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JollyJoker
Honorable
Undefeatable Hero
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posted January 23, 2012 01:51 PM |
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Well, DESTINY is the name of the primary hero stat that influences creature Luck. 
As is LEADERSHIP the name of the primary hero stat that influences creature Moral.
Heroes have now 6 primary stats:
Might Power
Might Resistance
Magic Power
Magic Resistance
Destiny
Leadership
and on level-up heroes gain two points, NOT randomly, but in a FIXED manner, so that every hero type is developing always in the same way.
The trouble is that the 4 M&M primaries are 3 times better than D&L - advantage Necro heroes, because they end with only 7 points in D&L, while all the others end with at least 14 (and Haven heroes even with 16).
To give you the values, all level 30 Inferno Might hero will look like this (without artifacts and location visits):
Might Power 20
Might Resistance 17
Magic Power 9
Magic Resistance 7
Leadership 4
Destiny 10
All NECRO Might heroes level 30 look like this:
Might P 19
Might R 22
Magic P 10
Magic R 9
Leadership 0
Destiny 7
The 7 points more in Destiny and Leadership can't make up for the missing 7 points in Might and Magic, though.
TRIPLE them, to Leadership 12, Destiny 30, Necro having 21 Destiny, and it would be more correct, although it might look more like:
Inferno
23
18
9
7
9
21
and Necro
20
23
11
9
0
12
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hobo2
Promising
Known Hero
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posted January 23, 2012 02:02 PM |
bonus applied by alcibiades on 24 Jan 2012. |
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First of all: yes you get Destiny effects on retaliation. You don't get leadership effects on retaliation. Also, extra damage you get from Luck triggers before retaliation while the extra damage from Leadership triggers after. Destiny, completely terrible as it is, is in all ways better than Leadership at base. The purpose of Leadership is that it allows you to get two "on action" triggers, which means that you can draw down healing from regeneration faster and get extra strikes out of Pressed Attack. There are a couple of other neat things about Leadership, like how if your pit fiends trigger their confusing rage on their first attack, Leadership will let them take a step back so that they don't get a retaliation-free swipe. Leadership is actually hard to compare directly to Attack power. But Destiny is easy, it's just a straight damage boost when it goes off so it's exactly the same as having more attack power except it has a different calculation.
Now let's get in to the attack and damage calculations for a bit. According to the Fan Manual, the attack damage equation is (1 + Attack/100)^2.5. Assuming that is true, that means that very roughly each point of attack makes you do 2.5% more damage than you were going to otherwise. Luck is a 1% chance of doing 50% more damage. For a starting creature, that is terrible. Going from Attack 0 to Attack 1 makes you do 1.025 as much damage (a 2.5% increase), but going from Destiny 0 to Destiny 1 is only a 1.005 increase in average damage. Sure it works on Might and Magic attacks instead of just one or the other, but it's still five times as ineffective.
Attack is a very slow exponent, but it's still an exponent. The first point of attack adds 2.5% of your base damage. Your one hundredth point of attack adds 7% of your base damage. Every point of attack is literally worth more than the one before it. Destiny on the other hand, is completely linear. The damage boost is always 1% of 50% (half a percent) per point of Destiny. It doesn't matter whether it's your 3rd point of Destiny or your 93rd point of destiny, the damage boost is the same. But, the damage from luck is actually multiplied across the damage boost from Attack, so while Destiny is completely linear, the linear bonus gets bigger when you have a higher attack skill. Every point of Destiny adds half a percent to your damage, not to your base damage. As your attack gets larger, your Luck effects also get larger. When you already have an Attack of 100, your luck effects are adding 2.8x your base damage when they go off.
Note that this means that Luck is still smaller than Attack, even when you have a huge amount of attack. But it's much closer. At Attack 100, Luck is 40% as big as another Attack point. Which considering that it applies to both Might and Magic makes it only like 20% smaller instead of 60% smaller as it is on the bottom.
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JollyJoker
Honorable
Undefeatable Hero
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posted January 23, 2012 02:41 PM |
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Yeah, but you won't ever have 100 attack, so I'm a bit puzzling about what your point is.
Sure, the Luck bonus will give 50% on damage, and that includes ALL damage, not only the base damage, but also damage increased by a spell or skill.
That's why Luck and Leadership never have been primary hero stats until now.
In any case, we shouldn't forget that Might stats determine MIGHT (a factor in hero sttack and skills) and Magic stats determine mana, which are added plusses as well.
Additionally, you cannot calculate with Luck. If your creatures have something like 20 Luck, it doesn't give them 10% more damage - Luck may trigger, when you don't need it, resulting in overkill, so I don't see any reason to make this overly complicated.
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alcibiades
Honorable
Undefeatable Hero
of Gold Dragons
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posted January 23, 2012 03:02 PM |
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I just think his point was that, apart from mentioning a number of factors that also plays in on balance, it was ok for Luck to be slightly weaker in beginning as it will grow stronger through the game as Attack gradually increases.
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What will happen now?
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JollyJoker
Honorable
Undefeatable Hero
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posted January 23, 2012 03:16 PM |
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But it isn't SLIGHTLY weaker, but SIGNIFICANTLY weaker.
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hobo2
Promising
Known Hero
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posted January 23, 2012 03:53 PM |
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My point was actually just to talk about the actual numeric differences, since your initial post was just ballparking it and not particularly well. Luck is worth one half of one percent of your total damage, linearly for each point of destiny you have. Total damage is multiplied by Attack, so the more Attack you have, the better Destiny is. And even at Attack 100, a point of Destiny is still only about 40% as good as another point of Attack (but applies to both Might and Magic attacks). I really don't know where your 1/3 guesstimate comes in, because that would only be true at the point in which a point of Destiny adds one sixth as much damage as a point of Attack (since Destiny adds to both Might and Magic damage). And it's better than that even at Attack zero.
Disregarding the serious implications of the fact that Might Attack makes your warcries bigger and Magic Attack makes your spells bigger and Destiny does jack all for you - Destiny would be about equal to a point of Attack if it gave a damage boost that was half as big as another point of attack. Something that never ever happens. With actual numbers you actually see, it's about 20-30% as big.
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JollyJoker
Honorable
Undefeatable Hero
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posted January 23, 2012 04:34 PM |
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If you had read the post you could actually see where the 1/3 comes from.
With the actual system it's not the question whether a point of Destiny may be worth 2.73 points or or 3.04. It must be an integer.
Of course, a point of Destiny might give something like a different percentage, like 2.43 or something like that, but that would of course need a change of the complete game mechanics.
However, I suppose that it would be simple to just set 1 point of Destiny to actually 2 or 3 or 4 points of Destiny, when you advance in Destiny, so the question is, what a point of Destiny (and Leadership) is worth ROUGHLY.
We can safely say that the Magic stats not only bring magic defense and attack, but are also worth 10 points of mana each, while the Might stats influence not only attack and defense, but also certain might skills. So one point of Might Attack and one point of Magic attack cover the attack power of the whole army AND give 10 Mana plus an unspecified amount of added skill efficiency.
A point of Destiny, however increases the chance to get 50% bonus damage for a specific attack or retaliation by 1%. Being Destiny it's incalculable which is decidedly a disadvantage, because you cannot plan with it.
A look to the attack table tells us, that if starting at 0 we need 18 attack points to reach 50% gain and 14 for the next 50. I took the liberty to build something of an average which would be 16, and since we need both Might and Magic points it would be 32 instead of 100 - 3 times as much.
Now, true, Luck adds to all damage, so it's something that gives a 50% interest on everything that adds to damage. But that's true for Might (added skill efficiency) and Magic attack (Mana to cast spells) as well - the effects add up for everything.
Considering that you cannot calculate with Luck - you cannot base more on it than probability assumptions, which doen't mean anything - Luck's efficiency will be not as good as the numbers suggest: if you cast something that will increase the damage of a certain stack, you will cast it on the unit that will make the most of it. With Luck, however, it may trigger on every stack, even your worst.
So while it may be true that Luck will give suddenly 75% additional damage, once you reach attack level 18, that's not due to Luck, but to the fact that you got 18 points in attack.
Another problem is, that the efficiency of a couple of points of Destiny are incalculable anyway. Creatures have a certain Destiny value to begin with, but the actual 5-10 points of Destiny you actually get via Level-up are rather insubstantial and may not result in anything.
But even IF you would factor that in, you'd still be at double value at least. which wouldn't change anything to the fact that the actual situation is not good.
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OmegaDestroyer
Hero of Order
Fox or Chicken?
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posted January 23, 2012 04:43 PM |
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Great contribution, JJ.
____________
The giant has awakened
You drink my blood and drown
Wrath and raving I will not stop
You'll never take me down
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hobo2
Promising
Known Hero
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posted January 23, 2012 05:09 PM |
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Quote:
With the actual system it's not the question whether a point of Destiny may be worth 2.73 points or or 3.04. It must be an integer.
That is bluntly false. The cost has to be an integer. The amount it is actually worth could very easily end up being 2.73 points or whatever. If Luck ends up not being valued at an even integer relationship with attack points, then it is a cinch that the skill that increases Destiny is going to be better or worse than the skills that increase Might and Magic Power. And that is what we have.
At attack power 20, another point of attack power adds 3.307% of base damage. At attack power 20, every point of Destiny adds 0.789% of base damage. At attack power 20, one point of Might and one point of Magic attack together are worth 4.1914 points of Destiny. You may not like that, but that is the actual exchange rate of damage. Destiny would be balanced at attack power 20 with Might or Magic attack (for creature damage output, not for spells) if it came 2.096 times as fast. Since it is not possible for that to happen, it is trivially easy to demonstrate that the Luck increasing skill is not going to be balanced and will probably never be worth taking except at the extremes (such as Inferno positions or ridiculously large attack values).
But if you're going to numerically evaluate the different factions, you should use the real numbers, not just made up ones. Sure, it might show that Inferno is .7865 as good as Necropolis or something, but that's important balance information. The actual value is the one with all the numbers after the dot, not some idealized integer list.
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odium
Known Hero
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posted January 23, 2012 05:41 PM |
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Edited by odium at 17:43, 23 Jan 2012.
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Hobo2 numbers are correct. At the moment, 1 point of Destiny is roughly worth one fifth of the damage increment value for 1 point in Attack.
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JollyJoker
Honorable
Undefeatable Hero
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posted January 23, 2012 05:50 PM |
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The actual numerical "worth" cannot be determined anyway - since many things are not exactly computable.
It doesn't actually matter whether a point of Destiny is worth less or more when you have attack 20, because you may never get to it. It's a mixed calculation anyway, while your MIGHT attack may have reached 20, your magic attack might be still 6, and vice versa.
It's not DESTINY that gets better or changes over time, it's the HERO who gets better and the army as well. Exact values on this level are not possible anyway.
I'm completely satisfied with the realization that the balance is SEVERELY wrong, because something is SEVERELY over- or under-valued. I'm not the game developer, so I just have to point out that something is not right.
I'm QUITE positive, that things would be more balanced if heroes would get 3 or maybe just 2 points instead of 1 in Destiny and Leadership when they level up, and the actual point of the whole thing is to point to something that should be readjusted with a view on Heroes and Creatures.
Also, what are you actually talking about? You cannot "pick" Destiny, you actually get the points automatically, and it cannot "come faster". The question is what does a hero actually get when they level up, and it was fairly meaningless, if they all got the same, but they don't.
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JollyJoker
Honorable
Undefeatable Hero
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posted January 23, 2012 05:51 PM |
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Quote:
Hobo2 numbers are correct. At the moment, 1 point of Destiny is roughly worth one fifth of the damage increment value for 1 point in Attack.
It's not.
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odium
Known Hero
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posted January 23, 2012 06:02 PM |
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Let me explain then:
I believe that everyone agrees with the simplification that one point in attack gives a 2.5% damage increase. (In reality is not linear and grows but it does so slowly).
We start with the desirable that 1 point of destiny should have the same impact as 1 point in attack. Let's call p the extra Luck chance our 1 point in destiny will add.
(1-p)*1 + p*1.5 = 1.025
LHS=average damage with the extra point in destiny
RHS=damage resulting with the extra point in attack
Solving it will give 0.5p=0.025 which makes p=0.05 or 5%. With the actual game mechanics p is only 1%. Therefore it is at least on fifth below the value that makes it roughly as valuable as attack.
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xerox
Promising
Undefeatable Hero
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posted January 23, 2012 06:02 PM |
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Edited by xerox at 18:03, 23 Jan 2012.
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I don't agree with introducing even more stupid healing in the game. There must be another way. imo the best and easiest solution would be to make ressurected creatures disappear after combat.
Personally I don't think that the Morale/Luck skills are THAT weak. Atleast in Duels, I find myself picking up passive abilities that affect the entire army rather than super situational spells that I will never use.
For Inferno, I would give No Enemy Retaliation to the Cerberus, No Melee Penalty to Breeders and increase Inferno's overall growth.
____________
Over himself, over his own
body and
mind, the individual is
sovereign.
- John Stuart Mill
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hobo2
Promising
Known Hero
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posted January 23, 2012 06:43 PM |
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Quote:
It's not DESTINY that gets better or changes over time, it's the HERO who gets better and the army as well. Exact values on this level are not possible anyway.
No. You're just wrong. Destiny provides a numeric damage bonus. Its value is numerically predictable, and the bonus it gives is directly comparable to the bonus provided by Attack because it enters into the same exact equation. Destiny adds to damage, that is all it does. It is directly mathematically comparable to every single other thing that adds damage. As it happens, the exchange rate of destiny to attack power gets more favorable (or rather, less horrendously unfavorable) as your attack value goes up. Your units have different attack values, so the exact exchange rate is going to be different on different units. That in no way means that numerical exchange rates don't exist.
Seriously, you might as well be complaining that Might Attack can't be compared to things because it adds more to the base damage output of a Marksman than it does to the base damage output of a Sentinel and no damage at all to a Vestal. Yes, the way the attack calculation works, more damage is added the more of it you have. And the damage increase is faster for Destiny points than it is for Attack points.
The damage calculation is a ghastly horrible thing. It is a fraction raised to an exponent multiplied by the base damage. Figuring out the numeric balance on that is really hard and requires a calculator - which is probably why Black Hole did such an obviously terrible job of balancing those numbers.
But that doesn't mean the numbers can't be compared or don't have exact values. They can and they do. And Destiny's exact value - which it has - is larger proportionately to the value of more increased attack the higher your attack already is. Nonetheless, Attack values are worth considerably more than Destiny values are point for point, and the skills that give you extra Destiny and Might Attack values are in no way balanced.
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JollyJoker
Honorable
Undefeatable Hero
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posted January 23, 2012 06:59 PM |
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Quote:
Let me explain then:...
I think you just forgot that there are two attack values.
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JollyJoker
Honorable
Undefeatable Hero
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posted January 23, 2012 07:25 PM |
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Quote:
Quote:
It's not DESTINY that gets better or changes over time, it's the HERO who gets better and the army as well. Exact values on this level are not possible anyway.
No. You're just wrong.
And you are just arguing for arguing's sake.
It doesn't matter whether the Luck bonus is getting better over time. The attack bonus is better as well depending on a lot of other things.
What hero would you like better?
17 17 17 17 0 0
or
0 0 0 0 34 34
Right. I repeat - it doesn't matter that the Luck bonus gets better when Attack is added. It doesn't matter either that the 10 Mana you get with every magic attack point become less percentually with a view on the developed hero.
It wouldn't even matter if there was a difference if everyone else had the same stats - however they don't.
This has consequences on the balance, of Heroes and of creatures, and one very simple way to change that would be to change the amount of Destiny/Leadership points a Destiny/Leadership level-up brings.
This would necessarily full points, and I think that 2 are not enough. That would make it 3, but if that would be considered too much, there was also the possibility to give alternately 3 and 2 points for a level-up.
And, no, as much as you and probably BH want to make everything comparable, it is not possible, not in an absolute way. For one thing , factions are different. Different creatures with different amounts of Might and Magic damage, which means, Might and Magic attack have different impact - add to that Mana and Might skilly plusses and the vagaries that Luck must be viewed at any time as a percentage bonus on the average army damage divided by the number of stacks, it's a question of weighing factors and their impact.
All this is based on a lot of assumptions about how certain factors influence a game. Obviously the first points in Magic attack and Resistance are extremely important, because without them you wouldn't be able to cast ANY spells. But the mana aspect wanes, the more Mana you have - how is that to be rated?
Generally, there is no constant value. At every time a point's value is different. A point has a value at the time you get it. Still, it makes no sense to take that into consideration, because if you would, you couldjust as well make linear formulas or let Luck work only for base damage.
If you want to argue for arguing's sake, go ahead, but I don't see the point. I don't even know what you are arguing about.
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odium
Known Hero
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posted January 23, 2012 07:29 PM |
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Edited by odium at 19:38, 23 Jan 2012.
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Quote:
Quote:
Let me explain then:...
I think you just forgot that there are two attack values.
Your saying that 1 point in Might Attack does not add to all stacks but only to those that deal might damage. The same for Magic Attack. Ok, I agree with you here, however take into accout that Might Attack and Magic Attack are not equal from the point of view of creatures' damage. The average number of creatures dealing magic damage in armies is 2 out of 7 (with the extremes: Sanctuary that has 3 and Stornghold that has 1 and... a half). So in a sense you are right and I would change the formula into :
(1-p)*1 + p*1.5 = 5/7 * 1.025 + 2/7*1 - for might attack
(1-p)*1 + p*1.5 = 2/7 * 1.025 + 5/7*1 - for magic attack
0.5 p = 0.0179 => p=0.0358 or 3.58% chance for might attack
0.5 p = 0.0071 => p=0.0142 or 1.42% chance for magic attack.
Please note the underestimate of damage from attack (2.5%) and the fact that attack influences other skills (especially magic attack that has other effects like more mana, more powerfull spells etc). So these values that results are not even enough to make it equal.
So, if I were to compare Destiny with Might Attack (this comparison is simpler to do) I would say that it is at least 1/4 less powerfull.
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hobo2
Promising
Known Hero
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posted January 23, 2012 08:27 PM |
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Quote:
Quote:
Quote:
It's not DESTINY that gets better or changes over time, it's the HERO who gets better and the army as well. Exact values on this level are not possible anyway.
No. You're just wrong.
And you are just arguing for arguing's sake.
Actually, I'm arguing because I'm still right and you're still wrong. In a mathematical, provable fashion. Do the math. The numbers are still the ones i said and still not the ones you said.
Quote:
It doesn't matter whether the Luck bonus is getting better over time. The attack bonus is better as well depending on a lot of other things.
I'm going to need to turn to Picard for this one.
YES it bloody well matters whether the luck bonus changes in size dependent upon the strength of the unit it is applying to. The fact that these bonuses scale and the rate of this scaling is completely central to any possible analysis of their effects. Attack scales with Attack. The more of it you have, the better it is. Destiny scales too, but it doesn't scale with Destiny, it also scales with Attack. The more Attack you have, the better Destiny is. And get this: Destiny scales with Attack faster than more Attack does.
If you don't take into account those facts when you are suggesting a mathematical analysis, your mathematical analysis is wrong. Period.
At Attack 0, +1 Attack is worth +2.5% base damage and +1 Destiny is worth +0.5% base damage. At Attack 100, +1 Attack is worth +7% damage and +1 Destiny is worth +2.8% damage. In the time an Attack bonus became 2.8 times as valuable, Destiny became 5.6 times as valuable. Luck scales twice as fast with Attack as Attack does. If your analysis does not take that reality into account, it is wrong. Because next to the fact that Destiny is much much smaller than Attack at all levels on a point for point basis, that is the most important fact about the Attack/Luck question. If your analysis disregards it, your analysis is useless.
What hero would you like better?
Quote:
Right. I repeat - it doesn't matter that the Luck bonus gets better when Attack is added. It doesn't matter either that the 10 Mana you get with every magic attack point become less percentually with a view on the developed hero.
Uh... no. Actually the fact that Mana becomes less valuable the more of it you have is actually really important as well. If blithely disregard that, your analysis is useless. If you have 10 mana, getting +10 mana is totally awesome because it lets you cast Regeneration. If you have 1000 mana, getting 10 more mana means nothing at all because you're never going to spend mana fast enough to meaningfully dip into the mana you already have. Mana, unlike Attack, is a diminishing returns quantity. Marginal utility drops on mana. The mana utiltiy function looks like this:
And if your analysis treats it as a straight line, your analysis is wrong.
Quote:
This has consequences on the balance, of Heroes and of creatures, and one very simple way to change that would be to change the amount of Destiny/Leadership points a Destiny/Leadership level-up brings.
This would necessarily full points, and I think that 2 are not enough. That would make it 3, but if that would be considered too much, there was also the possibility to give alternately 3 and 2 points for a level-up.
What you are going to get, if you make Destiny and Leadership numbers even vaguely comparable, is a utility function in which Destiny is slightly weak until it hits a breakeven point and then becomes slightly strong. Because it still scales twice as fast with attack power as more attack power does.
3 points of Destiny is worse than 1 point of attack at attack 0 (+1.5% vs. + 2.5%). It's better than one more attack at attack 100 (+8.4% vs. 7%). 2 Points of Destiny is worse even at Attack 100 unless you're a faction like Sanctuary or Necropolis that legitimately values Might and Magic attack roughly equally (in which case of course, it is better to add 5.6% to two different attack types than to add 7% to one, just as it's better to add 1.5% to both types than it is to add 2.5% to one).
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alcibiades
Honorable
Undefeatable Hero
of Gold Dragons
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posted January 23, 2012 08:31 PM |
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Jesus guys, you don't have to bite the heads off each other when you're essentially saying exactly the same thing.
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What will happen now?
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This thread is pages long: 
