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Heroes Community > Heroes 6 - The New Beginning > Thread: H6 - Stats and calculations
Thread: H6 - Stats and calculations [ This thread is 5 pages long: 1 2 3 (4) 5 ]
Polaris
Polaris


Promising
Known Hero
posted October 10, 2011 12:51 AM

I think it is better to look at it as each additional point of attack/defense now improves your result by 2.5% (including all the bonuses up to that point), it's a "2.5% with interest" if you will. The same applies whether you are ahead or behind in the stat balance.

Whereas the previous formulas were linear so very large differences started to matter less and less just how large the difference is, now every incremental point has a uniform 2.5% value relative to the previous point. From this perspective it's not really all that complex, but it certainly has the potential to change the game more.

I think the best results will be for players who focus exclusively on one stat or the other- a mix of attributes appears less favorable now because two small exponents are inferior to one large exponent. If you have 10A and 0D it should always be better to improve A from that point and never raise D (mathematically, ignoring strategy). If the situation was reversed you should always raise D. The exponential benefit is greater by focusing exclusively on one attribute.

Mathematically:
(1.025^(X+Y) + 1) > (1.025^X + 1.025^Y)

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DoubleDeck
DoubleDeck


Promising
Legendary Hero
Look into my eyes...
posted October 10, 2011 08:12 AM
Edited by DoubleDeck at 08:14, 10 Oct 2011.

Quote:
No it's not. They are both equally exponential.


@Warmonger -> I disagree.

The hero's attack stat to damage ratio increases MORE with each increase in attack stat.

The hero's defense stat to damage absorption increases LESS with each increase in defense stat.

That's why you can never go up to 100% damage reduction, it never gets to 100%!

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alcibiades
alcibiades

Hero of Order
Really, Ubisoft?
posted October 10, 2011 09:52 AM

DoubleDeck > Although it should be added that what you say is only true if your Attack is greather than the Defence of the opponent and you're performing the attack. If situation is the other way around - you're being attacked by someone with greater Attack than your Defence - you'll want to boost your defence, as that will eat a larger part of his Attack bonus. So the only real case you can generalise is when facing neutrals, who will generally have Attack and Defence lower than yours.
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solariusyang
solariusyang

Tavern Dweller
posted October 10, 2011 09:39 PM

if we purely discuss on 2 units beating each other, and disregard couterstrike 3 which lets you retaliate before enemy attack, you lose the moment the enemy strikes you first.

Once the enemy struck the first blow, you will have less units to strike back and the battle goes downhill. Besides, there are 2 more reasons contribute to this result:
first, as i've been stated in the very first post in this thread, the system is slightly attack biased. boost your defense to the same value as your attacker's attack won't cancel out his advantage. the enemy do more damage when he has 30 atk and you have 30 defense than when both sides have 10. You will need more defense than the enemy's attack to even the odds.
Second, defense attribute is no more easier to aquire than attack. Both attributes are weighted the same in charactor growth and skills, and artifacts are also not defense favored.

The conclusion is: better get counterstrike 3 instead of boost your defense in vain when the enemy has higher initiative or longer reach. Consuming the same amount of resource, you won't be able to turn the tide of battle by dumping defense

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alcibiades
alcibiades

Hero of Order
Really, Ubisoft?
posted October 11, 2011 02:03 AM

Quote:
boost your defense to the same value as your attacker's attack won't cancel out his advantage. the enemy do more damage when he has 30 atk and you have 30 defense than when both sides have 10.
Is this actually true? It seems to be in contradiction to the formulas listed previously in this topic, which say that whenever ATK = DEF, they cancel each other out.
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Elvin
Elvin

Hero of Order
Stillness within Movement
posted October 11, 2011 02:07 AM
Edited by Elvin at 02:09, 11 Oct 2011.

Not so. Remember this? At lvl 20 that's 57.7% damage boost versus 37% reduction.

Quote:
Some calculations I had made some time back.



Creature Might Damage (might based attack)=Creature Default Damage*(1+Hero Might Power/100)^2.5 (min-max)

Creature Might Damage with 1, 5, 10, 15, 20 attack. The below are the modifier by which you multiply the creature range:

1: (1 + 0.01)^2.5= 1.025 ~ 2.5% extra damage
5: (1 + 0.05)^2.5= 1.129 ~ 12.9%
10: 1.1^2.5= 1.269 ~ 26.9%
15: 1.15^2.5= 1.418 ~ 41.8%
20: 1.2^2.5= 1.577 ~ 57.7%



Creature Might Resistance=1-1/(1+Creature Might Defense/100)^2.5*100 [%]

Let's assume the unit has 0 defense

1: 1-1/1.01^2.5 = 1-1/1.025 = 1-0.97% = 3%
5: 1-1/1.05^2.5 = 1-1/1.13 = 1-0.88 = 12%
10: 1-1/1.1^2.5 = 1-1/1.27 = 1-0.79 = 21%
15: 1-1/1.15^2.5 = 1-1/1.418 = 1-0.7 = 30%
20: 1-1/1.2^2.5 = 1-1/1.58 = 1-0.63 = 37%

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alcibiades
alcibiades

Hero of Order
Really, Ubisoft?
posted October 11, 2011 03:16 AM

Quote:
Not so. Remember this? At lvl 20 that's 57.7% damage boost versus 37% reduction.
Yes, which will negate each other, because performed damage is:

100 %    x   1,577   x   0,63    =   99 %   ~   100 %
Original    Attack      Defence
damage       bonus     reduction


The diference is probably caused by rounding in numbers.
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DoubleDeck
DoubleDeck


Promising
Legendary Hero
Look into my eyes...
posted October 11, 2011 03:52 AM

@Alcibiades -> I like what you did here but I think it's not fully correct as this is how H5 worked with Attack and Defense being part of the same formula for Damage output.

H5 damage =
If A > D: Stack size x Damage range x [ 1 + 0.05 x (A - D) ]
If D < A: Stack size x Damage range / [ 1 + 0.05 x (D - A) ]

In H6, the damage =
Stack size x Damage range x (1 + Hero might power / 100)^2.5

The defense reduction only happens after this damage of the attacker is worked out (i.e it's not part of the damage output formula).

So your formula above comparing 57% attack bonus to 37% defense reduction would only work if the random damage range was at a minimum. If the damage range was average or maximum, then the bonus would be alot higher for the defense reduction to absorb.

Not sure if this is correct, I am just trying to work out things in my own little brain




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Gweret
Gweret


Adventuring Hero
posted October 11, 2011 04:12 AM
Edited by Gweret at 04:13, 11 Oct 2011.

According to fan manual page 140 alciblades is correct.
Elving and solariusyang forgot that these calculated bonuses are used in multiplications of each other to get final "boost", not subtraction.

final damage boost is = attacker damage boost x defender damage resistance.

In other words damage and defense boost if equal negates each other.

Every thing is explained in fan manual.


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Vicheron
Vicheron


Known Hero
posted October 11, 2011 04:32 AM

They really should have kept the traditional attack, defense, spell power, and knowledge for heroes.

Make it so that creatures' might damage and defense gains bonus from a hero's attack and defense like in previous Heroes but make magic damage gain 50% bonus from a hero's attack and 50% bonus from a hero's spell power, and magic defense gain 50% bonus from a hero's defense and 50% bonus from a hero's knowledge.

That way you still keep the same dynamic of magic heroes making magic based creatures more powerful and might heroes making might based creatures more powerful but at the same time make spells, especially offensive spells, more useful.

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solariusyang
solariusyang

Tavern Dweller
posted October 11, 2011 04:58 AM
Edited by solariusyang at 05:01, 11 Oct 2011.

I haven't forgotten it's multiplying. The conclusion of defense can¡¯t cancel out attack comes from the fact that hero¡¯s attack alone can affect attack modifier while hero¡¯s defense + creature¡¯s defense (which is static, positive figure) affect defense modifier.

In the above example, 20 point of attack actually means 20 point of HERO attack while 20 point of defense means creature¡¯s defense + HERO defense got a total of 20. It¡¯s not a good example to discuss balance, because in this case attacking hero use up more resource than defending hero. It could be better artifact or higher level that contributes to the higher attribute score.
A better example would be this:
When attacking on a unit with defense 40 (archangel)

When attacking hero has 0 attack and defending hero has 0 defense, the affecting variable is 0 (hero attack) and 40 (40 creature defense + 0 hero defense)
The attack modifier is 1 and defense modifier is 0.431, so final result is damage reduced to 43.1%

When attacking hero has 10 attack and defending hero has 10 defense, the affecting variable is 10 (hero attack) and 50 (40 creature defense + 10 hero defense)
The attack modifier is 1.27 and defense modifier is 0.363, so final result is damage reduced to 46.1%. we can see from here where the trend goes.

When attacking hero has 40 attack and defending hero has 40 defense (top lvl hero + epic gear), the affecting variable is 40 (hero attack) and 80 (40 creature defense + 40 hero defense)
The attack modifier is 2.32 and defense modifier is 0.23, so final result is damage reduced to 53.3%

53.3% divide by 43.1 equals 1.24, which means even if the defending hero can always keep up with the growth and gear of attacking hero, the damage his angel suffers increases by 25% as game progresses.

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forest001
forest001


Known Hero
posted October 11, 2011 05:32 AM

@solarius: read alcis post again... it's that simple

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Gweret
Gweret


Adventuring Hero
posted October 11, 2011 05:57 AM
Edited by Gweret at 05:59, 11 Oct 2011.

@solariusyang

if hero Might Power == defense, then
final dmg boost = (1+Hero Might Power/100)^2.5 * 1/(1 + defense/100)^2.5 = 1

these are inverse functions.

Quote:
53.3% divide by 43.1 equals 1.24, which means even if the defending hero can always keep up with the growth and gear of attacking hero, the damage his angel suffers increases by 25% as game progresses.

You are decreasing damage REDUCTION, you are not increasing your damage above 100%. Yes you are doing more damage, but below 100%.
It means that in time defense is less effective but it does not mean it is useless or less preferable. And this is fundamental difference.

You can not make more damage if hero attack and opponent defense are equal.

Quote:

The conclusion is: better get counterstrike 3 instead of boost your defense in vain when the enemy has higher initiative or longer reach. Consuming the same amount of resource, you won't be able to turn the tide of battle by dumping defense


it is not better if enemy has retribution aura cast on it. If your stack damage sucks. And still defense helps.

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solariusyang
solariusyang

Tavern Dweller
posted October 11, 2011 08:27 AM

Quote:
@solarius: read alcis post again... it's that simple


read MY post and understand what my "attack biased" means, it's also not hard.

If it's still too hard for you (i hope not), what i mean is the hero attribute growth versus outcome curve, hero attack value out weight hero defense instead of even. What alcis talks about and what i mean are 2 different things. If there is a "unit attack" value in the formula then i won't have any issue at all, but now every unit have the damage attribute renamed "attack" and got a attack value of 0. It makes:

1, every unit will do reduced damage unless lead by a hero who's got a huge attack, i also don't like this.
2, it's favorable to choose attack over defense in skill, artifact or attribute bonus location choices as the effectiveness curve is bend towards attack, so make the choice of go defensive useless.

I wish the unit attack value back to solve 2 problems in one go

Have I made my self clear?

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SKPRIMUS
SKPRIMUS


Promising
Supreme Hero
The One and the Prime
posted October 11, 2011 08:49 AM
Edited by SKPRIMUS at 08:53, 11 Oct 2011.

Misconceptions galore!

Man you guys seem to have complicated everything, like the designers intended I suppose...

While I do not agree with the significance of the bias, the numbers solariusyang mentioned in his last post before last for celestial attacking celestial is true
Hero atk 0 v enemy hero def 0 --> atk 0 v def 40 gives 0.431 x 54 = 23.3dmg
Hero atk 10 v enemy hero def 10 --> atk 10 v def 50 gives 0.461 x 54 = 24.9dmg
Hero atk 40 v enemy hero def 40 --> atk 40 v def 80 gives 0.534 x 54 = 28.8dmg
Well you could have seen the trend of numbers in my post on page 3

This comes about because every creature has attack of 0 while defence is non-zero.  If every creature had defence of 0 & attack of non-zero, the minor bias would be other way around.

====

But I'm not sure I would pay too much attention to it since most games don't have stats as high as 40.

To give more realistic hero stat numbers
 a hero with atk 13 def 7 vs
 a hero with atk 7 def 13
If everything else was equal, damage will very slightly favour the hero with atk 13 def 7. (0.469 vs 0.452 when attacking each others' celestials)

====

AND

For example, in my H5 experience, it's not good to soley focus on one without the other.

Generally a hero of atk 20 def 0 will get hit harder on retaliations so during creeping (attacking neutrals) they are more likely to get losses than a better balanced hero. [you can't kill every enemy stack with one-hit kills before they act]

Conversely, a hero of atk 0 def 20 will kill less creatures on an attack...so more enemy creatures & stacks remain to be able to do more damage (less one-hit kills) & more likely to get losses.

When creeping (fighting netural creatures for xp), a hero with atk 7 def 13 would be more likely to kill enough of an enemy stack while having enough damage reduction to withstand retaliations without losing too much....even better with regeneration around.

It's also why I prefer boosting defence stat/artis for demonlord/orc & boosting attack stat/artis for ranger/knights in H5 since it tries to counter their weaknesses.

===

Of course H6 has different skills & creatures with complementary abilities which is probably more important to balance than this
Quote:
Funny how the original post made it seem more complex than it actually is because it can be rewritten:

Dmg = Base x Atkmod / Defmod

where
Atkmod = (1+atk/100)^2.5
Defmod = (1+def/100)^2.5

and the normal attack & defence are made of hero + creature
and there are separate might and magic atk/def

and it seems all creatures now have an attack stat of ZERO! (like ThunderTitan said)...
Thanks for red star alcibiades!  I still would have preferred H5 dmg calcs over this, unless it completely complemented the skill system which I don't think it has been.
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alcibiades
alcibiades

Hero of Order
Really, Ubisoft?
posted October 11, 2011 09:56 AM

I think the new system would have been fine, if just they had retained the unit attack as well as defence modifier. But no, that was "too complicated". Really, UbiSoft?
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SKPRIMUS
SKPRIMUS


Promising
Supreme Hero
The One and the Prime
posted October 11, 2011 10:02 AM

True giving each creature an attack stat (which will be near the defence stat) would reduce this small bias too
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Hope defeats despair - "a blatant clue"
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forest001
forest001


Known Hero
posted October 11, 2011 10:24 AM
Edited by forest001 at 10:25, 11 Oct 2011.

don't think it's needed, as fights are quite slow anyway and it's nicer to see those big hits instead of smaller and smaller ones

besides, bias is quite small anyway, don't think we will be seeing anything like 40 atk vs 40 def

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Gweret
Gweret


Adventuring Hero
posted October 11, 2011 11:08 AM

Lets do the math for Pretorian:
This creature have 10 might defense.
Let say one Pretorian is attacking other Pretorian.

Lets say we have two heroes one putting in attack only and one putting equally in attack and in defense.


Let say that their base skills are:
Attack hero(AH) - 20 attack and 0 defense.
Equal hero(EH) - 10 attack and 10 defense.

AH - increase only attack by 10 every "round".
EH - increase both attack and defense by 5 every "round".

Damage boost by attack hero to Pretorian:
On the left side is attack boost for AH, on the left defense increase for EH.
1. ((1+20/100)^2.5) * (1/(1+20/100)^2.5) = 1  
2. ((1 + (30 / 100))^2.5) * (1 / ((1 + (25 / 100))^2.5)) = 1.1030199
3. ((1 + (40 / 100))^2.5) * (1 / ((1 + (30 / 100))^2.5)) = 1.20354327
4. ((1 + (50 / 100))^2.5) * (1 / ((1 + (35 / 100))^2.5)) = 1.30134883
5. ((1 + (60 / 100))^2.5) * (1 / ((1 + (40 / 100))^2.5)) = 1.39630363

Damage boost for Equal hero:
On the left side is attack boost for EH, on the left defense static value. It does not increase.
1. ((1+10/100)^2.5) * (1/(1+10/100)^2.5) = 1
2. ((1 + (15 / 100))^2.5) * (1 / ((1 + (10 / 100))^2.5)) = 1.11753951
3. ((1 + (20 / 100))^2.5) * (1 / ((1 + (10 / 100))^2.5)) = 1.24300078
4. ((1 + (25 / 100))^2.5) * (1 / ((1 + (10 / 100))^2.5)) = 1.37655421
5. ((1 + (30 / 100))^2.5) * (1 / ((1 + (10 / 100))^2.5)) = 1.51836669



The best strategy for a hero is to put equally in attack and in defense.



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SKPRIMUS
SKPRIMUS


Promising
Supreme Hero
The One and the Prime
posted October 11, 2011 12:52 PM

LOL, the numbers don't show same trend when using celestials as an example.

From a purely mathematical point of view:

 When the overall modifier is greater than 1, more defence would "seem" better.

 When the overall modifier is less than 1, more attack would "seem" better.

Because each creature has 0 attack and non-zero defence, the modifier has more chance of being less than 1...anyway, other things have more impact than this stuff because not many would want exact mirror matches
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