The balance formula thread

[Llamadeus]

It's why most serious Starcraft games in Korea rarely involve many tech upgrades

High-end StarCraft play is short, and is not played on large maps, because that's where the initial economic peaks are, and the games are invariably played for rush.

This is so wrong I can't believe how wrong this is.

[Argh]

Show me a serious, for-money match that involves the whole tech tree, or a huge mapsize. I can't claim to have watched every Korean replay ever, so I'd be very, very interested in seeing that if it exists, tbh.

[Llamadeus]

http://www.youtube.com/watch?v=dKFthNcxTZ8

This was the final game of the final match of one of the OSLs of last year, basically the most prestigous Starcraft tournament in Korea. It's not uncommon to see both players reach the ends of their respective tech and/or upgrade trees.

I'm not sure if you'd qualify the map as a huge one, but even the smaller ones can reach the endgame in a similar fashion.

Sometimes the game gets to a point where both players are running around with maxed-supply armies and the size of their economies translates to not how big or powerful their army is but how quickly it can be replenished.

It's pretty map/matchup dependent though. This map (http://www.youtube.com/watch?v=dBaQTznNZxU&fmt=18) basically devolves into battlecruiser standoffs/stalemates half the time in pro TvT, whereas even the longest zerg versus zerg games don't go beyond two bases per player.

bonus video: http://www.youtube.com/watch?v=YaoOPKP5LJY

[Evil4Zerggin]

Regarding models:

Some may criticize models that only take into account a subset of unit stats, which are themselves a subset of the entire game design, for being too limited in scope. I would reply with the following:

• More general models are rare, especially ones that are any good.
• Even a good (but conceivable) general model would almost necessarily be approximate in ways that are not well-defined.
• Even specialized models with clearly understood limitations are rare. What makes you think someone is going to suddenly going to come up with a general model with clearly understood limitations?
• I would say it is more useful to have a specialized model whose limitations are clearly understood than a general model whose limitations are not.

[Pressure Line]

I would say it is more useful to have a specialized model whose limitations are clearly understood than a general model whose limitations are not.

the important part of that point is the part about UNDERSTANDING the limitations. every single one of these threads (including Tired's original) thread has pretty much been "omg i balance with this formula, ur all doin it rong." with the proponents of formulaic balancing sidestepping the issue of what the formula does/doesn't include and simply saying "Well a formula is obviously better than best-guessing based on personal experience because its more scientific, and uses maths and stuff."

btw, has anyone (who isn't Tired or one of his cronies) actually seen the formula? or studied it in depth? do we even know what's in it?

[BaNa]

btw, has anyone (who isn't Tired or one of his cronies) actually seen the formula? or studied it in depth? do we even know what's in it?

I think the "my formula owns all" was just tireds ego. He did post a spreadsheet somewhere. Also, aegis has a new formula based balance, with posted formula methinks.

Argh:
I think talking about chaos in a game like spring is silly. The words chaos, chaotic are usually used to denote deterministic chaos. That refers to systems where small differences in starting parameters have a bigger and bigger effect as time goes by. Note that these systems are defined by the starting parameter set, and are wholly deterministic. A game like spring has active agents making decisions every second, so it can hardly be called deterministic. You could say the system is nonlinear, but so what? All that means is that superposition of things doesnt work because F(A+B) != F (A)+F(B).

Using game theory to model it fails on the specific level (you may be abe to model theoretical strategies) because there are so many options.

I agree with evil up there, lets not try to say we can model player decisions for the whole game and just stick to simpler theories.

[Argh]

I think talking about chaos in a game like spring is silly. The words chaos, chaotic are usually used to denote deterministic chaos. That refers to systems where small differences in starting parameters have a bigger and bigger effect as time goes by.

There's a lot of chaos in most Spring games, though. And there is definitely a point where things get so messy that it's hard to imagine a mathematical way to prove the outcome.

For example, shots may fall in random places. With some units, this may matter a lot (P.U.R.E.'s MortarTank is a really good example of this). A unit may swerve right or left due to the pathfinder stuff. There are so many small details like that, that are in Spring that aren't in Starcraft, for example.

Players may make somewhat random decisions during various moments that have affects that are crucial in retrospect- those "so, that's when I really lost this game" moments. Sometimes it's the decision to move some units right, instead of left, at one moment. Sure, we can argue that these decisions are "rational", but that's bullshit, imo. One of the biggest things about most RTS gameplay is that players do not know everything. So their decisions are often hunches, not necessarily rational behavior.

As for general theory stuff... meh, my general theory is that time and space are the two largest factors in terms of how well players can cope with their situation. If players are pushed too hard on either by circumstances, it becomes more and more difficult for them to win, regardless of other factors.

That, and RPS stuff is very important. Everything must have a counter that works. It doesn't matter if it's "balanced" at cost. There are so many other ways to achieve "balance", in the sense that players mean, like making a counter hard to use, making it have a recharge time, making it cost significant resources, etc., that cost is just one factor, and may not even be the decisive one.

@Llamadeus: I'll check that out when I have some downtime. I'm actually very interested in what that looks like, frankly.

[BaNa]

Argh: Random does not equal chaotic. Chaos is when a deterministic system gives you results that are so sensitive to starting variables that they seem nondeterministic.

Even if we discount the fact that a game in spring is not a deterministic system, it would be hard to support the fact that such small differences have such huge weight. In most games it doesn't matter if my stumpy paths one elmo this way or that.

Yes, there may be important moments in gameplay but imo it is rare that one such moment decides everything. When you micro lines of rockos, it usually isn't 1 stray rocket that hits which fucks up your game, but things on a bigger scale: your overall quality of micro, whether the command time you spend on micro would be better spent on eco, things like that.

IMO a formula that calculates cost can be a good starting point for balance, then manual balance / tweak is inevitable

And btw, when is a game balanced? Is it when all units are played with the same frequency?

[Argh]

And btw, when is a game balanced? Is it when all units are played with the same frequency?

I'd have to say that my answer to that is when all units are useful for their given roles, and that the roles actually matter on a frequent enough basis to justify their presence in the game design.

IOW, if you have a unit nobody builds, because there is no point, or a whole class of units that nobody builds most of the time, because something else does the same job better except under spurious circumstances, it's a game full of newbie traps, which is bad game design practice, and you should either cut stuff or fix the problems.

I'm not saying that's easy to attain, but I think that's the gold standard.

[aegis]

IOW, if you have a unit nobody builds, because there is no point, or a whole class of units that nobody builds most of the time, because something else does the same job better except under spurious circumstances, it's a game full of newbie traps, which is bad game design practice, and you should either cut stuff or fix the problems.

Sea and air!

[smokingwreckage]

because something else does the same job better

because something else does the same job better

because something else does the same job better


See how when you read it a few times it doesn't quite apply to sea and air? (Except w.r.t. hovers)

[Sleksa]

Argh in da house yo, teaching blizz how to balanze shizz!

[KDR_11k]

I still say balanced is when the set of viable actions is equal to the set of intended actions, i.e. the game plays as the design says it should. Yes, I'm pushing all the weight on the design but that's because only the design can say what's right and what's not. The design may be faulty, may be no fun but the balancing is there to make sure the design is implemented properly. Let's say you have two units with different cost effectivenesses, if the design says they have to be like that then it's properly balanced. Of course the design better has a reason for saying that (e.g. tech levels) so the result makes sense. What designs usually include is a certain occurrence rate for different units, e.g. intending an attack group to consist of mostly infantry, some tanks and a radar vehicle and getting those right is a part of balancing. Of course I somehow doubt that people here design their mods with ideas like that and often go for "let's just throw a random amount of units at the player and let's see what happens, then tweak it until everything gets used".

[Thor]

"let's just throw a random amount of units at the player and let's see what happens, then tweak it until everything gets used".

You just described how absolute annihilation was created

[Tired]

Well, you kids certainly haven't improved much since I left. ~~

Regret, looks like you pulled that out of your butt. Nothing wrong with that if it works though. Could you run 7 units through for us please and post results?^^

A few fundamentals:

1) Most of the comments here don't directly address the issue. Personally, I think most of you are too dumb to follow the basics of the argument, which is all I've ever outlined. If this offends you, feel free to post off-topic blather about Math = smileyfucks.

2) Argh, your propositions are terrifically vague, and couched in the sort of egotism I'm pretty well known for. I resort to egotism to demean those who debase arguments that they don't even try to understand. That, and because I'm sexy. Why do you use it?

That being said, you're outlining potential key concepts and discussing the subject matter seriously. Most people here can't manage that. Can you offer anything more concrete, or possibly integrate notions not entirely of your own device? I'd like to see an expansion on practical implications of spatial control if you have one, as it's definitely a key concept in game play. Are you thinking of statistical methodology?

3) My "proponents" might tout my test formula as complex, but I never have. Initially run as a proof of concept, my explanations were an attempt to initiate the sort of dialogue that has also failed to initiate here. Nature has managed to balance out the universe in strict accordance with mathematics. If you believe that a game is impossible to balance, then I believe that you're selling your own intelligence short. Then again, maybe you're not.

4) Raptor, in the case of your Janus that would obliterate static defenses, you'll find a hefty vulnerability to Fleas. Also, you are using someone else's cost for a HLT. The argument you put forth as my own was a straw man constructed of your own impressions of my arguments garnered from "interviews" conducted where you barely understood the questions. If you don't know what a straw man is, look here: http://en.wikipedia.org/wiki/Straw_man.

Key Concepts:

1) 1 Metal = X Energy = Y WorkerTime. Solve for X and Y. In the event of different resources, 1 Resource A = X Resource B = Y Resource C = Z Resource D.

2) Median Battle Time: The amount of time required for one homogeneous unit to kill another. In Spring mods with bombers, this also equals the amount of time required to complete a pass and reload.

3) Relative Travel Time: The amount of time required for a unit of an arbitrary speed to travel from one end of an average map to an opposite end.

That's for starters. If anyone doesn't understand what these mean, or their implications, how about asking instead of commenting? Everyone has an opinion, independent of correlation with factual evidence. Absent the latter, what meaning in the former? Since those who bothered to read that statement are about to go off and ignore it, you suck; crawl into a hole and die.^^

I've so not missed you guys. =)

[Saktoth]

The feeling is mutual tired.

Raptor, in the case of your Janus that would obliterate static defenses, you'll find a hefty vulnerability to Fleas.

You're assuming a mod with fleas, and you've just described an RPS counter structure. Janus is being balanced by your theoretical flea, not by its stats/cost. Design is the key. I know that you 'assume that OTA has given you a good unit setup' (Id argue its barely the case in OTA, that it is just using the shotgun approach to balance) but that isnt the case in all games, and the balance relies on that unit setup. The weight or value of an individual attribute, speed, range, etc depends on which units exist already in the game and how they are used.

2) Median Battle Time: The amount of time required for one homogeneous unit to kill another. In Spring mods with bombers, this also equals the amount of time required to complete a pass and reload.

A 'homogeneous' unit? How do you determine the stats for this? You cannot simply average the stats of all units, as in practice some units are used more than others and thus change the pace and flow of the game and the in-practice median battle time (and which are used depends on balance). You can take one unit as a baseline, or create a theoretical baseline, but this is arbitrary. It doesnt reflect the actual game.

Ugh and dont get me started on the bomber thing. 'Spring mods with bombers'? Bombers in several mods have to refuel after every bombing run, how does that relate to your median battle time? What if a mod has a very low actual median battle time but its bombers manouver very slowly? What you mean here is 'In TiA, my calculated value also happens to match the bomber reload time, which is convenient.'

3) Relative Travel Time: The amount of time required for a unit of an arbitrary speed to travel from one end of an average map to an opposite end.

If the speed is arbitrary then you are just inventing numbers again. If speed is just an average of all units then it doesnt reflect the actual percentage use of units within game (Which will change actual average travel time). Garbage in, garbage out.

Im not saying mathematical balancing isnt possible and useful (though only as another tool in the cabinet), but it needs an empirical foundation.

[KingRaptor]

4) Raptor, in the case of your Janus that would obliterate static defenses, you'll find a hefty vulnerability to Fleas.

Right. So, in lieu of building any of the possible counters (counter-spamming Flash/Peewee/AK/more Fleas/Jeffy/Leveler - and that's just the BA set - or making forward LLTs), we can scale the Janus to fire five times as fast at one-fifth the damage per shot. According to the formula, this should require no change in cost.

Additionally, as I said before, this is not specific to one unit. Try having double-range LLTs that cost 50% more, for instance.

Also, you are using someone else's cost for a HLT.

I never mentioned the cost of the HLT or any other unit than the Janus in the stated example. The HLT was mentioned because it provides a useful benchmark for range. The example would hold whether HLTs cost 150 or 1500 apiece (and here we can see the issue of utility in costing - if HLTs cost more, the outranges-HLT-Janus would be more effective against them as it can kill more of them in the same time - yet it would be less useful, because HLTs would be weaker and there would be less need for a specific counter to them).

The argument you put forth as my own was a straw man constructed of your own impressions of my arguments garnered from "interviews" conducted where you barely understood the questions.

Actually I didn't have our conversations in mind at all when I wrote the essay; instead I considered your forum posts and what I think is a fair interpretation of the changes you made in TA/SA.

If you don't know what a straw man is, look here: http://en.wikipedia.org/wiki/Straw_man.

Cute. Did you look up "ad hominem" too, while you were there?

Key Concepts:

1) 1 Metal = X Energy = Y WorkerTime. Solve for X and Y. In the event of different resources, 1 Resource A = X Resource B = Y Resource C = Z Resource D.

Falsely assumes a constant relationship between the value of the different resources, ignoring issues such as availability (especially in games where the resources cannot be interchanged, or where the exchange rate varies such as in Age of Empires or with CA's overdrive). On, say, a Starcraft map which had a mineral count off the charts but only a tiny handful of geysers, Vespene gas would have more comparative value than on a map where the two resources existed in more proportionate amounts.

2) Median Battle Time: The amount of time required for one homogeneous unit to kill another. In Spring mods with bombers, this also equals the amount of time required to complete a pass and reload.

Such a median is a number of very low significance. It's completely useless even for estimating how long two significantly different units will spend fighting, and forget about factoring in unit intentions (running past the enemy instead of stopping to engage, for instance), other effects of unit movement, or unit mixing. There's a reason statisticians consider numbers like range, interquartile range, standard deviation, and the like.



What it boils down to is this: At the level you're doing it, mathematical balancing is on par with trying to use classical physics to explain the spin of the electron, or quantum mechanics to work out the forces acting on an ocean-going supertanker.

Actually it's worse; it's akin to using either branch of physics to predict the stock market or explain population fluctuations within an ecological community!

[lurker]

Actually it's worse; it's akin to using either branch of physics to predict the stock market

[smoth]

HEY GUYS! I HERD THERE WAS SOME DRAMA IN HERE!

+1 drama thread post.

Can't be caught missing out on some drama.

[JohannesH]

Tired, do you think that any unit which fits to the formula is (equally) useful?