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Heroes Community > Heroes 3.5 - WoG and Beyond > Thread: Ballance quest. Unit power calculation.
Thread: Ballance quest. Unit power calculation.
Baronus
Baronus


Promising
Supreme Hero
posted September 11, 2020 10:09 AM
Edited by Baronus at 10:18, 11 Sep 2020.

Baronus

In this thread I want to give method which I use to calculate creatures power since years.
First public explanation. It works for all games.
How strong are units?! We can calculate something with precision not only with our subjective feelings opinions.
What are creature parametres in all games? Attack and defense.
Attack is the number of given damages and deffense are ,health points'.

So if you have unit wih 1dmg and 4 hp which another unit is the same power? 2 dmg 2 hp!
Because if they fight.
Round 1
1dmg vs 2 dmg
Hp now are 2 and 1
Round 2
1dmg vs 2 dmg
Hp now are 0 0
As in heroes IV both units are lost.
So thats the same power.
...
Nearly the same calculation is if we have one unit 4h1d vs 2 units 1h1d. Of course we have problem that unit 1h1d is dead in first rund but unit with 4 hp has now 2hp is still alive. But now we adopt that first unit give in second turn only 0.5 dmg because lost 50% power 4-2= 50% lost. So in two next turns all units are lost.
So units 4h1d= 2x1h1d units.
Now we can find how to calculate.
4x1=4
1x1x2=2
So its wrong calculation because should be the same.
We mus use square root.
V(4x1) =2
V(1x1) =1x2=2
Now is correct.
So in all games unit strenght is:
V(hp x dmg)
....

Now we must calculate heroes attack and deffense points.
Attack gives 5% more defence 2.5% fewer but 1att=1def. We have some truoubles with this ,maths'. We must calculate average 1.05/0.975 ~ 1.076923... next V (...)~1.037749.... So 1 point att or def gives more attack ~ 3.7749% . You must add it to dmg or hp. But not using + only rising ^.
It is in fact easy.
So eg pikeman 9 atdef 1.037749 ^ 9 = ~ 1.3958
x 10 hp x 2 dmg = 27.9
V27.9 =~5.283
Now we must add next value speed. Hard to calculate. To make it faster in will be no a big mistake to give about 2% so like att def.
So we can simply ad speed to att def.
So pikeman 13 atdefsp 1.037749 ^ 13= ~ 1.6188
x 10 hp x 2 dmg = 32.38
V32.38 =~5.69
At the end special skill. Charge negation. Its very weak skill only two units can charge. Units are +- 150 because 3 city towers and ballista are units too! But calvary is in our own faction! So its must be castle counter castle fight! Its maybe 1 for 150 fights. Charge gives 7-9 x 5% but not always all movement has 7-9 points so average 4 points x 5% is 20%. V1.2= 9.5% /150 = 1.0006 benefit :0))
It gives 5.694 final pikeman power.
We can compare with eg swordsman. Its is similiar unit.
Swman 27 atdefdmg 1.037749 ^ 27 = 2.72 x 35hp x 7.5 dmg = 713.87
V = 26.72 no skills.
5.694 vs 26.72
Cost of swman is 300 so pikeman should be 64 in fact 60. So we can see that cost these two units is good ballanced.
So maybe I stop here. Again time next questions.

...

edit

Square root symbol doest work I mus use V

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Hourglass
Hourglass


Famous Hero
posted September 11, 2020 09:04 PM

Interesting, althrought I belive your math skills are clearly better than mine.

However, I would want to note that system like this has it's limits, and can only give kinda raw idea of creature's power.

For example, there some thresholds when it comes to stats. Creature such as Silver Pegasi would be far less useless, if they only had 11 speed. Since they have 12, they're capable of reaching the other side of the battlefield, probably even blocking enemy shooters before they can shoot.

Then there are creatures such as Vampire Lords, which is unit all about their special ability. And how would you mathematicially track down the value of bone dragon's -1 morale ability, for example?

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Baronus
Baronus


Promising
Supreme Hero
posted September 12, 2020 04:07 PM

Yes ofcourse movenent value is how many rounds takes attack enemy.
So longest road is from corner to corner its 12 hexes to and 8 to corner. Heroes battlefield is 13/15.
20 is movement you can attact all. But you must fly! And be 1hex unit 2hex in heroes 1 often cant stop on 1 free hex behind walls ;0)))
So if you have like peasnt its 3/20 = 6.67 turns. Phoenix 1 round. Phoenix is 6.67 better in movement.
But of course unit value depends on situation. Eg dwarves in battle are to slow to often attack but behind city wall are very usefull!
Of course to calculate all theres no computer in the world! To much variables! But we can make very approximate calculation much much better than ,fellings' or hp calculation only!
Vampyre Ghost dragon calculation?! Slowy! First castle calculation. Im plannig looong thresad!
....
So Halberdier the same ability, 3 points and 25% dmg more. V this bonus = 18,193% better than pikmen.
It means 6.73
...
Archers.
Now we have big problem. Its compleyly unstabile unit! May give a lot of damages without casualities or completly blocked be destroyed. Hard to calculate. We must to establish.
He has 50% melee dmges So atack/2 but all shoot destroy enemy without counterattack. 50% dmg is too if unit is 10+ hexes far.
Shooting unit is better than only statistics. But how much?
How many shoots can give this type of unit before blocking?! I think maybe 1 for 50% 1 for 100% it gives about 35-40% enemy casualties so enemy has 62.5% power but next is melee fight and shooter has 50% dmg so V0.5 = 70.7% 70.7/62.5 = 13.12% bonus. But we must give more because noone use shooters for melee fights. Often is better doing nothing this unit. And in city defence its hard to block so shoots more. Enemy can be reduced 50% and more. So bonus is 40-50%.. Near average 13-45% = 30%. So all shooter is about 30% better than stats

Archer points V(2.5 x 10 x 1.037749^13)=6.351 * 1.3 = 8.257
Cbman 2 shoots and 2 speed more = 1.037749 two shoots give bonus x2 but calculated from 70.7 because melee penalty. (V0.5)
1.3 - 0.707 59.3 so bonus for cbman is 59.3 + 30 =89.3
6.351 *1.037749 * 1.893 = 12.477 so about 50% better than archer. Like NWC price 100/150 is accurate cost.

This way I will calculate all shooters.

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Baronus
Baronus


Promising
Supreme Hero
posted September 15, 2020 10:18 AM
Edited by Baronus at 12:33, 18 Sep 2020.

Baronus

Now we have griffins and interesting quest how to rate flying unit. Fly is very usefull in castle siege. On normal battle field its not very important. So we can rate it from maybe 1% on battlefield to maybe 20% in siege. I thik that average 10% is enough.
V (25*4.5*1.037749^22)=15.944*1.1= 17.538
Now interesting ability. Griffin can counteratack 2x but attack 1x so this is 3 times by turn. 50% bonus. But enemy must attack! It can not work if enemy attacks only one time. So bonus must be reduced about 1/2 . Sqare rot this is about 10%.
Royal griffin always counter attack but its more hard to use this ability. So I  give duble as griffin 20%.
Griffin 29.0
Royal griffin = griffin * V 1.037749^5= 17.491 x 1.2 = 20.99
Cost 200/240 as you see is accurate growth.
...
Swodsman as Iv calculated 26.72
Crusader has two attacks always it means 2 attacks 1 counterattack so is 3. It means 50% to dmg.
Crusader = swordsman * V (dmg more 1.1333 * 1.037749^3*1.5= 36.83
Cost 300/400 is good calculated. Relation between griffins and swordmans too.
...
Next part.

Calculation of monks is easy because its the same unit as archers.

V(11 x 30 x 1.037749^24)=28.338 * 1.3 = 36.839
Priest has no melee penalty so simply we can ad to 70.7 penalty 29.3 = 1.414% x 1.3 = 1.84% instead 1.3
V(11 x 30 x 1.037749^29)=30.958 * 1.84 = 56.963
As you see price 400/450 is failed! Sholud be 600 because priest is the same melee andnshooting unit and hard to eliminate this fighter! Cant be blocked because fighting normal! So best is fast upgrade.

Champion
Ability is charge 5% to attack for each point of movement. Movement is 1 to 7 or one 1 to 9. Average 4 and 5 so its 20 and 25% bonus to img
Cavalier V(100 x 20 x 1.037749^37*1.2)=97.233
ChampionV(100 x 22.5 x 1.037749^41*1.25)=113.355
So price 1000/1200 is nearly accurate.

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