The ideas of a Wesnoth Rebalance

[The_Other]

There are too many variables for this to ever be as precise as I think it's supposed to be. Consider:
What is the value of the Submerge ability? Tell me now, without knowing what map is being played.
Even if you know exactly how much water is on a map, the value of the ability varies depending on your start position (is the water in a place you will never need to go?).
Even if you know where you are starting, it depends what faction(s) you are playing against - are they likely to place units in the water? Do they have Submerge themselves?
Even if you know what faction you are playing against, different players use different tactics, which will affect the usefulness of Submerge.
Even if you know your opponents' playing style, their precise behaviour will be affected by external factors - for instance, they may play more aggressively if they have had a bad day.
And of course, if your opponent is a mischievous son-of-a-gun like me, they may deliberately make random or illogical decisions, just to mess with your equations.
And that's just one - pretty uncommon - ability...

You can't formularize the worth of a unit in a precise way, because even if you eliminate all random elements, the game is a chaotic system in the sense that it cannot be predicted without access to every single piece of information, including the future actions of strangers. For this reason, 'points systems' as seen in many games are always flawed to some extent. The best you can ever hope for is an acceptable approximation - such as, for instance, the one we have at the moment...

[AxalaraFlame]

sry for letting this topic spared here for a week, but recenly l am working on the campaigns and game tests. l need some time more, and soon, l will reveal the possibility for defining and rebalcing general units.

the-other get a very crusial point: even now many problems are not solved. some are critical ones. The biggest problem l met is those [censored] abilities and weapon specials. All those things shall be dealt by establishing a new way particularily focus on them

[The_Other]

Sorry to be so blunt, but I think you're missing the point.
It isn't he abilities that cause the problem - it's the players.
Any unit, and indeed any single function of a unit, varies in value depending on how its owner uses it, and how the opponent chooses to counter it. It's the human element, even more than the random numbers, which make the game unpredictable.

Also, if you're able to analyze and quantify a chaotic system in such a precise way, wouldn't you be better off applying that to the stock market, rather that a game?

[AxalaraFlame]

The 3.0 version of Wesnoth Rebalance:
Flight training

Due to the awareness of former mistakes, the third faction and balancing experience is founded on an even steadier basis. In retrospect of the slips, most probably made of ignorance, I thought it over and over, and tried to find what are the initial criteria of Wesnoth (which l strongly believed to have existed but now l know it does not). Bitter, it came out to be vain. I failed to find any intrinsic relationships between a unit’s hp, atk, mobility and its set price. Very normal units (do not have any complicated abilities and weapon-specials) in a single race do not have any equations to reach price stability.

After thousands of times’ counting, l finally got the data of series of plausible assumptions. None of them is completely right (in this tone “wrong” is better), but some basic simple equations can work. I didn’t make anything useful that can be applied to balancing directly further than 2.0 (though 2.0 can’t, either lol~); instead, some methods for counting the game’s rationality are developed, but it is not much digressed after all.

The new formula:
█(atk-melee*x+atk-ranged*y+hp+mobility*z)/$=k

“K” is a constant. As usual, this formula is designed for inter-faction balancing. Define base unit “1” as 1hp point, for atk points can be output again and again if a unit survive the battle. Atk-R shall be more expensive than atk-M because most units don’t have ranged attack. A unit has melee weapon but no ranged weapon is very common; but a unit has ranged weapon but no melee weapon is rare (i.e. dark adept), sometimes just looks bizarre. Among the whole wesnoth lv1-3 default line, there is only one unit fight in this way.

This formula should be near successful, but l was confused for getting many errors from it. But after all, its basic principle is significant, that is to unite all three kinds of units into one formula with relevant coefficients. See those problems below and you will know why it cannot be applied into use:


1. “Summing up” hp points and atk points is practical, but the movement points……it may not be so. Mobility works much more different than other things. It is the most valuable part of a unit. For humans, quick trait make them crossing the wild as quick as an animal (you know who l mean, hehe). It enables a unit to have more opportunities to charge into battle, sometimes critical ones. This influence is an indirect one. Should their relationship be a simple addition relationship, or a multiplication relationship, or a piecewise function relationship? Using this “Z” do can reach equivalency, but the fact is “Z” seems to be DAMNED BIG! So I deeply doubt it.
█((atk-melee*x+atk-ranged*y+hp)*(mobility*z))/$=k

Z can be 1, l am not sure about it. Applying this would take risks.
Or: f(x)={█(mobility*z1 x∈(0,5)@mobility*z2 x∈[5,8)@mobility*z3 x∈[8,11))┤

I think perhaps it may have different usages if segmented into these three parts above. As an attacker/defender, fake scout whose movement points=6, 7 or quick normal unit, or scout and super scout (8+movement points), their mobility may play different rules on a battlefield. Their movement points and atk points also affect each other mutually. I.e. if a scout can move extremely fast but only deals little damage, it is comparatively less useful.

But as a common sense we can see, high mobility + high damage is really a suppressive combination. These units, i.e. the whole knight line and gryphon, are all very expensive examples. They are known for both high damage and offensive attack types, which mean most of their damage output is controllable, compare to those units having both ranged and melee weapons but both deal less damage, who does not really deal high controllable (offensive) damage per turn.


2. Terrain defense level and resistances are neglected again.
Again and again did I neglect them. But why? They are very crucial factors affecting a unit’s surviving ability. Well, my superstition of a belief that Wesnoth has a “stably subtle but brittle balance” harmed me a lot. After all it shall not be overlooked, let alone I meant to overlook them. I once believed that all units are inherently the same useful, the same viable, and the same favorable. The world of Irdya should not in favor of any creature particularly. Dwarves dodge less but resist more, elves are invincible in forests but trashy in caves……until I realized that drakes are innately not so viable than dwarves, and then I just came to doubt about this problem.
This problem is not solved till today (WIP), and not even realized till someday someone told me “wesnoth does not have solid formulas for measuring units’ value”. Thanks god I got this prompt at last.


3. X, Y, Z all vary a lot, depending on how many units you would want to include in the system; they can’t work far in a little group of units. It is good on the other hand, indicates that any unit’s existence can affect another, though the relation is xagzfe, as I conjectured before. But in some ways it can be also bizarre. I deeply suspect the possibility whether they are irrelevant with a unit’s price. See some examples:

Dark adept: within undead faction, they shall only worth $15±0.30 (15). But for the multi-faction, they worth $17±0.15 (17), while mages seems to have no choices but to be given 29 or 30 hp. Insofar, UD has already become too crappy

Skeleton: $14. Well, not a big surprise for me. This way is for reconciliation: if a skeleton only worth $14, dark adept is solid for $17

All Drakes: All of them get +2 or 3 hp, or get+10% blade or pierce resistances. While within drake race, I strongly believe that their mobility is too high and is underestimated.

Tree: its hp is an irresistibly turbulent element. With regenerate ability their hp can release greater potential (incalculable). I reached a conclusion that they might better get a slice less (49? I am not sure), or the price shall rise to 21
………etc.

Trying to determine them is worthless, albeit they should be constants theoretically. There is always something impactive against the set price and the default hp, atk, mp numbers. At last, I involved only 33 units with controversial X, Y, Z numerical value. They are already junks now, due to innate defects (problem1 and 2).

[AxalaraFlame]

Sorry to be so blunt, but I think you're missing the point.
It isn't he abilities that cause the problem - it's the players.
Any unit, and indeed any single function of a unit, varies in value depending on how its owner uses it, and how the opponent chooses to counter it. It's the human element, even more than the random numbers, which make the game unpredictable.

Also, if you're able to analyze and quantify a chaotic system in such a precise way, wouldn't you be better off applying that to the stock market, rather that a game?

sry, didnt see this. But it actually the same thing we are talking about...l may have not express it in a right way. Players are highly unstable factors, however they have a limit can't be broken: the rules. Within the rules everything is technically controllable--it doesnt mean we can control them, and doesnt mean we have ability to reach its border. We can't know and control many things in wesnoth till now, and remain some factors which l don't believe can eb determined someday. l only evaluate those can be valued and ascertain those can be determined.

btw, randomness is not necessarily to be eliminated. In a computer's sight, the state of chaos and cosmos have no differences; there is only an additional probability calculation process. They still execute every command as they always prefer to do in chess games before

[The_Other]

I will make this point, if it's the last thing I do...

Let's ignore the element of human unpredictability for a minute and focus on what we can, theoretically, quantify - the units. Let's further assume that every game is played on the same map, and that you have invented some (probably incomprehensible) formula to accurately measure the value of a unit, which I shall refer to as V.
The problem is that V is not constant, even for a single unit type. It will change every time any unit enters or leaves play, advances, or takes damage.
Suppose a given unit has Leadership, which has been accounted for when calculating its V. But Leadership increases in value based on the number of units who are able to benefit from it - thus, V for this unit goes up and down as you recruit and lose other units. A unit with higher total damage potential benefits more from Leadership, and so will result in a greater change in V. Only 6 units at a time can benefit from a single units' leadership - so after the 6th is recruited, the change in V per unit is reduced - but not eliminated completely. Units who are far from a leader will not affect its V - meaning that V changes every time anybody moves. I could go on, but you get the picture.

All of this means that no strict mathematical formula for V will ever be viable. Yes, it is theoretically possible to calculate V for a specific unit, on a specific map, against a specific enemy or combination of enemies. But in the real world, it will never be precise enough to be worthwhile. As I stated, a game as complex as this is a chaotic system. Chaotic does not mean "random", as many people think - it means "theoretically predictable, but governed by more variables than you can possibly process".

[AxalaraFlame]

I will make this point, if it's the last thing I do...

Let's ignore the element of human unpredictability for a minute and focus on what we can, theoretically, quantify - the units. Let's further assume that every game is played on the same map, and that you have invented some (probably incomprehensible) formula to accurately measure the value of a unit, which I shall refer to as V.
The problem is that V is not constant, even for a single unit type. It will change every time any unit enters or leaves play, advances, or takes damage.
Suppose a given unit has Leadership, which has been accounted for when calculating its V. But Leadership increases in value based on the number of units who are able to benefit from it - thus, V for this unit goes up and down as you recruit and lose other units. A unit with higher total damage potential benefits more from Leadership, and so will result in a greater change in V. Only 6 units at a time can benefit from a single units' leadership - so after the 6th is recruited, the change in V per unit is reduced - but not eliminated completely. Units who are far from a leader will not affect its V - meaning that V changes every time anybody moves. I could go on, but you get the picture.

All of this means that no strict mathematical formula for V will ever be viable. Yes, it is theoretically possible to calculate V for a specific unit, on a specific map, against a specific enemy or combination of enemies. But in the real world, it will never be precise enough to be worthwhile. As I stated, a game as complex as this is a chaotic system. Chaotic does not mean "random", as many people think - it means "theoretically predictable, but governed by more variables than you can possibly process".

well, that is an idea too, and l heard kinda of this view very frequently. A single, normal unit, which does not have trisky weapon specials and troublesome abilities can be accurately evaluated, and these kinds of units take 32 seats among 43 default units. I will never give up this point because the external bonus damage, i.e. leadership, illuminates, inspire etc. couldn't give the fury crack of this unit's behind. There are none of their business. The benefits are given by leader units or other supportive units, and leadership are used most probably offensive, so this kinds of variables should be counted on them as an support skill (values certain ammounts of gold) but not limbolic variables that make benefitted units unstable.

The problem is not that much necessarily concerned, because leadership is one of those chaotic ability, which usage is nearly completely up to a player rather than both sides. Other stuff, like heal, cure, illuminate, obscure or whatever the hell of these AOEs, are all currently uncountible. Many things that seem to depend on subjective purposes turn out to be another form of objectivity. If we can't know these abilities' value, which is proven by some methods, I would accept this consequence; but now we scarcely know how it works (we don't even really know anything about them). The only impressions of these variables we know are only impressions. How can we just give up studying them by some intuitions which suggest that "their potentials are countless" in this very early stage? I don't think so this far.

[AxalaraFlame]

Let me set apart this section and talk about why I made so much effort in doing this program. I don’t really believe this game need rebalance before, as you guys can see above and another post asking about “the formula” which I strongly believed to exist and dominate wesnoth.

Well, I am not silly with it and my idea is not complex. I thought wesnoth is so enthralling so good such a damned good game that makes me eager to perfect it, and reach greater perfectness. Open source games are open to changes, so anyone can step in it with ease.

But I am not interested in making some units awesome or simply cheat—that will lose all my fun and the game loses its profound meaning. Each time, before I changed an element, I would doubt: would that make this unit tougher, and after I abused them to win a campaign, even win with little advantage of enhancing 1 hp per unit, would I lose the pleasure for victory? For, called, “cheating” it? Let alone guilty, though it is only a game……but perfectness, what we could have got and from those details hard to recognize that can be modified to approach nearer to it, I just think such neglect is IRRESISTABLE！

To know how to perfect something, one must know how it works, what is its principle. Well, I dunno, and I didn’t ask the right people about it. All in all wesnoth is not a well-known game, and my friends scarcely know about it. I registered my id in the late 2011 and got access to net wars since then, while before this point of time I had already played wesnoth a year, only campaigns campaigns and campaigns……btw, to reach perfectness I played all campaigns on nightmare level (last accomplished version 1.93, in which footpads are extremely lame) and got all passed without save/load, so I am actually already a master of main line campaigns, a self-appointed one.

Guess what I did next. First, my spare time in school is a lot; second, I have photographic memory. With these two prerequisites, I dauntlessly assume those laughable models that look plausible and simply charge into these meaningless calculations, solo. One year passed. To remedy my hatred for not fully enjoyed some games by changing some particular units, I played all campaigns, on average, nearly 3 times on hardcore level without save/load (curse Infested Caves and fxxk Human Alliance forever).

That is my hapless history for wesnoth balancing. Until now, still have no solid conclusions yet. But I will reveal it soon because I believe mathematics is invincible!

[pyrophorus]

May I make a suggestion ?

I must say formulas like yours is to me like adding carrots and cars, then dividing them by the age of the captain: meaningless.
So maybe you could use a statistical approach: evaluate statistically how much turns an unit will survive in battle condition against standard opponents (i.e. range and melee attacks), knowing it has some (parametred) probability to benefit healing, leadership and so on.

Then you could deduce the average damage this unit can inflict to other sides during its "lifespan".
This way, you will have a model to play with, for instance, changing the healing probability parameter to see how it influences the result (and its standard deviation which as important as the result).
Friendly,

[battlestar]

I couldn't read all that besides getting a rough idea of what's said, but here's something to throw in about factions.

Factions are made of a collection of units. It's a cooperation of units instead of a collection of individual units. Thus all stats need to be looked at individually instead of added together. Otherwise you can end up with a faction that can deal with, for example, drakes very well but can't do anything against undead.

On an individual level looking at units, you still can't estimate the worth of a unit. Strategy games like this run on a principle similar to rock-paper-scissors. Do they have equal values? How about when you compare an army of rocks with an army of scissors, do they still have equal values?

IMO, expert player opinion is just about the only thing that can be depended upon in these situations.

[AxalaraFlame]

thanks for this idea. But say it is meaningless...really frustrated me a lot. l am always collecting data of players, but not top players l suppose. many things can not be counted in this system may still need gaming experiences and replay statistics. if u guys can suggest me someone why mastered wesnoth, l would be appreciated

[tadpol]

The ladder is at http://wesnoth.gamingladder.info/ladder.php you can probably find someone high on the list camping the server at anytime. Also most of them have accounts here that you could pm. I'd suggest trying to be nice about it if you're going to be sending out unsolicited mail.

If I was running your project I'd try to quantify descriptive laws of the current balance without making any proscriptions. If general laws are broken by a few units I'd note them as exceptions rather than try changing them since I haven't mastered playing with them as they are. I'd be interested to see how closely any large set of units fits to a single formula.

Your last formula looks something like the qualitative one I think with; deadliness toughness and mobility vs price determine goodness. But the virtues all depend heavily on the situation. I understand the current faction balance is aimed at making the 21 different match ups about even on well made maps. But for each of those match ups and maps the virtues of each unit are a little different. Is a fish faster or slower than a foot? Is an adept more or less deadly than an archer? Can a wose hold out longer than a shaman?


I'm curious to see if you can come up with anything useful, and I think I hope for your success.

[AxalaraFlame]

yep, l am on ladder. l dunno how to inform that administrator...he didnt reply my email for 2 weeks. l meant to delete my files and l wont play ladder anymore.

well, l am now getting clearer that all formulas will not work unless an integer version is developed. lt is only maths problems so l suppose it will appear, so any work would become easier

[BasiC]

People are being very ignorant and counter productive.
I think this effort is very welcome and the result, if The OP keeps working on it, will be much better than anything pure intuitive balancing can achieve.
I have some experience balancing RTS games using equations and i have some tips i think might help.

First of all we must remember that balance of strategy games is not only about tweaking units stats, there is another major issue and its the map set allowed to be played on, in the ladder.
The point of equations in a game like Wesnoth is not to precalculate all possible moves and unit combinations on every map in the map set and than based on that information change the stats so all factions are balanced(again balanced for who, since a player will never be able to play perfectly and make the perfect decision so even if a computer could recalculate all moves the balance it will eventually generate will only be balanced to other computers playing the game while precalculating evrything).
This is impossible, just like its impossible to precalculate all possible moves in chess to decide at every moment what is the perfect move.

What equations are good for is to allow us to minimize intuitive guessing and improve consistancy...
Equations will never be able to say how much exactly should the heal ability costs(for example) however it will allow us to intuitively decide the cost of all the different abilities and resistances and defense values and than based on those costs correctly give every unit a proper price.

Instead of having to intuitively guess the cost of every ability on each unit we will only have to give values to things once and than calculate the costs of every new units.
We do not need to start from scratch.
We take equations, Assign, intuitively, based on our game experience, values to all the basic stats like resistances defenses ratios all the abilities, movement points, dmg etc...After values are set by us we see if those values and the unit costs they generate are close to the unit values we got in Wesnoth now.
we do this because Wesnoth already has an OK balance, work has been done and the balance is not terrible.
Whe nwe see the values placed in the equation for all the different stats generate unit costs similar to the current unit costs we will know we are makign progress.
After this is accomplished we can begin tweaking and seeing what units are wildly standing out of the cost the equation assigned to them.
These units will be the unbalanced units.

In short, using an equation to calculate a unit's cost based on its stats will allow us to make cross-section balance tweaks and allow us to correct wildly unbalanced units.
Instead of tweaking a single unit's stats cause it seems OP just to find out that that tweak has now contributed to another unit being OP or UP we will be able to say, "ok this unit is wildly unbalanced compared to the other units and we need to nerf this and this GLOBAL value to put it into the balance frame" or "the healing stat is too cheap we need to assign it a new, higher or lower, GLOBAL value and than correct the pricing of all units that use this value,heal".

This process will add consistancy and allow less intuitive guessing and trying to make sure you thought of all the possible outcomes of nerfing or buffing just a single unit.

[pyrophorus]

People are being very ignorant and counter productive.

I'm sure this proud declaration will get you a *lot* of friends and enthusiastic listeners !
It would be even better if you put it into your signature. Then everyone could see the good opinion you have on them.

Friendly,

thanks for this idea. But say it is meaningless...really frustrated me a lot.

Sorry, but I remember you study physics and maths. So you know the way in physics one model a system, searching values which can describe it accurately, like entropy in thermodynamics. You're making the assumption some linear combination of the existing parameters should work. It's an empirical approach, not a theoretical one.

Friendly,