NOTE: i'm using unicode subscript and superscript characters in this message, sorry if you still use some windows xp with ie6 (this website doesn't work on such systems anyway, last time i tried ...)
NOTE: this thread is NOT about balance in warzone. I do not right now want to discuss whether machineguns are overpowered or not in the current game, though it may give some clue.
Just wanted to point this out, i had a certain misconception in my head, probably many others had it too. In fact, the whole NullBot balancing mechanism is based on that misconception
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If your enemy uses pure tracks, should you make pure rockets?
Consider the following abstract example. Suppose the enemy uses only lancer python tracks, and you can choose between lancer python tracks and heavy machinegun python tracks (and nothing else). Research was equal on both sides. For simplicity, let's think that any lancer tank deals 16x more damage per second ("DPS") to tracks, costs 2 times more than a mg tank and has 2 times less hit points ("HP") than a mg tank.
NOTE: these numbers aren't related to the real balance, and are given as example only; i hope nobody starts saying things like "NoQ said that lancer is 16 times more powerful than heavy machinegun".
Will you produce any mg tanks at all in this situation?
Consider the generic strength of a unit template defined as follows:
DPS x HP / Price²
That is, if you double up a unit's HP, you also double up the price to compensate it. If you double DPS, you also double up the price. Probably Iluvalar will come up with a more accurate model that considers factors like unit repair and micromanagement and other stuff, but we will try to keep it simple right now to make things clear (in fact, we're getting closer to some "high oil game" situation with large armies and little combat tactics). This formula is sort of obvious, i suppose you will trust me on that. If you don't:
Spoiler:
The following differential equations come up from a very simple combat model:
(H₁x₁/P₁)'=-(D₂x₂/P₂),
(H₂x₂/P₂)'=-(D₁x₁/P₁),
where x₁(t) and x₂(t) are ranging from 0 to 1 and represent the fraction of each army still surviving (we assume that x₁(0)=x₂(0)=1, which represents that two armies of the same total price engage in combat), and Dₙ, Hₙ, Pₙ are constants representing DPS, HP and Price of each army's units respectively. Solving the differential equation we see that the duration of the battle is the smaller of the two values
where c²=D₁D₂/H₁H₂ is a parameter controlling battle intensity, k₁=P₂H₁/P₁D₂ and k₂=P₁H₂/P₂D₁. If t₁>t₂ then the first army wins in combat (that is, second army dies first). If accidentally kₙ < c·exp(-c), then we start having "quantum effects": the battle will never end in this model, for the enemy dps decreases a lot faster than your health; the model will no longer applicable to the real life when you start having very little amount of units (e.g. less than 1 unit). What i really wanted to say is that it all depends on {kₙ}, n=1, ..., 2 only, for the values inside logarithms are monotonic functions of kₙ when positive. This immediately leads to calculating the army strength as described above.
Note that the generic strength calculated this way isn't directly proportional to army survivability or something like that. You can only believe that the higher this value is, the more the army will win, but the formula for exactly how much will survive the battle is a bit dirty.
With that formula, we can calculate that rockets are "2 times better" than machineguns in our example. That is, an army of lancer tanks will doubtlessly easily win against an army of mg tanks of the same price.
Now consider an army that includes N% mg tanks. Then it will also have ((100-N)/2)% lancer tanks to have the same price. For which N we get the strongest army? The misconception is that it's for N=0. But by now you can easily see that it's wrong.
For simplicity let x=N/100. have (16-18x)/(x+1) average DPS, (3x+1)/(x+1) average HP and 2/(x+1) average price. Even if we still keep forgetting about micromanagement effects, such as making sure mg tanks take damage first, we have the average army effectiveness
y = (3x+1)(8-7x)/2
represented by the following graph:
4.0 here is the strength of lancer tanks (an army with x=0 mg tanks), and 2.0 is the strength of mg tanks. This means that the strongest army you can make will be composed of ~40% mg tanks and ~60% lancer tanks, and it will be ~1.5x stronger than a pure lancer army! Moreover, even with around 80% mg tanks in your army, you will still not be weaker than a pure lancer army. That is, there's no point in having an army with ridiculously huge firepower and little health, it is always better to keep the two more or less balanced.
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Of course, in a real warzone game these values will be quite different. Yet i believe this "combined arms effect" is highly underestimated by many players. For a rocket player it is not only necessary to build machineguns to counter cyborgs, but also to provide the army with necessary hit points, probably even if it means spending more on research.
Last edited by NoQ on 03 Mar 2013, 13:05, edited 4 times in total.
i'll try make my own model of battle without annyoing misunderstanding math
NoQ wrote:This means that the strongest army you can make will be composed of ~57% mg tanks and ~43% lancer tanks, and it will be ~1.5x stronger than a pure lancer army!
as i understood 100% of rocket tanks can be 10 tanks, but 100% of MG tanks can be 20 tanks, is not it?
Fixed some mistakes Please read again everybody (:
i'll try make my own model of battle
What else do you expect to see? What is written is precisely "the army's overall hit points take as much damage per second as the enemy army inflicts per second", i don't think you'd easily come up with anything else.
First of all, i totally agree that a mixed army is usually stronger. The reason is simply that every weapon supposedly has a weak point. A MG tank will take out cyborgs fast, but will die when facing lancer tanks. But gunner cyborgs at the same price can take out that lancer tanks by outnumbering. Which actually seems to be the main effect in your toy example: since the HMG tanks are half as expensive, they will survive longer against the lancers.
As for modeling such cases, I suggest looking at randomized methods, such as Monte-Carlo simulation. The problem with the mathematic-analytical approach is that it does not take into account that our armies usually are finite, with a low number. If the optimum mixture is to have 3.5 lancer tanks, then you will have a hard time achieving the optimum...
So maybe instead look at a fixed budget, then try those n combinations that arise from this.
The same thing arises with damage. If a unit can deal one shot with 1000 damage (and the enemy units die at 100 damage), it will still kill only one unit, not 10 with this shot. A unit that can deal only 500 damage, but with 50 shots instead of one, it can take out 5 enemies in the same time.
The simplest way to handle these things is actually by simulation. Choose the weakest enemy in range, deduct the damage, if dead remove the unit. Repeat with the next unit to fire. You can trivially even take the chance to hit into account here, except you then need to run multiple iterations.
I wouldn't be surprised if the optimum even varies slightly with the mixture used by the opponent! If the opponent also has some MG tanks to pack the damage while the lancers go for the kills, you might need to further increase your MG tank amount to survive until you destroyed the opponents MG tanks first and then face their lancers. You need enough lancers to take out the opponents MG tanks before your MG tanks are out, and then some more to take out their lancers, too...
Yeah, right. The "quantum effects", i mentioned it a little too. I think most of them don't change things significantly. Some change things to the right direction (such as lancer overkill effect or putting mgs in the front row). There is also a lot of effects of things like repairing units, which you will hardly emulate anyway.
The reason is simply that every weapon supposedly has a weak point. A MG tank will take out cyborgs fast, but will die when facing lancer tanks.
To agree with that you don't need to calculate anything. Everybody understands that if you don't make a weapon with modifiers specially suited for killing cyborgs, you're doomed, this is trivial.
since the HMG tanks are half as expensive, they will survive longer against the lancers.
And this is actually what i was trying to say. Even if they did no damage at all they could still be useful. But many players straightforwardly make pure rockets when they see their enemy making pure tanks, believing that modifiers will outweight everything.
Speaking of "damage takers" and "damage dealers", a strategy which seems to be in place in MMORPGs already. Has anybody experimented with deliberately designing tanks for maximum defensive capability? Sensors seem to offer the best HP/cost, interestingly enough.
It would actually be an interesting add-on to warzone if we had a shield weapon that takes 1 turret slot. Most people will use it with dragon bodys I guess. But say it has a radius of 3 tiles, and it reduces damage to 1/4, 1/2 and 3/4 depending on the distance from the shield generator.
That would open up strategies such as maxing a really heavy unit with nothing but the shield generator and moving it in front to take the damage, or also rather light shield units and keep them just behind your main damage dealers, maybe intermixed with repair units.
In the first case you might want to ignore that tank mostly - and focus on the others (but your base defenses probably won't ignore it!). In the second, it may pay off to take them out first to do full damage to the MBG.
Speaking of new weapons, I'd also like to see a suicide bomber unit. Huge splash damage, also on death, and 1 tile of range. Don't use it on features in your base accidentially. Could be an interesting strategy to destroy defenses, send suicide tanks there. Could be a fun use for VTOLs: have enemy sucide tanks explode right in their base or MBG... better not leave them around unused and unattended. They will likely be harder to use than one things - say if you have them explode at 50% damage, they likely won't make it to a fortress (unless you protected them with enough distraction). Maybe make the damage based on the weight of the unit, so that a light hover does just take out a wall, while a heavy tracks sucidie tank can take out a fortress if he gets through (and supposedly the C4 weapon is heavy, making such a base destroyer tank really slow and dangerous to use).
Add in radar jammers, and try to sneak a heavy sucidie tank into the back entrance of a base...
While testing out new builds of NullBotSW, I've been noticing that, oftentimes, enemy units would barely survive one or two shots from some weapons, with only a tiny bit of HP remaining. In this case, units armed with low-damage, rapid-firing weapons, such as a Twin Assault Cannon, Twin Assault Gun, or even a group of Light Cannons or Minipods, would be sufficient to finish off these stragglers quicker, and I'm considering having NullBotSW start producing these kinds of units to supplement its anti-tank forces (at a rate of, say, 1 per 4 anti-tank units), which mostly use high-damage, low rate-of-fire weapons such as Heavy Cannons or Lancers, which are meant more for penetrating the thick armor of heavy tanks than for quickly taking down light tanks.
By the way...
NoQ wrote:Consider the generic strength of a unit template defined as follows:
DPS x HP / Price²
That is, if you double up a unit's HP, you also double up the price to compensate it. If you double DPS, you also double up the price. Probably Iluvalar will come up with a more accurate model that considers factors like unit repair and micromanagement and other stuff, but we will try to keep it simple right now to make things clear (in fact, we're getting closer to some "high oil game" situation with large armies and little combat tactics). This formula is sort of obvious, i suppose you will trust me on that.
I tried to apply that kind of price-per-HP and price-per-dps model (where the price was doubled whenever the HP or dps was doubled) while Contingency was still in its early balance-planning stages, but quickly saw that it had its share of balance problems due to the simple fact that a unit with as much HP and dps as the combined HP and dps of a group of 2 or more smaller units would be able to deal more damage before dying than the group, since whenever a unit in a group dies, it can no longer attack stuff, which would mean that the group's dps would be reduced.
Edit: I believe that I started talking about this kind of system's shortcomings here.
Creator of Warzone 2100: Contingency!
Founder of Wikizone 2100: http://wikizone2100.wikia.com/wiki/Wikizone_2100
a unit with as much HP and dps as the combined HP and dps of a group of 2 or more smaller units would be able to deal more damage before dying than the group, since whenever a unit in a group dies, it can no longer attack stuff, which would mean that the group's dps would be reduced.
I already explained twice what i think about it in this thread, i think. Of course i'm aware of the shortcomings of the model, i'm just saying they're not relevant to the final result.
What you mean is that since all bodies in the standard game are "light" (by which I mean they fit for cheap weapon). Viper: lightest. Cobra: lighter, python : light. And there is actually no REAL option dedicated for expensive weapons (like lancer), they end up with all the same design flaw to have much less HP than DPS. And thus fail to be "squared". Right ?
Than you argue that throwing smg bugs (really best at HP/cost) in the group would increase the HP and therefore balance the DPS/HP square ratio and therefore have a positive impact on the whole army. Ok I got it . But here is where you got it kinda wrong :
« Even if we still keep forgetting about micromanagement effects, such as making sure mg tanks take damage first »
You are assuming that it is the owner of the units that mostly choose where the bullets will go and you got it wrong ! It's the opponent that will chose his target. What if the lancer die first because they are targeted by the opponent ? I believe it's what the targeting AI should try to do all by itself, even if the opponent input no direct orders. Even if you try to micromanage it as much as possiblem your lancers gonna die first. Gaining only tiny to none grouping bonus. Than you end up with a misfitted army that have much more HP that it have firepower and you are not is so much good position anymore.
By the way, you next major improvement is to replace the price part of your evaluation "/price²" by my figure count function :
Effectiveness modificator = (f²+f)/2
Where f (stand for number of Figure) = Power avalaible / price
Unless you're caught unprepared, being completely unaware of the enemy army location (which may be possible in fast unit battles involving hovers or cyborgs, but hard to imagine in our example), or failing to micromanage properly during a retreat, you normally have a chance to put meat shield tanks in front of your army, making the enemy hit only them no matter what droid of yours they click on or what did the micro-ai decide.
my figure count function
Just curious: was it ... documented anywhere? That is, the reasoning behind it, whether it's purely empirical or arises from certain calculation? What particular extra factors does it consider?
Unless you're caught unprepared, being completely unaware of the enemy army location (which may be possible in fast unit battles involving hovers or cyborgs, but hard to imagine in our example), or failing to micromanage properly during a retreat, you normally have a chance to put meat shield tanks in front of your army, making the enemy hit only them no matter what droid of yours they click on or what did the micro-ai decide.
Assuming you can move a group of unit behind and that it can still fire 100% properly while behind distant enough so you cannot be rammed into. Which sound far fetched.
Seriously, pretending you can choose which of your units will receive the damage is dubious. Otherwise, everybody would build walls every where on the battlefield. .
I don't mean that you can't use your mg units as a meat shield if you have those, but assuming that they gonna be 100% efficient and blend perfectly is another story.
NoQ wrote:
my figure count function
Just curious: was it ... documented anywhere? That is, the reasoning behind it, whether it's purely empirical or arises from certain calculation? What particular extra factors does it consider?
I mentionned it many time.
It's the integral of X+1 which is itself the integral of 1 (unit compared to itself) with C=1 because of rounding (damaged units do full damage). I figured that C=1 empiricaly. After I compared my first try with the facts ↓ .
You can easily verify it by mentally simulating some low figure count :
1 unit = (1²+1)/2 = 1
2 units = (2²+2)/2 = 3 units in a row
3 units = (3²+3)/2 = 6 units in a row
...
We don't really have a "units in a row" thing in the model. In fact, as i mentioned in the first post, the computed power has no meaning at all, apart from "the army with more power wins"; double power wasn't supposed to mean "it can take two armies like this". It might be a nice improvement, but does it actually affect weapon mix ratios this model provides? (didn't think yet) I guess it's, at most, just yet another quantum effect that appears when unit counts are low enough and the model isn't applicable anyway for many other reasons?
I don't mean that you can't use your mg units as a meat shield if you have those, but assuming that they gonna be 100% efficient and blend perfectly is another story.
You were just saying that they gonna be -100% efficient, which is also far from the truth. All i need is to have their efficiency positive.
We don't really have a "units in a row" thing in the model. In fact, as i mentioned in the first post, the computed power has no meaning at all, apart from "the army with more power wins"; double power wasn't supposed to mean "it can take two armies like this". It might be a nice improvement, but does it actually affect weapon mix ratios this model provides? (didn't think yet) I guess it's, at most, just yet another quantum effect that appears when unit counts are low enough and the model isn't applicable anyway for many other reasons?
Well, it's a multiplication of the power. It's the exact direct effect on the total efficiency they have due to number (or price). So I guess, it's an improvement
NoQ wrote:
I don't mean that you can't use your mg units as a meat shield if you have those, but assuming that they gonna be 100% efficient and blend perfectly is another story.
You were just saying that they gonna be -100% efficient, which is also far from the truth. All i need is to have their efficiency positive.
I'm not saying it have negative effect. The question is if the mix have better efficiency than lancer alone. You say 40% seem the best. I will have to disagree with that for the reason above.
But maybe 5% or 10% ? Yeah, I'd estimate that. For the reasons you mentionned. But not 50/50 like you are implying A pure lancer strategy would be better than that. Unless you play against an AI and you could use your meat shield stuff at some epic level.
Dunno if I am doing it right, but I put 10 tank killer against 6 twin assault mg and 4 tank killer, the ten tank killers only lost one unit. Maybe only works with lancers?
Tank killers are pretty tough, but not as tough as the equivalent amount of twin assault cannons, however it depends if you can get them close enough en masse - I put a group of 150 TK against 150 AC and the AC one was left with like 30 odd units left so it was a massacre on both sides lol. The main thing was that the AC were on hover and got real close fast, then they just chewed them up...I think if they were on tracks it would be a different story.
Thinking on this, it is important to bring in grouping to the equation, ie with TK and the like if you don't hit them en masse you are done for. I will try with TI techs a little later, ie lancer and hmg.
Moving back instead of forward
Seems to me absurd
~
Metallica - Eye of the beholder
Please read again everybody (:
Could be an interesting strategy to destroy defenses, send suicide tanks there. Could be a fun use for VTOLs: have enemy sucide tanks explode right in their base or MBG... better not leave them around unused and unattended. They will likely be harder to use than one things - say if you have them explode at 50% damage, they likely won't make it to a fortress (unless you protected them with enough distraction). Maybe make the damage based on the weight of the unit, so that a light hover does just take out a wall, while a heavy tracks sucidie tank can take out a fortress if he gets through (and supposedly the C4 weapon is heavy, making such a base destroyer tank really slow and dangerous to use).
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