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| Thread: Common Misconceptions | |
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Orc
Famous Hero
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posted March 18, 2015 03:03 PM |
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Edited by Orc at 05:26, 19 Mar 2015.
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Common Misconceptions
Section I
offense and offense effectiveness. I have seen a lot of people here and there speaking of offense being less effective on crag hack than with Gundula. This is simply not true, assuming you have superior attack power
as you know, the Formula with offense factors is:
Input Damage X (0.05 attack dif + offense bonus)
offense bonus is 30% = 0.3 meaning that, (again in case of attacker superiority), meaning that it is worth exactly 6 attack points. Furthermore, each level Crag and Gundula gains give them: 0.05 Offense 6 Attack/Offense skill = 0.3 points of attack worth (i.e. gaining 10 levels is like gaining 3 attack points)
Now, stating that Gundula benefits more from offense is identical to stating that each consecutive attack point is worth less than the previous one! No way! each attack point increase damage output exactly 5% of the Base damage
Section II
In this section explains How to find the "usefulness" of certain reduction % (defense, armorer, shield, etc). Many of you might be already familiar with it, so (if you sure you know this) you can skip to section III
Damage reduction does not work like the attack amplification we saw above
Lets have a look at few examples:
Reduction of 20% (i.e. factor of 0.8) will make you receive damage equivalent to 125% of your units hitpoints Because 0.8 X 125% = 100%
so if you have genies who were attack by some archers (say 5 grand elves, bless, and 12 attack points) they will give him damage of 25Xtwo shots = 50 HP
genie having that reduction factor will absorb this damage 125% and only 100% will die (taken only as 40 HP) so having 20% reduction helped him to absorb 25% more of genie's total HP
now with similar calculations:
25% reduction is equivalent to 33% Bonus HP >>>>>> Total HP will be 1.33 X base HP >>>> let us call this HP factor
33% reduction is equivalent to 50% Bonus HP >>>>>> HP factor of 1.5
50% reduction is equivalent to 100% Bonus HP >>>>> HP factor of 2.00
67% reduction is equivalent to 200% Bonus HP >>>>> HP factor of 3.00
75% reduction is equivalent to 300% Bonus HP >>>>> HP factor of 4.00
80% reduction is equivalent to 400% Bonus HP >>>>> HP factor of 5.00
90% reduction is equivalent to 9 times HP (900% HP) > HP factor of 10
95% reduction is equivalent to 19 times HP >>>>>>> HP factor of 20
98% reduction is equivalent to 49 times HP >>>>>>> HP factor of 50
99% reduction is equivalent to 99 times HP >>>>>>> HP factor of 100
and the list goes on (and actually between these values)
anyway, as you can see from the list, A hero that can reduce by 75% can absorb twice damage as another hero who can only reduce by 50%. He is twice as good in physical battle. Hero A is liking having an army of twice the size of hero B (in terms of HP not of damage output)
Now this reminds us of the beginning: a hero that can reduce the damage by 50%, having 200% HP, is as good as hero who can amplify the damage by 2 (20 attck more)
so actually, it is at 20 Defense more than attack when defense has as good value as attack skill
another point to notice, is that due to this, having armorer specialist with Level 4 armorer (20% reduction again, im thinkin wog again) and he being level 78 will reduce by 98% and he is at level 79 he will reduce by 99%. Therefore, at level 79 he will be twice as good as he was at level 78 Because he can receive twice as much damage input
Section III
Armorer and damage reduction misconception
I also see lot of people (im thinking same people) say something like "armorer is more useful for heroes that have less armor"
and example will be
20 armor reduce damage by 50% =0.5
level 4 armorer (im thinking wog, it serves same purpose with easier calculations) reduce by 20% =0.2
but due to the combined effect: R1 R2 = 0.5X0.8 = 0.4 = 40% total reduction
see??!!! its useless now, it only reduces damage by 10%
No my friend, its not less useful at all
To get the actual value of damage reduction, one needs to convert the damage reduction factor and convert that into "equivalent hitpoints" or how much more damage can we absorb
lets now look how useful armorer is with 6 defense (15% defense 15% armorer)
1-) Defense reduction = 0.15 >>>> Damage received = 0.85 Base dmg. alone this is equivalent to a bonus HP of 17.65%
2-) Armorer reduction = 0.15 >>>> same as above Therefore it will give (alone) 17.65% Bonus HP
However, the combined effect of the two reductions is not the sum of the two bonuses (as you might already know), but its something like this:
Damage received = Base Damage X 0.85 X 0.85 = 0.7225 Therefore the equivalent hitpoints given from that is 138.41% and thus the bonus HP is 38.41%
It not exactly the addition of the two, but slightly higher than that. In some other cases, it might be a lot higher.
Generally, two combined effect of equivalent hitpoints will be
(base hitpoints + Bonus 1) X (Base hitpoitns + Bonus 2) -------------- (these things between brackets are the HP factors if you remember)
and so on with as many bonuses as you want.
now the total bonus is you subtract 100% of base HP from that (because you already had 100% HP, so how much did it increase? Final - initial = increment)
doing another example now of defense +20 and armorer, lets see what happen
1-) defense reduction = 0.5 > Hp factor of 2
2-) Armorer HP factor of 1.1765 (as we have calculated just above)
therefore, the total benefit (HP increase) is 2.353 -1.00 = 1.353=135.3%
anyway, without the defense he only has 17.65% increase. clearly, having Defense makes armorer more beneficial (cuz when you can look at it that armorer give 17.65% without defense and 35.3% with the defense, but then again its combination, not armorer alone keep that in mind)
another way to look at it is that armorer gives 17.65% of the 200% HP that the defense already gave (kind of increasing base damage)
So I think this section proves that armorer is better with higher Defense-Attack difference than without it even though it reduces less of that damage input. If I convinced you, then you shouldn't say "oh, when you have 28 defense-attack difference, armorer only reduce by 4.5% it became useless. 4.5% from the 30% is like 15% from the hundred, and actually better"
Section IV
Having seen Section II, this raises the question of how better the Defense reduction could have designed been better. I have seen another game, Warcraft III, where they use the effective hitpoints to calculate the reduction of defense points.
the function proceed from the following:
1-) each armor point is worth 6%
2-) Defense X 6% gives you the HP% bonus. 10 Defense gives you 60% bonus
3-) they work it reverse way from HP factor to reduction
HP factor = 1 + HP bonus
Base Hp / (HP factor X Base HP) = 1 / HP factor = Lets call it reduction factor
Therefore, reduction will be = 1 - Reduction factor
Thus, substituting all the stuff in one formula:
Reduction = 1 - 1/HP factor = 1 - [Hp factor - 1]/HP factor =
= 1 - [Defense X 0.06] / [1 + Defense X 1.06] (0.06 here is 6% which is the % they associated each defense point with]
plugging in value of defense = 10>>> reduction = 37.5% ~ 38%
you might say defense getting better and better do make sense, and maybe that's true, but it ruins (slightly ruins) the game to make defense not work as some odd function rather than linearly, having each defense point being with different "preciousness" or "value"
Appendix I
Want to highlight
in Heroes Of Might and Magic III
attack-defense difference benefit (i.e. increment in damage output) work linearly: D(x)= ax + b (a here is 5% b is base damage x is attck-def)
defense-attack difference benefit (i.e. increment in equivalent HP) works as the function: Eqv. HP = f(x) = 1/[1 - aX] (a here is 2.5% x is def-attck)
and for values of ax << 1 it almost become becomes ax, and since a is of lower value for defense than that of attack, defense for these lower values will be of less value than attack. however, as ax in defense become ~~ 1, its equivalent in attack will be going close infinity (actually going up indifiently)
_____________________________
so that's about it. I have to admit that Warcraft III mechanics did inspire me to have all these thoughts: there where I learned the equivalent HP
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kicferk
Known Hero
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posted March 18, 2015 07:26 PM |
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I think for section 1 and 3 what you should be going for is specify what effectiveness is.
Ad. 1: For hero having more attack the extra damage provided by offence speciality is a smaller part of total damage. You can derive that from formulae if you want to. That is why "some people" say that hack's speciality is "less effective" on Hack than on Gundula. And I can see their point.
Ad. 3: Armorer obviously absorbs more damage points if your hero has smaller defence. Moreover, I feel your analysis is flawed in assumptions. If your hero has 20 defense advantage, then clearly he can't have much attack. So the 'extra hit points' are cool and all, but low attack means that the creatures he is fighting are dying slower, and can attack multiple times... In short, I feel the test cases don't really reflect reality well  It's not about how long you can last, it's about how much of your stack will you lose to win the fight.
I feel the way it is designed in H3 is pretty good.
Cheers
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Orc
Famous Hero
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posted March 18, 2015 08:29 PM |
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Edited by Orc at 20:32, 18 Mar 2015.
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kicferk said:
Ad. 3: Armorer obviously absorbs more damage points if your hero has smaller defence. Moreover, I feel your analysis is flawed in assumptions. If your hero has 20 defense advantage, then clearly he can't have much attack. So the 'extra hit points' are cool and all, but low attack means that the creatures he is fighting are dying slower, and can attack multiple times... In short, I feel the test cases don't really reflect reality well It's not about how long you can last, it's about how much of your stack will you lose to win the fight.
I feel the way it is designed in H3 is pretty good.
Cheers
The things I said come from the assumption that a hero who can amplify damage by [Amplification] is as good as a hero reduce the damage he receive by 1/[Amplifiication]
because when they fight, these two factors will cancel each other. The only argument I can is that "hey, damage amplification is better than the equivalent amount of reduction you assume"; you'd be saying this assuming they don't have to fight each other, but how good they will do fighting another enemy, i.e. is it better to amplify by 2 or reduce by 50% ? (excuse me for speaking on your behalf, you can always disagree if you don't believe what I just said)
Now this the case when you have the initiative striking, but it is not the case when you do not have the initiative. Ofcourse, generally speaking, amplification might be better, esp vs map, because wondering creatures do not have that good of a plan. However, I still believe that the assumption they are of equal value is valid (or at least close enough) and can thus be used theoretically to measure things in the same terms, or units.
kicferk said:
I think for section 1 and 3 what you should be going for is specify what effectiveness is.
Ad. 1: For hero having more attack the extra damage provided by offence speciality is a smaller part of total damage. You can derive that from formulae if you want to. That is why "some people" say that hack's speciality is "less effective" on Hack than on Gundula. And I can see their point.
What you are saying here is equivalent to saying that stepping from +4 attck to +6 attck is much worth than stepping from +20attck to +22 attck (im talking attack defense difference here)
The reason you will be right is might come from the assumption that you will spend these points into other things instead of attack (i.e. due to game complixity and other factors)
it is true that if you can bring something of better outcome instead then you are right. but I do not think that means stepping from 4 to 6 in itself is better than stepping from 10 to 12
and when I said game complixity above, I meant something that in the damage factor stuff, since morale will make you strike again, it will amplify the total damage (again, theoritically) and not just the the base damage
Edit:
let me attempt answering you in another way
lets say you have 2 stacks with same base damage output. you can attack same enemy and he dont retaliate.
First stack having same attack as enemy defense
Second stack having 14 attack more than enemy defense
you can apply blood advanced blood lust to one of the units. Is it better to move from is moving from 0 to 6 better than moving from 14 to 20? Let's find out
1-) damage output = 1.3 X Base + 1.7 X Base = 3.0 X Base
2-) Damage output = 1.0 X Base + 2.0 X Base = 3.0 X Base
same result
Does this convince you now that stepping from 0 to 6 is as good as stepping from 14 to 20 and that each attack point, and similarly offense + attack or any combination) is worth exactly the same value?
Does this convince you that the only way stepping from 0 to 6 might be better than stepping from 54 to 60 is to find something that can amplify you damage depending on the attack you have already, e.g. like mirth? i.e. saying that stepping from 0 to 6 is better than having + 2 morale, but having + 2 morale when you have 54 attack is better than stepping from 54 attck you have to 60?
what do you think
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kicferk
Known Hero
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posted March 18, 2015 11:17 PM |
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Starting from the end.
Perhaps I didn't put it clear enough. Going from 0 to 6 attack means a 30% of previous damage. Going from 20 to 26 means only a 15% increase.
That is what I mean that Hack's speciality is "smaller part of total damage". Because it is. Because if Hack does 400 dmg and Gundu does, say, 350, with 50 provided by their specialities(equal for both), then speciality is 1/8 for Hack and 1/7 for Gundula, more important for Gundula.
I know (and I don't know why you seem to think I don't) that the bonus is the same in value. But since total dmg for different heroes is different, so is the weight of speciality.
Think about this in the following way:
You attack a blue dragon with your hero, with 0 attack but expert offence. Then your troops do just around 30% from base dmg and gain 30% from offence skill. That means offence here is responsible for 50% of damage, it's damn important.
But if you have a blue dragon and huge attack, it does this 400% of his base dmg, and gets 30% from offence. WOW, less then 7.5% thanks to offence. In this case offence gives the same bonus, BUT it contributes to way different part of total damage.
That's why I feel it's fine to say in first situation offence is way more useful than in second. And by the same logic, Gundula's offence is a bit more useful for her than Hack's.
About the first part, [amplification] is an ambiguous term. I also can't figure out what 2 options you are comparing, please specify.
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Orc
Famous Hero
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posted March 19, 2015 03:35 AM |
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Edited by Orc at 03:37, 19 Mar 2015.
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kicferk said:
About the first part, [amplification] is an ambiguous term. I also can't figure out what 2 options you are comparing, please specify.
Expert Archery, 0 attack, will give
Damage output = (1 + 0.5) X Base damage = 1.5 X Base damage. The amplification is 1.5
Expert archery, orrin lvl 20, 0 attck
Damage output = (1 + 1) X Base Damage = 2.0 Base damage. 2.0 is the amplification.
similarly, tazar lvl 20 expert armorer, 0 defense
Damage received = Damage output X 0.7. Reduction factor is 0.7
kicferk said:
That means offence here is responsible for 50% of damage, it's damn important.
This is where we disagree: it not important at all, given that no other thing affect the damage, e.g. morale etc etc and the ADD is not negative.
I will use what you just said in my calc. below.
2 Angels, 100 damage
If they has 5 more attack will do 125 damage instead. 25 is bonues, which is 20% of total damage. Each attack point is thus responsible for 4% of THAT 125 damage
similarly:
10 attck 33.33%, thus each attack point is 3.33%
20 attck 50%, each is 2.5%
30 attck 60%, each is 2.0% of total damage
40 attck 75%, each is1.875% of total damage
What I did above is exactly what you were saying, but applied to each attack point.
However, the percentage above is not meaningful. Calc. the % of total damage the attack was responsible for is irrelevant. the relevant thing is the % of the base damage.
I can't just that attack is getting more and more useless just because of my calculation above. no It makes no sense.
anyway
Orc said:
Appendix I
Want to highlight
in Heroes Of Might and Magic III
attack-defense difference benefit (i.e. increment in damage output) work linearly: D(x)= ax + b (a here is 5% b is base damage x is attck-def)
defense-attack difference benefit (i.e. increment in equivalent HP) works as the function: Eqv. HP = f(x) = 1/[1 - aX] (a here is 2.5% x is def-attck)
and for values of ax << 1 it almost become becomes ax, and since a is of lower value for defense than that of attack, defense for these lower values will be of less value than attack. however, as ax in defense become ~~ 1, its equivalent in attack will be going close infinity (actually going up indifiently)
As we know, the 1/x function creates bijection between the two sets of A = (0,1) and B=(1,infinity)
What I did in my calculation was mere to convert Defense, armorer, and other reduction factors from set A to set B to help measuring Reduction and amplification in the same scale (you cant compare without same scale)
the reason I Rescaled reduction value to match amplification is because it felt intuitive for me (better to wrok with ax rather than 1/ax : rather than rescaling amplification into the reduction scale
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kicferk
Known Hero
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posted March 19, 2015 10:08 AM |
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The percentages you calculated with attack points are the base for saying that the difference between 0 and 10 is more significant than between 40 and 50. You can say it and then justify it, and sicne 'significant' can well mean 'how big part of total damage it contributes', the statement can be defended.
It's not a misconception about mechanics, it's a misconception about meanings of word. But to be honest, consider a real life example: running competitions.
Imagine you add 5 km to a race length to check if it has the same importance for all initial lenghts(initial lenghts correspond to initial attack values, added length corresponds to increase)
If you add 5km to a 100m sprint it will have a rather dramatic effect on the race. But if you do it to a marathon, the result will be minimal. Clearly, adding 5 km is more important if the distance is shorter. But by your logic, it is not more important for any length, because total length added is the same.
You could even give examples, like, suppose we have 2 races, and add length to one of them and the total length is the same. Does not really change my point. You can define 'significant' or 'important' however you want, but usually these terms are dependant on the base value.
Also, to give an example in H3 scenario. Imagine you have 2 heroes with the same stats, each has 2 stacks of angels, (1,10) and (1,20).
Then is the single angel in first army more significant than in second? Of course it is, I don't see why it would not be. It is a bigger part of army. But, by your logic, he is just as significant as the angel in second army, because his stats and damage are the same.
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