How to balance your faction

[thespaceinvader]

First off: please don't double post. We have edit buttons on this forum for a reason.

Secondly: Units are not balanced against units, factions are balanced against factions. I'm pretty sure that better era designers than me could come up with a situation in which a 14gp 10mp scout could appear in a balanced era.

Even if you create a wonderful formula which guarantees balanced factions... Those factions will become formulaic. Such a formula is highly unlikely to take into account unusual UMC units, stats, abilities, specials etc that a human can look at heuristically and play-test. Sure, it could be a basic guideline on balance, but so is the eye of an experienced designer, and PLAY TESTING.

You're also, once again, COMPLETELY IGNORING maps. A 10mp unit is immensely useful if it has 1mp costs on most common terrains. But if it has 1mp only in, say, desert, and there's only one desert tile on the map, it's pretty hampered.

That being said, feel free to continue on your hiding to nothing.

[fog_of_gold]

Please don't be confused if I'm not answering for about two weeks. It's going to be a long post and I've got no time to write on this in these two weeks. However, I'll post now the most important things:
1st: Thanks to the analysis of pauxlo. They helped/will help a lot to things clearer.
2nd: To Dixie:
a/b/c:=(a/b)/c, afaik
If not, it is meant to be so and therefore it's your third and second possiblity being right.
3rd: Thanks for correcting the standard degression to standard deviation, thespaceinvader.

[ahyangyi]

First off: please don't double post. We have edit buttons on this forum for a reason.

Secondly: Units are not balanced against units, factions are balanced against factions. I'm pretty sure that better era designers than me could come up with a situation in which a 14gp 10mp scout could appear in a balanced era.

Even if you create a wonderful formula which guarantees balanced factions... Those factions will become formulaic. Such a formula is highly unlikely to take into account unusual UMC units, stats, abilities, specials etc that a human can look at heuristically and play-test. Sure, it could be a basic guideline on balance, but so is the eye of an experienced designer, and PLAY TESTING.

You're also, once again, COMPLETELY IGNORING maps. A 10mp unit is immensely useful if it has 1mp costs on most common terrains. But if it has 1mp only in, say, desert, and there's only one desert tile on the map, it's pretty hampered.

That being said, feel free to continue on your hiding to nothing.

If "double post" means me, I apologize. However, I thought it would be more clear if I split two irrelevant posts, instead of merging them into one. If "no double post for any reason" is a hard rule, then I have to say sorry again

Regarding the map problem, in my opinion, the factions should not rely too heavily on maps first. If you really make a 10mp unit who can only move very fast on sands, you're giving the mapmakers troubles. Such units are definitely imbalanced. Similarly, a 10mp 14gp scout unit will make the faction heavily rely on the map choice. If you balance such a faction on one ladder map, it might probably be imbalanced on another. My suggestion is: everyone should avoid making such units, unless you're feeling absolutely right.

And while maps are very different, balanced ones have many aspects in common. To name a few: have an adequate amount of shallow water; do not have large connected component composed of the same type of terrain in the main battlefield, instead, mix flat, woods, hills and mountains around; do not overly use one of the bad terrains (snow, sand, swamp); have a town reachable from your leader at turn 1, no matter which leader you choose.

[thespaceinvader]

You're not getting the point here: map balance is not universal. You could make an era that was hopelessly imbalanced on mainline maps that was perfectly balanced on its own map set. Just because the mainline maps are balanced for the mainline factions doesn't mean they are balanced for UMC factions and vice versa.

Similarly, your rules for map balance apply to mainline maps, but do not necessarily apply universally.

If you push and pull all the variables enough, you can probably come up with a formula that 'proves' default MP is balanced. This won't be a universal balance formula.]

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NB: If you want to split parts of a post that aren't relevant to each other, do it like this

[ahyangyi]

You're not getting the point here: map balance is not universal. You could make an era that was hopelessly imbalanced on mainline maps that was perfectly balanced on its own map set. Just because the mainline maps are balanced for the mainline factions doesn't mean they are balanced for UMC factions and vice versa.

Similarly, your rules for map balance apply to mainline maps, but do not necessarily apply universally.

If you push and pull all the variables enough, you can probably come up with a formula that 'proves' default MP is balanced. This won't be a universal balance formula.]

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NB: If you want to split parts of a post that aren't relevant to each other, do it like this

Nice point. The factions which looks badly balanced on most maps should be played on specially designed maps, and these maps should be distributed along with these factions.

So any analysis should focus on a given context of "balancing". We cannot talk about "balance" without previously clearly define them. I should say like "you can't have mp10 gp14 scouts, if you want your faction to be balanced on common maps, against a default faction".

However, I do feel that, when people are discussing about "making a new faction balanced", they usually assume a common setting: mainline maps, mainline factions and other factions in the same era. (I know some eras are famous for balancedness only inside the era, but the factions are constantly stronger than mainline ones. However, I don't understand why can't they scale all the numbers down a bit to make them also playable with mainline ones, even if not specially designed to counter each other.) So, can't us assume fog_of_gold also assumed a similar setting in his mind when he talks about balancing?

[thespaceinvader]

NB: there's also no real need to quote entire posts in your response. Generally accepted etiquette on this forum is to quote specifics if you're responding to specifics, but generally, not quote much =)

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You're right, I think, that the problem is in defining the term 'balanced'. It's a much misunderstood term. Partly because it can be a little variable.

In a campaign, balance is 'is this campaign too difficult or too easy', basically. Altering balance is usually accomplished by fiddling with gold values, enemy levels etc, once the campaign is written completely. Accomplishing campaign balance reliably can be a very difficult art. But it's not really what we're talking about here.

Multiplayer balance can be similarly difficult - do you want to balance for every player? Or do you want to balance for expert players? Default can be a case in point: the tactics and strategies that make the Drakes effective can be difficult to grasp, and new players often have more difficulty with the drakes than with other factions. Does that make them unbalanced? No.

But the most important point is that units are not balanced against units. Units are, in fact, inherently imbalanced against other units. I would pretty much always expect there to be a clearly superior unit when two non-identical units are pitted against one another. One of them will win more often. If it wins often enough that it kills more GP worth of the enemy than you lose per time it dies, it wins. A faction cannot be balanced on its own, excepting mirror matches, which can be considered balanced, if boring, by default. Balance in MP can only be factions against other factions.

A formula to decide if a unit is balanced simply won't work, because an era can be balanced with a given unit in one faction, but hopelessly imbalanced with an identical unit in a different faction.

[fog_of_gold]

Now, finally, I'm able to answer. First, I want to eliminate some misunderstandings and answer general opinions:

"Factions are balanced against Factions, and not units are balanced against units":
This formula isn't meant to balance factions. This will come (maybe) later. You are, however, completly ignoring the balance of the units INSIDE factions. You mustn't have in a mainline faction a unit with 1 hitpoint, one 1-1, beserk, melee attack, 100 recruitcost and one move. The faction would stay as counterable as it was before and still you mustn't do that. Every unit need to have its uses and you can

abilities:
There are some abilities you are able to include and some you aren't. It is true they are making false assumptions and they are in general very crude, but it's better than nothing. I'm going to add a list with their reasonings later.

"This is a prooved formula":
You are right, I exaggerated with "this formula is prooved". Of course, this formula isn't proofed. To be true, I didn't expect that anyone would read it and I wanted to be sure you understand I won't think it isn't possible to get a formula to caculate balancing.
I named it to reasoning. If I forgot anything, tell me.

"You forgot maps":
No I didn't. If you'd read more carefully, you'd discover I've written "You aren't able to get the average defence of a unit". If it wasn't clear enough, you are also not able to include movementcosts. But what you are forgetting is that a lot of units have exactly the same movementtype.

"Instead of thinking of formulas it's better to just playtest the factions":
Of course it is always better to playtest a faction of an era, but this formula helps you to avoid units like 7 moves, 5 gold (which I've seen in a faction which is meant to be balanced against mainline). It's just meant to help people haven't got a lot playtester and especially this formula is meant to save time. This is what I've always said and for what this formula is meant to be used. It's nothing more; it's nothing less.



A lot of you tried to falsify my formula. Expect pauxlo, you all failed. I'll first show what you've done wrong and then I'll do the analysis of the analysis of the reasoning:

[...]Now it would be an odd era if there was a unit like a wose or a heavy infantry that moved like a scout and it was still balanced but it could be done. Example alright, your factions scout has 40 hitpoints, good resists, 8 mp, with a 10-2 melee attack for 17 gold. This is fine because the other teams has a unit with a 3-3 ranged berserk attack, that is balanced by the fact that most units in this era have ranged attacks and thus the ranged attack is actually a vulnerability in most cases but it does mean they have a hard counter to your scout available with relative ease.

On the flip side a unit with 1 hitpoint, 7 movement, costing 10 gold, and having only a 2-1 ranged berserk attack would probably be overpowered in mainline despite being about as much an utter wimp as you can get in terms of pure stats and not even having the speed to act as a reliable 8mp scout.[...]

I didn't ever said you are able to include beserk and accuratly of this reason you aren't able to include this ability.

More on the origional topic: As a particuarly exadurated example of how to break this, let us theorise a unit with a movement of 2 and a 10000-100 melee attack no ranged attack, poor dodges, 90% resistance to everything and 1 hitpoint, and a cost of 15.

Unless the faction it is in excels at making numerous good walls this unit would be utterly useless against any faction that has a skirmisher with a ranged attack. The damage rating 10000-100 can essentially be equated to: if I hit you I will kill you and if you do not kill me I will have enough strikes to land a blow. However this is a quantitative effect that cannot fit into a mathmatic formula, we could keep pumping that damage rating until this unit is theoretically godlike however the fact that it would never get first strike and any enemy with a ranged unit can kill it easy without fear of retaliation (and any faction with first strike on melee can easilly make a wall against these things.

What you've done wrong, is, that a unit with the attack x-x with x->[infinte] doesn't do infinite damage per turn since your unit is only able to attack once per turn. For reasons I'll explain later, your unit would need to get the damage set to a value about 60, if you calculate them. Having that in mind, your unit would need to cost 7 gold - this is, looking at some UM eras, even balanced. Also, let's say you have an era with only these units. Your named counter unit would be highly unbalanced. If you expect, the skirmisher/firststriker is balanced, and add a new unit, they needn't stay balanced and exactly this happens.
By the way, I am, for accuratly these reasons, not able to include these abilities.

[...]Your first assumption, for instance, is that a unit should always attack the weakest enemy. That is just plain wrong. I can think of plenty of cases where the strongest enemy is the best one to attack, and the weakest should be ignored until you have a hole in the enemy's defences that you can exploit. Or when you should attack with your most-damaged unit in order to damage an enemy, lose the damaged unit and leave the hex open for another attack.

1) the part of the moves is still in developing
2) I didn't already used this assertion so it won't change anything, so why did you mention this?
3) Your "strongest" enemy is meant to be my weakest enemy: This enemy giving you the most advantages if you attack him.

[...]This sort of formula, on simple units without many specials, could give you a very vague idea which units were more powerful and less powerful. But you should be able to do that without a formula. It only takes common sense to realise that certain units are powerful and others are not. Or it should. It CANNOT tell you explicitly that a unit or faction is or is not balanced. It has been tried before, and it has failed before.

EDIT: viewtopic.php?f=12&t=26558&hilit=formula

This sort of formula, on simple units without many specials[...]It CANNOT tell you explicitly that a unit or faction is or is not balanced.

Please don't expect things I've never said.

But you should be able to do that without a formula.

I guess you've never really seen the low-downloaded eras since you wouldn't say that then.

It has been tried before, and it has failed before.

Because, afaik, it has been tried false: You can't just add move, damage and hitpoints multiplied with special, constant factors. Every children know it is always better to get good in every field (resisting attacks, attacking and flexibility) rather than specialize. Also, this is no reason. Look at the well-known four-colour-theorem: It's proovement has been tried, it has been failed. But was this a reason to give up? -No. After more than 100 years, it got prooved.

analysis of analysis of proof:

Therefore a unit lives [hits]/d.

You forgot healing (on villages, by healers or by level-up). (And there should be a "averagely" in this sentence.)

His absolute, total damage in a whole battle is [staketime]*[damage] with [staketime]=[hits]/d.

You seem to assume that a unit does attack in each turn attacks (and is attacked). This is not the case on usual multiplayer games (and also not in campaigns).

[hits]/d is meant to be the time you are in battles. There are rarly healings within battles. Also, if you attack, you are not always but very often attacked and the other way arround.

A unit always try to attack the weakest enemy, since its looses are the lowest one, even comparing to the enemy.

There are often cases where this is not done - maybe you want to gang up on an enemy unit (or the enemy gangs up on you), or you have to kill a critical unit first.

To be true, these units are meant to be the "weakest" one. However, I'll properly remove this part.

It can reach everything in its range.

Nice assumption, but not true in Wesnoth.

But this isn't (if you ignore skirmisher, which is need to be done) affecting the unit. You'd properly mention now movementcost, but as I already said, you aren't able to inlcude that. So you need to compare units with the same movementtypes. This means, you may say, every unit has the same movementcost. This means again, the movementcosts are nothing else then a "space curvature" and if you then say you'll always get to a special point per beeline (which is really rarly incredable wrong), then it won't change something.

There are infinte powersteps of a unit's power. If a powerstep is x times weaker than your power, your power will will be multiplied with y.

Huh? I can't really parse this. What do you mean with "powerstep"?

So our new formula is const=[powerstep_factor]*[its_liklynesses]*[hits]*[dmg].

I don't really see the "so". How did you get this formula from the last formula above?

The [powerstep_factor] is of course constant since it doesn't depend on these values. The liklynesses are, what we need to get now.

As I don't understand the powerstep concept, ok.

I'll need to redone this; you are right.

First, it's important to get the total area of where our unit is able to catch a unit with the powerstep we are looking at. To have no disturbings by the map, its size needs to be set to infinte. This means, I may ignore this value for now.

Aha, so our formula won't work on real world (Wesnoth Maps), only on simple ones where our unit can move with 1MP/hex, and without any border.

You are in "the "real" world" not really often affected by the borders and corners. This is the reason I've done this.

The total result need to be therefore [reachable_area]=area([range])*const1=[range]²*hexes*sqrt(3)/2=(([moves]+1)²*hexes*const2 inwhich const1 isn't a real constant; it is more that its value doesn't depend on your unit.

As mentioned above, the reachable area (in which "reachable" means "hexes we could attack if only there and nowhere else is an enemy unit") is
area([range]) = 1 + 3*([moves]+1)*[moves] = 1 + 3*([moves]²+[moves])..
Your "const1" seems to be a constant for "hindrance by bad moving terrain and other enemy units", is it? I'm not really sure this is constant, as units may be build a wall so you can't get to the other side, and how much this blocks you may be dependent on your movement rate (and other factors, like the skirmisher ability).
So, I have const * ([moves]²+[moves]), which is less than ([moves]+1)² (by [moves]+1).

You are right about that. After I've redone the reasoning, I'll properly rechange it to *[MP]. [BTW, it used to be that way so it's a little bit funny]

Resistence and defence, if given right-formated, just change the enemy's damage by multiplying with it. Therefore, multipling with d, the hitpoints are still divided by them both:
[power]*const=[hitpoints]*[damage]*([moves]+1)²/[resis]/[def] To be very precise, these "formations" are the WML-stats. Remember, every constant is on the other side of the equation so it can but it mustn't be 0 to 1, just stay on one.
Yes, naturally. But you should be able to kill them both by any power-10-unit, don't you?
(If you have a sensible measure of power, which I still don't understand.)

Yes, you are, but that isn't what I wanted to say. I wanted to make clear, you may not just divide by the cost; this is just wrong.

Why? I understand that the enemy needs to deplete the total hit points [hits]*[amount] and you can deal [dmg]*[amount] damage, but why can you simply multiply?

This is a thing which isn't prooved, but there are two signs of thinking that:
1) If you set hits(A1)=hits(A2), dmg(A1)=dmg(A2) with A1 and A2, the units of the two armies, you'll to the well-known formula to simulate battles [I'm sorry, I forgot its name]:
dA²=A²-a²
with A, the stronger army, a, the weaker army and dA, the survivors of A.

2) Imagine an army as one unit with swarm. For reasons I'll explain later, swarm will multiply the damage with 0,5. You are right, if you set the amount to 1, this is false but the reason of that is, that the factor 0,5 gets the less precise the less attacks you have since you haven't 0,346 attacks and such, which I expected.

(And what happened to your move-factor)?

It's a part of the damage

And what is the relation to our previous formulas?

It was meant to show the previous formula is wrong.

[pauxlo]

I still say: try out your formula with mainline units, to see wether you get at least similar values.

[Atz]

I still say: try out your formula with mainline units, to see wether you get at least similar values.

You don't.

Let's take the Loyalist's spearman and mage, for instance. Conveniently, they have the same resistances, defence, and move, so we can just ignore those. This gives:

Spearman:
36 [HP] * (7*3 [melee] + 6 [ranged]) / (14*14) [cost] = 36*27 / 196 = 4.959

Mage:
24 * (5 + 7*3) / (20 * 20) = 24 * 26 / 400 = 1.56.

Quite a difference! This isn't quite fair, though, because we're not taking into account specials. The mage has magical, so let's be generous and pretend it's a best case scenario for that - a unit is standing on a tile with 70% defence, meaning the spearman has a 30% chance to hit while the mage has 70%. We can model this by multiplying the damage by .3 and .7 respectively. However, this still gives a score of 1.488 for the spearman, and 1.092 for the mage.

This is in a best-case scenario for the mage (and actually inaccurate in the mage's favour because I didn't bother separating non-magical melee damage from the magical ranged attack), and we haven't included the value of the spearman's firststrike special at all, so if anything the discrepancy will only get larger. Therefore, it's clear that mainline isn't even close to following this formula.

[fog_of_gold]

[[...]Quite a difference! This isn't quite fair, though, because we're not taking into account specials.

Why do you calculate to falsify and then explain what you've done wrong? -It's true, there is a big different between these two units, but it's "only" a factor of 2.

The mage has magical, so let's be generous and pretend it's a best case scenario for that - a unit is standing on a tile with 70% defence, meaning the spearman has a 30% chance to hit while the mage has 70%. We can model this by multiplying the damage by .3 and .7 respectively. However, this still gives a score of 1.488 for the spearman, and 1.092 for the mage.

You've done something wrong. If you do it that way, you have a score of 5.95 and 4.73, so a factor of 1.26. Thanks, by the way, for this. You've shown my how to get my formula more precise and to be true, I developed the formula while I had a wrong feeling of BfW balancing [balanced for novices and masters] so I'll properly change my complete way of how I include abilities and specials - it'll take even more time until I try against mainline.
[edit: We both have done something wrong: L={~1.49,~0.97}. The differents in factors are about 30%, so because of this and the fact that my current idea of solving is easier, I'll keep my current idea even if it's wrong.]

This is in a best-case scenario

You are right. It's maybe a good idea to always compute with the "usual" best-case scenario - I'll test that.

we haven't included the value of the spearman's firststrike special at all

How often do you get an advantage of this special? -You usually wouldn't attack with a that wounded unit he'd kill you before you did any damage to he expect if you want/need to use the kill-unit-by-suicide, or how you'd call that. If you want/need to do that, you can use every other unit.

so if anything the discrepancy will only get larger. Therefore, it's clear that mainline isn't even close to following this formula.

This is, in my opinion, VERY actuary especially for a such a special unit and it is pretty enough for the usual UMC.

[ancestral]

The only true way you will achieve faction balance is to playtest.

[fog_of_gold]

Sorry to say that to you, but please read the topic before you write any senseless posts. We all are clear about that.

[thespaceinvader]

Seemed pretty sensible to me. You'd do well to follow your own advice. The fact that plenty of people have tried and failed to produce a balancing formula, and you're being told by many experienced developers that it can't be done with any effectiveness, really, REALLY ought to clue you in that they're right and you're wrong.

[fog_of_gold]

it can't be done with any effectiveness

I've never heared that of anyone else than a usual user expect of you, even not from Velensk. Also, it'll prove after I've done the standard deviation so just be patient. And what you do think is better: Having a tool, even if crude, to balance or having no tool to balance?
By the way, I also know a little bit which units are calculated too strong and which too weak. I'll properly need more experience to give clear statements, but I think it's good and helpful to have that. [That it is possible to say that there are special groups are weaker or stronger than this formula tells, tells me, that it isn't a crude formula because it isn't possible to have one, it's because I've done something wrong. But let's discuss about this statement after I've given the groups.]

edit:
I did the standart deviation and the results are partly amazing:
-standart deviation ~22%, ~26%
-with the not includable abilities [lvl0: ability to save gold] and without them makes a different of nearly 20%
-my formula is a very little bit preciser than pauxlo's one
-average power is ~130, ~140

I believe, even a lot of "masters" aren't that precise.

[fog_of_gold]

I just want to be sure you all, if you already looked in this topic, notice I've edited the post. If you want to post something, pm me to make me delete this post or, if you are able to, just delete it.