Ballance in Warcraft 3 maps

[Thunder_Lord]

I have been spending the past week or 2 on trying to develop a formula that i can plug in different stats for any unit and it could give me an effective "combat rating"...units with the same combat rating would be equally effective in fighting...for example, putting range, ability and all other factors aside, A unit with 100 hp, 0 armor, and dealt 10 dps would have the same "combat rating" as a unit with 200 hp, 0 armor and 5 dps, or 50 hit points and 20 dps.
One of the maps i hope to use this formula in is a footmen frenzy map. I came up with these 2 formulas to calculate a units "Value Hp" and "Dps"
B/(1-((A*.06)/((A*.06)/((A*.06)+1)))=C
Where B= Hit points, A= Armor and C= "Value HP" or the number of points a unit can take before he dies (factoring in armor)
D/E=F
D is damage (accounting for base damage, attack dice and sides per die, the average damage per attack) E is attack Rate and F is Damage per Second (DPS)
So using the value C and F i need a formula that will Give a value "G"a combat rating that rates units proportionally on how powerful they are in combat. For example A unit where C=1000 and F=100
would have the value of G be twice as much as a unit where C=1000 and F=50...if that makes any sense...
I made an attempt to come up with such a formula. I made a formula for my footmen frenzy map, for this formula i came up with a "Base Unit" essentially it was a unit that i used as a reference point for all my other units. the unit i chose was the "Brutal Knight" witch was one of the final tier type (the other two are Head hunters witch should be half as powerful as a brutal knight and spawn twice as fast, and gladiators witch spawn half as fast and are 2 times as powerful)
The Brutal Knight has 11 armor 2150 hit points and deals 106-116 damage at a rate of 1.45 So after plugging in these values A=11 B=2150 D=111 ((106+116) divided by 2) E=1.45 these values gave me C=3569 and F=76.552 so the formula i came up with was
(F/76.552)*(C/3569)=G, so the value of a brutal knight (by this formula) is 1, this provides a Base for my formula, I thought this formula would be fine, but i have ran in to a flaw with it. When i plugged in C (5146) and F (166.437) of the Gladiator, the G i got was 3.1348. this value is way too much, this value suggests that it would take about 3 brutal knights (3569 hp and 76 dps) to kill 1 Gladiator (5146 hp and 166 dps) this formula did work however when i doubled or halved the DPS or HP (one or the other) it doubled/halved the unit combat rating but the formula needs to be able to compare any 2 units.

So if you know what im asking and can help me i would appreciate it a lot, i don't know if im just spewing gibberish or if you can actually make some sense out of this, anyway, any help with this balancing formula would be much appreciated

 

[Shura]

Are you saying that with your numbers, the G value of a gladiator should be double the G value of a Brutal Knight? Of course a gladiator is going to be about 3 times as strong as a Brutal Knight. You're more than doubling their DPS as well as increasing their Hit Points.
The formula looks like it is working just fine, it seems like it will compare units accurately.

 

[Thunder_Lord]

I'm not sayin the g value of a gladiator would be exactly 2 times, but as it stands. If a galdiaors valuse is 3 x that of a brutal knight it should take 3 knights to kill one gladiator. If you do the math the brutal knights c value • 3 and f value •3 is alot more than the c and f values of a single gladiator. What I need is a formula that uses the variables c and e to give me g. Where g is Proportional to a units combat strength. For example (putting aside the effects of focus fire of one big unit bs smaller ones) it wod take 2 units with a G value of .5 to kill one unit with a g value of 1. Or 3 units with a G value of 2 to kill a unit with a g value of 6.
If that makes anysence

 

[Shura]

>putting aside the effects of focus fire of one big unit bs smaller ones

Then your formula would hold true. If by ignoring the effects of smaller units "ganging up" on the larger units, you assume that they can only fight one on one, then a knight would only be able to take out a third of a gladiators hit points.
The Knight has 3569 hp. The gladiator has 166 dps. If you do 3569/166 you get 21.5 hits to kill the knight. That would mean the knight gets 21.5 hits off with 76 dps. That would deal 21.5*76 which is 1634, which is about one third of the gladiators health.

Unless I'm misunderstanding something here.

 

[Thunder_Lord]

Sorry i guess I worded that wrong wheni say putting the effects of units ganging up aside I ment that all 3 knights are attacking at the same time only... The effects of one knight would die before the others for example unit X has 200 hp and 10 dps. Unit x is getting attacked by unit Y. Unit y has 100 hp and deals 5 dps. If the damage of unit x was evenly split between both of unit Ys then the battle would tie. But that is not how it works unit x would attack unit one of the unit Ys after 10 seconds oneof the unit Ys would die so it stops doing dps. The next 10 seconds unit x is only taking damage from the second unit y (5dps) so 10 seconds later the second unit Y dies and unit X is left with 50 hp

 

[Shura]

Your formula will only work when comparing a unit fighting one on one with other units. In order to compare how a unit would fight against multiple other units, you would need to include the number of units in your equation. Something like this:
(B/E)/(A*E) + (B/E)/(A*(E-1)) + (B/E)/(A*(E-2)) + ... + (B/E)/(A*1)=(D*E)/C
where:
A=Unit 1 DPS
B=Unit 2 HP
C=Unit 2 DPS
D=Unit 1 HP
E=Number of Unit 1

This way, you can compare 2 units while including the number of the weaker unit.

If any of that was confusing, I could try to explain it better.

 

[Thunder_Lord]

Okay after working on it for awhile I found that I take value G from my older formula (g being the number of units, with I G value of 1, a unit can kill.) and a square root the old G value and I get a new value H, H is the number of units with a G (or H) value of one a unit can kill when fighting them at the same time (assumeung all dps is evenly sores between targets)