The ideas of a Wesnoth Rebalance

[AxalaraFlame]

Post 1:

Let me clarfy this: though it seems to be a scientific one, but without those super computers settled in Oak ridge national park, I still need many many feedbacks and test wars. All high rank players are welcomed, all developers are welcomed, all maths genius are welcomed to this vast project.


Post 2:

Dear dudes, l am AxalaraFlame. l am glad to tell you that l have already reached great success in wesnoth by pure arithmetic and mathematic balancing works. l have got vast data about this project, and l am confident that l will make greater progress no soon.

Before l open those progresses to you, l have something to tell you guys. Though, according to the "feedbacks" l collected from another topic, for this idea, most of you guys, well as far as l know, couldn't give the furry crack of a rat's behind. I am disappointed, but l didn’t and won’t give up, because it is doable, as l knew for a long while.

Why do l say that wesnoth is mathematically balanceable rather than conventionally balancing it with high rank players' advice? Many reasons:

1. Wesnoth is a battle chess. Micro Control and manipulating velocity that deeply influence RTS do not ever exist to be threats in this game. Anything units are terms that are perfected and counted by quantized calculation, which is inherently, axiomatically, calculateable.

2. Humans are not perfect. They can only be very smart, prudent, make the least faults they can but never be perfect. Since we can do it by formulas, why do we rather trust inaccurate experiences?

3. l must reveal something that some of you may know or have never known before. Wesnoth is only ROUGHLY balanced. See this, http://units.wesnoth.org/ check 1.0, 1.2, 1.4, 1.6, 1.8 and 1.10 version's change, you will find that all major changes are +4 or -4 or other sort of things, which is made so rough that is hardly convincing.


Post 3:

Once wesnoth is perfectly balanced, we will have a new future of it. We may revolutionize it, in a scientific way. These are the advantages that l can count by now:
1. Wesnoth will reach a triumph of mass introducing new units and new factions, completely free of any limits of balancing works, which was greatly annoying once before.
2. There are very few games on this earth balanced that l can count with fingers by doing pure maths, not even to mention an open source game. We will start a new era, and prove it doable, set to be a model for other games. Well on the other hand it is very very hard, hehehe…
3. All level Wesnoth units can be balanced quite precisely, which means we don’t have to play default era on ladder anymore. Instead, we will have REAL WARS on ladder by using Heroes Age, even lv3 Champions Age with lv4 leaders LOLOLOLOL!


Post 4:

Don't merge my posts into one, administratord. I have sorted them in a good sequence, very clear


Post 5:

The version 1.0 of Wesnoth Rebalance: a bird tends to fly without wings

The first version of my rebalance works is a crap. l use only this one formula below, which cares no mobility and speed's influences, and even so naively believe that all attack types, range or melee attacks, HP points, use a same base unit, in which condition l believe that bow based long range weapons are generally set at wrong prices.

(atk_melee+atk_range+HP)/$price=k(a constant)

This ridiculous fragile balance was kept by the magical “k”. For all units, the k shall be a same constant.
But no soon l found this is very impractical. You can check those data and find what had happened:
Dwarvish Fighter 40hp
Dwarvish Scout $17
Lich 54hp 14*3 atk-cold 10*3 atk-arcane
Horseman $24 10*2 charge-pierce 40hp
Horserider $16 34hp (at that time, the standard is 38hp)
Troll Whelp 40hp 8*2
……etc.
Those kinds of errors are made, with surprise, while within my prediction on the other hand. I list these out to warn you others, some of you may make same errors as l do.
This formula is very useless in counting the importance of mobility. For instance, the most valuable part of price of scouts is their movement points. This formula makes a very common error, underestimating the power of mobility.
I was highly enthralled and affected by the original version’s perfection, so I did not really firmly follow the already wrong formula. At that time I hadn’t realized that the balance was actually based on nothing scientific. Instead, l only did many little changes to the original wesnoth.
Resistances are ignored. I thought the type of HP is born with a unit inherently. Damn, l was too naive!
I can’t deny that most changes are made for my own favor. For instance, Dragonguard has 59hp. Oh you be damned why you have a prime number HP?? FXXK. So I gave him 60. In many cases l did so, like 29hp elv archer, 59 hp fxxkin steelclad, 79 hp dwarvish lord……etc.

The conclusion for 1.0 version of Wesnoth Balancing:
VERY IMMATURE A FAILURE STUPID [censored]
But, not completely washed out


Post 6:

At least l gave a try, so l made a little progress from it. I realized that settling some basic laws for units upgrading, and introducing more units to certain factions to suppress certain units from another faction is the essence of expanding current version.

These laws are still been used in the WIP balancing works:
Law1: When a unit gets leveled, leveled and leveled again, whatever the resistances got advanced, or new abilities learnt, it shall be EVEN ADVANCED each time.

This will be easier for manipulating those units which do not have special abilities and weapon specials. Otherwise, for now l have known, counting their prices will always cause vast calculation (which can’t be done simply by a human with a calculator in most situations), and involve more series of formulas specially designed only for evaluating a simple weapon special or ability.

Law2: Whatever the level a unit has, comparing level to level, it deals the damage of a proportion of hp of another same level unit. When they both get advanced, without conspicuous resistances changes, the former shall still deal the same damage of proportion of hp of the latter.

For instance, undead archer deals 7*3 damage to a cavalry once, which is 61.76 %( 21/34) of its hp. Then, when they both get advanced to another level, a Bone archer shall still deal a damage of 61.76% of a Dragoon’s hp. This means, the Dragoon shall have 58 hp (which is too much you may say) , or Bone archers shall only have 8*3 damage (not very cool, too). But if we changed all units according to this law, all leveled units will be largely changed and never the same as before. I guess if I can balance lv1 default era very precisely well, so can we do with the lv2s.


Post 7:

These above are the spoils l have gained from first stages. I am tired already, especially after typing so many words, so i am gonna sleep. Later l will unveil my second version and third version, how do they get perfected around thess two years, and how Brute Force Algorithm show its great power in Wesnoth game balancing.

[taptap]

Prepare your equations first. Most importantly your set of equations has no solution (as long as you have different units) for it is mathematical impossible to always have the same max. damage / hp ratio on each level for all unit pairs because units do different damage / have resistances etc. E.g. the elvish ranger and the marksman have a max. ranged damage of 28 or 36 respectively, should you now base the HP of other units on the ranger or the marksman, either way it will not be the same max-damage/hp relation for both of them.

You can make a point system - many RPG's have such character generation - you can even use it to customize a hero for a RPGish Wesnoth campaign. The idea of a scientific balancing of Wesnoth, however, looks dubious, when you don't even get the basic math right.

[alluton]

As stated always when talked about balancing: Wesnoth is supposed to be balanced faction versus faction. So create formula that takes account: Cost of every unit, How often used(try to observe,ask opinions etc..), how well this faction can handle against this type of damage, how well it can kill those kind of resistances and so on,( perhaps number of special units could be one aswell). Collect data faction versus faction and try to put that all together.

Hard one to do, but i would say possible one. But I suggest forgetting unit versus unit balancing. That just woudnt create interesting game.

Some values need to be set by humans from theri gaming experience meaning that those values may change over time when players behavior changes and they use different kind of tactics and strategies.


I hope this post has enlighted you in your difficult path towards calculating and balancing stuff.

[AxalaraFlame]

Thank you for putting my posts in order, administrator, whoever you are. But l want to seperate them into two parts, thus my ideas can be seen clearer.

Plz seperate post1-3 and post5-7 into two parts. Post1-3 are only introductions, post5-7 are the abstraction of my early stage experiments. l do not want they mess together. If you an help me, l will appreciated.

And l think now you can simply delete post4. l am fine with this.

[alexanderthegre]

I really don't think that this era is a good idea unless all traces of randomness are removed. Maybe giving all units a 100% CTH, multiplying HP and damage by 10, and apon hit, recucing damage by resistances as normal, but also defensive values?
I'm a precalulus student; please don't kill me if my math is bad...

Anyway, I've been thinking, and under a 0 random system like the one I described avobe, this formula might be a good one:

V= value, C= cost, A*= attack* damage, M= moves, N= number of attacks the unit posesses (with 0 random strikes are irrelevant.), R*= attack* range (1 melee, 2 ranged), TAV=total attack value (see below.), D= average defence, R=average resistances

To calculate the TAB, do the following (it's supposed to be a sigma, but the forums don't have the best formatting for that):
N
Σ(Ax(R))
x=0

Now calculate net unit worth:

V=(TAB + M + (D/10) + R) - C


Now for factions.
Assign all factions a certain number of points. Let's put this at ~40. All the units in that faction's total values should add up to this number.

I haven't tested this formula, but it should generate a mostly balanced era.

[TheCripple]

(atk_melee+atk_range+HP)/$price=k(a constant)

This ridiculous fragile balance was kept by the magical “k”. For all units, the k shall be a same constant.
But no soon l found this is very impractical. You can check those data and find what had happened:

Right then. Lets talk about why this breaks down.
1) It doesn't even include things special abilities (Heal, Poison, etc.) at all.
2) It assumes the value of a single HP and point of damage is constant. For instance, 1 and 2 Hp are worth different amounts, despite those effectively being 1 hit dies in game. Similarly, damage past a certain point is guaranteed to be wasted, and the amount of damage wasted is dependent on the number of units with HP greater than the damage, which means that there is a point of diminishing returns. Is that modeled? No. If the maximum Hp were 100, 100 damage minimum is functionally identical to 10,000, even though the latter probably costs at least 50 times as much.

In practice, these extremes aren't likely to show up much, but the same principles of wasted damage and largely pointless hit point variation exist, to the point where having each hit point of equal value is absurd.

[Iris]

it's supposed to be a sigma, but the forums don't have the best formatting for that

That’s what Unicode is for. Fixed for you.

[AxalaraFlame]

nonono, it is still not fixed for me now, dude.

And for The Crippe:
I know this, and I said it is only the first stage works done 2 years ago, when I first get involved with Wesnoth. I have listed out all errors I made, and I admit this is very immature.
I had realized every words you mean two years agao, but still, thank you

for Alexanderthegre(at?):
You are approaching near to it! congradualations. But this is not so simple as you thought. Later I will explain my every stages of works. Patience, dude

[pyrophorus]

Hi !
If you *really* have some elaborate idea, I think it would be fine of yours to unveil it fully now.
As many persons here, I don't think one can build an accurate mathematical model for factions balancing, but it could prove to be useful anyway if it could produce drafts.
So please, to the point...

Friendly,

[AxalaraFlame]

l am still typing on Word2007. They warned me that l can't send posts one after one, so l have to sort them and merge them into one long post. Patience, dude

[AxalaraFlame]

The version 2.0 of Wesnoth Rebalance:
Fledgling

Far advanced formulas are designed for dealing resistances, but still, the mobility is underestimated, but luckily it is not ignored. In this version, I introduced RH1 (real hp) to explain the direct relationship between the apparent hp and their resistances. However, the RH is not really practical for the current wesnoth version, for it ignores something important.

{(Hp/RAP*600) +atk-range+atk-melee +movement points}/$=k
“K” is a constant, as you saw above. The RAP is ResistancesAddedPercentage. A unit has no resistances would inflict 100% of a damage, when its resistance works, it will suck in less. L assume they all have basic 600% resistances (100% for each type), any additional resistances are added on this. For example, a skeleton fighter has such resistances:
Balde+40%
Pierce+60%
Impact-20%
Arcane-50%
Fire-20%
cold+60%
Then, his real hp is: {34*(690/600)}
This calculating method is very simple and can roughly reach a unit’s real hp when it works on battlefield. But the key problems were still remains a shamble.
Problems of version2.0:
1. Does a unit’s movement points use the same units as the hp, melee attack points and range attack points do? Do all four of them use the same units? Obviously no. The mobility reveals to be an independent attribute; though deeply and strongly affects the influence atk and hp’s efficiency, they share no characteristics to be united in one. Not even to mention that atk points and hp points using the separate units.
2. i still didn’t set the coefficient of range atk price comparing to the comparatively “cheaper” melee atk, which means, they are still the same thing in this formula. L think l hadn’t known their differences that time 2 years before.
3. The fatal terrain defense level was still not counted in! If the last version is a mess (l didn’t mention this, yet, l really didn’t count in terrain defense level’s influences), this unprofessional error shall not be made this time. Say, I missed a key point twice
4. The formula itself is an error. All races deal different sums of pierce, blade, impact, fire, cold and arcane damage. Among lv1 units, only ghost and adept possess fairly weak arcane damage, not to speak of they are all of undead faction, so “arcane” weakness of skeletons is overestimated; and for drakes, cold too etc.
But this time we still make progress. Then why should I show you guys these two washed out experiments at first? I must say, should l hadn’t tried so persistently, without these two failures, l will never realize what kind of faults l made. Any exploration has a process; this stage is called getting up again and again after fell off.
My progress:
This conclusion is made far earlier than the experimental course develops: Law2, by some extents, is paradoxically against Law1. So I set Law1 as the only norm.
This may be better comprehended by an example. Why does Law2 not practical? It seems if that all units’ level up by a same standard level, it would never happen.
Yet, this is the crux. Should all units level up by a same standard, then Wesnoth will become a [censored] when we happily leveled up our knight only to find the Paladin should and must have 71.1455 hp (lol). How does that happen? Well, all units “shall be EVEN ADVANCED each time”, but if the leveled-up-hp bases on a certain ratio of lv1 units damage output, which is not PROBABLY ALWAYS HAPPEN TO BE an integer! To say nothing of different types of units leveled up with same amounts of hp and atk, while the ratio differs one after another, which means if a spearman leveled up, get a 25%atk bonus, a bowman shall get +25% too. But this is impossible; as we know, Wesnoth thrives from the default era balance and the high level unit variations.
Maybe the smart you has seen my dilemma: to make wesnoth completely a balanced game, we could only take either of these laws. But Law2 cannot be realized, and it will ruin wesnoth’s diversity, make it through in through bromidic. So l picked Law1, and did some changes.

Law1 (fixed): Every unit shall level evenly each time. The superior choice is always those which make a unit approximately twice tougher than its predecessor (due to the technique difficulties), and does the price.

Say, an orcish warrior shall be twice stronger than a grunt, a warlord twice stronger than a warrior, four times stronger than a grunt. Coincidentally, E.S.R once gave us the same gist to balance, but l just didn’t know about this that time:
“Therefore, the Equal-Cost-Equal-Power Rule (ECEPR): you can balance armies fairly effectively by giving them the same amount of gold to recruit with. The Wesnoth maintainers tune units and factions with the main goal of ensuring that ECEPR stays true.”
“Here there is a rule of thumb. L2 units tend to be just about twice as powerful as L1s, and L3 units roughly three times as powerful. Thus, you can multiply a player side's starting gold by the average level of its recruiting list to get a number roughly comparable to an AI side's starting gold.”
Cited from:
http://www.catb.org/~esr/wesnoth/campai ... difficulty
Actually this is very hard. I realized this enigma of balancing failure just recently, when I got known from another topic, tended to ask why can’t I find any regular order or principle from unit to unit, until I got to know that wesnoth balancing works are done by conventional top players’ feedbacks.
What l tend to say is, wesnoth really did failed to balance high level units, or we may already have the chance to hold Hero Ages ladder wars. But that does not bother much, because we only use default era to hold ladder duels; high level units are vast in amounts, which are far more difficult to balance. What’s more, no war data of Heroes Age were collected before on ladder, means this absolutely an open field not been exploited.
According to the ECEPR, set lv2 units twice stronger than lv1s sounds like quite an easy task. But in wesnoth high level world, price becomes an inferior factor, which is fatal in default era; it cannot measure a unit’s ability anymore. So I set price as a key menstruation, is depending on two ideal assumptions:
i. The lv1s have all reached perfectness, with perfectly fair price to recruit
ii. We have already or will figure out a way to evaluate a unit’s price extraordinarily precisely
What shame, actually both are incorrect at that time. But the Law is eventually established, which is my always effective measuring gauge, and enlightened my way of the final aim.

[pyrophorus]

Hi everybody !

I fear you'll need a couple years more to realize you're running into a bag end. In the topic you quoted,(http://www.catb.org/~esr/wesnoth/campai ... difficulty) it is said some factions associations are unstable. This means battles in Wesnoth are some kind of stochastic processes (because the high randomization of the system of course). This means you can't solve this using a deterministic model. Maybe Markov chains or something of the like could help here, but certainly not your little arithmetics. I think this is what Zookeeper has in mind saying it's undoable.

Just an example: substract 2 hitpoints to all lv1 of elves faction and give them to the Elvish shaman. In your models, the faction power don't change, but ask experimented players if it would really be so. IMHO, this change would boost the whole faction.

Friendly,

[alexanderthegre]

I fear you'll need a couple years more to realize you're running into a bag end. In the topic you quoted,(http://www.catb.org/~esr/wesnoth/campai ... difficulty) it is said some factions associations are unstable. This means battles in Wesnoth are some kind of stochastic processes (because the high randomization of the system of course). This means you can't solve this using a deterministic model. Maybe Markov chains or something of the like could help here, but certainly not your little arithmetics. I think this is what Zookeeper has in mind saying it's undoable.

Just an example: substract 2 hitpoints to all lv1 of elves faction and give them to the Elvish shaman. In your models, the faction power don't change, but ask experimented players if it would really be so. IMHO, this change would boost the whole faction.

QFT!

That's what I've been saying the whole time! Wesnoth is not battle chess.
The randomness throws a rather massive wrench in this whole idea.
That's why I suggested making it 0 randomness; as then it neatly avoids all mention of the calculus.

[Mabuse]

For example, a skeleton fighter has such resistances:
Balde+40%
Pierce+60%
Impact-20%
Arcane-50%
Fire-20%
cold+60%
Then, his real hp is: {34*(690/600)}

btw it should be 670/600


and i dont wanna destroy your hopes, but resistances do not have an equal weight, you must take defense values (of each terrain) into account, whch also dont have the same weight, and movement (once you find out how to put it into a senseful relation to the other values) depend also on the movement costs for each terrain (which also dont have the same weight). a unit with movement 20 isnt very mobile if it must pay 20 moves for the most common terrains.

in any case the chance is high that the formulas you THINK OF are incorrect.
in the end since its up to you which weight you ASSUME a certain value has, all the formulas you might get will not be an absolute truth, it will be what you think is the truth

i would rather base my formulas AROUND existing and proven to be balanced units, just for the sake to make balancing for UMC units more easy. to make it more easy you should give the several movement types (which include defense and resistances and movement costs) own values rather than sepearate them all into the tiny single values (which is impossible)
the value is then multiplied with the actual movement-points.

an own formula how to estimate the value of each movementtype (in order to create new ones) is appreciated of course



but no matter what you will come up with, it will always express your own opinion

[Temuchin Khan]

Though, according to the "feedbacks" l collected from another topic, for this idea, most of you guys, well as far as l know, couldn't give the furry crack of a rat's behind. I am disappointed, but l didn’t and won’t give up, because it is doable, as l knew for a long while.

Well, I wouldn't say I didn't care. I would need some convincing, though.