### Dr Super Good

Spell Reviewer
Level 63
Movement Speed (this does not affect "battle" in Warcraft III, but still..)
This is a common mistake beginners make. If I have ranged units against melee units and my ranged units are faster than your melee units I will win 100% of the time with 0 losses.

Even if I am not faster, as long as I am ranged I can lower your attack speed by timing my shots to match my movement pattern while you will have to stop, attack and catch up each time.

Why the above gives you the values it does...
2 * (Unit A: 10 dps * 100 hp = 1000 impact)
1 * (Unit B: 15 dps * 200 hp = 3000 impact)

Except, the problem is that if there are 2 Unit As... That translates to a unit with the following characteristics...
Unit A: 20 dps * 200 hp = 4000 impact : both units alive
Unit A: 10 dps * 100 hp = 1000 impact : one unit alive

#### Elfansoer

Level 4
Well, I mean that, when 3 enemy's footman [1hp, 1atk] and 1 enemy's knight [2hp, 1atk] attack a UNIT together:
n = 4, The UNIT is fighting with 4 enemies at once.
L = 5/4hp, it's the average max life of all enemies the UNIT take at once (3 Footman 1 Knight).
D = 1 dps, it's the average dps of all enemies the UNIT take at once (3 Footman 1 Knight).

(that's what I mean)...

And Dr Super Good, you're true, but i think this is about unit(s) vs unit(s), without our control...
(they're fight AI'ly... I mean, it's their pure strength, without strategy. It's the strategy that overcomes unit's value)

Plus, if it's melee vs ranged, i think the variable that change in "durability" is the dps's, that the melee must approach the ranged attacks... assuming that the ranger doesn't have min. range, so that she will stay on her place even if attacked, like the "archer" do.
(the melee's dps will decrease, as the ranged one attacked all times meanwhile the melee must approach then attack at the defined dps)

#### rulerofiron99

Level 25
Ah, so you're balancing a group of units together. I'll see if I can somehow incorporate that into my balancing spreadsheet.

#### defskull

Level 33
This is a common mistake beginners make. If I have ranged units against melee units and my ranged units are faster than your melee units I will win 100% of the time with 0 losses.

Even if I am not faster, as long as I am ranged I can lower your attack speed by timing my shots to match my movement pattern while you will have to stop, attack and catch up each time.

And Dr Super Good, you're true, but i think this is about unit(s) vs unit(s), without our control...
(they're fight AI'ly... I mean, it's their pure strength, without strategy. It's the strategy that overcomes unit's value)

Yeah, if you play DotA or (1-unit control per Player map), you can give this statement.

Micro-ing units is different than what you stated.
Micro-ing in a war (war usually takes 50++ units) is like using abilities, checking HP, etc, not order your Range Unit to attack-move, trust me you don't have the time to do this, it's better for you to focus on Priests healing abilities, Sorcerer casting disables, Heroes escaping from being trapped.

Movement Speed (this does not affect "battle" in Warcraft III, but still..)
That's why I quote the word battle, it means "war", not 5 Range Unit VS 5 Melee Unit.

#### rulerofiron99

Level 25
Ironically, it's in this map that units overcoming their expected values is quite visible. There's a spell you can cast during battle to take direct control of one of your units, so you can take control of an artillery unit to maximise area effect of your attacks, or take control of a fast knight to flank around and kill your opponent's archers.

#### Elfansoer

Level 4
Yeah, that's my very basic thought....
(actually, he doesn't know about what's his basics at all...)

That's the use of friendship: by together, we can take down all [individual units]!!!
(Can I have rep please?) [hey, that's not polite! only he has the right to give me or not! show some respect! Sorry about him, rulerofiron...]

Well, that's a unit's pure level, isn't it? You can also define it's level "Qualitatively" by adjusting their abilities...
(Such as the ultimate ability on Wc3's heroes have a lot more affects than her standard spell. and if a unit have much ultimate abilities, her level is greater, isn't it?)

And defskull, you're very right. that's what we called "Strategy".

Just want to remembering, that rulerofiron just wanna ask about defining levels for units, so that we can know how strong her is in battle...

#### rulerofiron99

Level 25
But you have so little to show at the moment...

#### claptomanic

Level 9
im really intrested in the formula existing at the end of all these thoughts ^^

#### rulerofiron99

Level 25
I'll add a tutorial when I have the right formula! (also to include extensive notes on range, movement speed, disables, groups, etc)

The only tutorial relating to balance here is a Hero Balance tutorial, which merely suggests the obvious things: hero categories (tank/support/carry), and that you shouldn't make things OP.

Some more mathematics would do this forum well.

Here's a good essay on the topic, although it doesn't help my specific problem.

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#### Elfansoer

Level 4
Have you read my updated post before this?

And just to remembering you that not every value can be defined only by Quantitative Point, but it also has Qualitative Point, am I wrong?

As for me, the "Durability" formula is the quantitative thing, and the level of abilities she has is qualitative thing.
(Just example. qual for Qualitative, quan for quantitative.
For tanker, he has little ability so his qual.point is E. but he has great point of Durability, ex. his quan.point is 13 point.
The support has good ability, his qual.point is B, and he has average Durability, ex. 8 point.
Then you can "average" them by converting the qual into quan...
ex. A is for "reduce quan.point by 10%",
B is for "reduce quan.point by 20%",
C is for "reduce quan.point by 30%"
or something like that...)

#### rulerofiron99

Level 25
Using your durability formula, I'm not getting that the units are equal. Unless of course I'm implementing it wrong in excel.

Forgive me, but I really struggle to understand your english.

I understand what you mean by Qualitative, and I already have a way to implement that into the equation, but I first want to get it right without abilities - just reducing each unit to a single number.

#### Elfansoer

Level 4
Um.. Forgive me too, rulerofiron, if my english was that bad...
(yeah, I just think his english is bad...)

Or, you can use some units as a "global measurement"...
(he means the standarized unit that is used to define the level, just like the mass of platina in France to define the 1kg of weight...)

For example in my Durability formula, let's just simplify it by
"How much footman is needed to take down the unit"....
If 3 footmans can kill unit1 [purely, without our help], and 5 footmans can kill unit2 [if using 3 footmans, unit2 wins], then unit2 is stronger than unit1, right?

(It's just like in physics! If you want to define how strong a type of wall can stand, you can measure it by calculating how much the minimum force we need to destroy the wall.

Also, the defining of an object's momentum is "How difficult an object to be stopped". If an object's momentum is high, it's hard to be stopped.)

#### Dr Super Good

Spell Reviewer
Level 63
All these formulas do not help ballance units. In the end it comes down to experimentation.

Create 2N Unit A and N Unit B and have them fight. Change attributes until they are approximatly equal. Remember to micro them where appropiate.

#### rulerofiron99

Level 25
All these formulas do not help ballance units. In the end it comes down to experimentation.

Create 2N Unit A and N Unit B and have them fight. Change attributes until they are approximatly equal. Remember to micro them where appropiate.

Thanks for repeating an idea that has been stated earlier in the thread with more relevance and less troll.

Or, you can use some units as a "global measurement"...
(he means the standarized unit that is used to define the level, just like the mass of platina in France to define the 1kg of weight...)

I think that might just be the best way Thanks

#### Elfansoer

Level 4
You're welcome...

(Don't forget to credit me! and can I have another rep?)
[I've told you, me. Please don't say that!!]

#### HappyTauren

Level 26
I am of different school of thought - I think balancing shouldn't be done so technically - I think it kind of sterilizes the gameplay in a way.

See, numbers are a great way to tell how 'strong' an unit is in wc3, but calculating everyting like this is ridiculos, I think it is actually better to play the game, and if you find an unit too strong/too weak, balance it. Of course, you could start the balance by calculating everything and edit it all later, I am just saying that doing this sort of makes it all the same. (you level up - fight your level monsters - by your calculations the battle's difficulty only changes by the number, not by the monsters you fight). Not to mention bash, evasion, critical strike, certain spells that can turn the tide of battle, etc. If you want to make an enjoyable map, it is impossible to balance it with numbers, you must balance it with gameplay. I know I am already saying what has already been said, but there's a reason to it.

It is also good to mention that attack's damage points also plays a giant role, as well as the motion range.

#### rulerofiron99

Level 25
I am of different school of thought - I think balancing shouldn't be done so technically - I think it kind of sterilizes the gameplay in a way.

See, numbers are a great way to tell how 'strong' an unit is in wc3, but calculating everyting like this is ridiculos, I think it is actually better to play the game, and if you find an unit too strong/too weak, balance it. Of course, you could start the balance by calculating everything and edit it all later, I am just saying that doing this sort of makes it all the same. (you level up - fight your level monsters - by your calculations the battle's difficulty only changes by the number, not by the monsters you fight). Not to mention bash, evasion, critical strike, certain spells that can turn the tide of battle, etc. If you want to make an enjoyable map, it is impossible to balance it with numbers, you must balance it with gameplay.

You make a very strong point, but I believe 90% of the work can and should be done technically.

Critical Strike and Evasion can easily be factored into DPS / EHP. Bash can be factored into EHP - how many seconds, on average, the average opponent won't be attacking you. Cleave and splash damage can also be factored in - how many units, on average will be damaged by the unit.

The main reason I need to specifically calculate each creep's value, is because the map uses a random creep/level generator, so in the interest of a fun map, I'm making it balanced.

So far I've been quite successful (using the impact formula), but this makes it difficult when I'm adding higher and higher level creeps, especially to determine how much gold it should drop.

So far I have 9 levels of creeps, each level has at least 6 creeps. Balancing each type, or each specific group against each other empirically is a nightmare.

#### HappyTauren

Level 26
Hmm, so we can agree that it depends on the map. Since creeps on my map are preplaced and they all have (sort of) a function, it means that they are doing exactly as they should be doing - which means that I do not have to use technical balancing. So, we're both right in a way, what you are doing could indeed work better for your map. Though, I actually like when there are certain overpowered units in the game - it means you need real experience in gameplay in order to know when to counter those units and when to fight them. This is a great method of rewarding the player for actually knowing what he is up against.

#### rulerofiron99

Level 25
Overpowered units can break the game in my case.

When you reach a certain level, you are expected to have between X and Y gold, and therefore army value. And each level typically requires Z value to defeat, so if an imbalanced unit spawns for that level, the level won't be balanced to the player's expected army value.

#### gorillabull

Level 17
do any of your units have any abilities anyway it does not matter. you dont need any formulas for balancing units it is much simpler all you have to do is make sure that each unit is capable of doing an exact amount of damage as any of the other units then when that is done just create different ways units deal damage. also remember that all units have strenghts an weaknesses so while your unit may deal more damage one way it will fail somewhere else for example a demolisher vs a building and a demolisher vs a tauren

#### Dr Super Good

Spell Reviewer
Level 63
you dont need any formulas for balancing units it is much simpler all you have to do is make sure that each unit is capable of doing an exact amount of damage as any of the other units then when that is done just create different ways units deal damage.
Which is where the problem starts. Doubling the power of a melee unit has certain reprecutions if used tacticly. If the strong units were used in a pinccer manuvour to surround the weaker units virtually none of the stronger units will be lost. Equally well if the same is done with the weaker units they will also win. Reducing the number of units by half or even a quarter might mean a surround manuvour is no longer possible this even if the unit wins 50% of the time anone vs many weaker units, it might lose 100% of the time if the weaker units are deployed tactically.

I have proved this in the past. Back before Blizzard had Warden turned on for Custom Games in WC3 I used to use map hack on various custom maps such as LoaPs or RPGs. In the one LoaP I played I was the police against a Maffia player where units were imballanced. He had units that made short work of me and he could retreat his heroes with no losses if his army did get worn down. As I had map hack on I knew his movements and decided to surround him from all directions, using my superiour numbers to the full so as many units as possible were able to attack at a time. Suffice it to say he lost all his heroes, all his army and I only lost a small part of my army despite his units being supperiour to mine considerably.

also remember that all units have strenghts an weaknesses so while your unit may deal more damage one way it will fail somewhere else for example a demolisher vs a building and a demolisher vs a tauren
Only if he goes for rock/paper/scissors type weakness system.

#### rulerofiron99

Level 25

1. The units will not be micro'd.
2. There are many levels of units.
3. I don't want lame balance as in Legion TD. (every unit has dps equal to 10% of hp)

I am using a rock-paper-scissors type system.

#### gorillabull

Level 17
Which is where the problem starts. Doubling the power of a melee unit has certain reprecutions if used tacticly. If the strong units were used in a pinccer manuvour to surround the weaker units virtually none of the stronger units will be lost. Equally well if the same is done with the w...

yea thats true it all depends on many factors the best tactic is to make as many units as you can deal damage, this is why ranged units can deal more total damage for a battle than melle only of course if both the melle and ranged units have the same damage type and amount .. there are just too many factors to start with and when you throw in a few custom spells it gets out of hand you will want not to use formulas especially if you are the only one balancing the map

#### rulerofiron99

Level 25
The formula has been working very well up until now, I'm just looking for a more accurate one.

#### Elfansoer

Level 4
OH, I think there's some connection! I remember what you said that Impact is equal to Damage Output * Survivability. Then, do you think that my "Durability" formula is to define the unit's survivability? I think the two words have similar meanings...
(So, basically the unit's Impact is determined by how much damage he can give out to enemies AND how long the unit can survive from the enemies, which is determined by my formula....
Or sort of like that...)

And if you're using rock/paper/scissor system, do they affects the unit greatly, or just only on damaging?

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