SleekDD

Join Date 05/2006

Yet Another Combat Suggestion: Balancing Attack and Defence

Introducing the Normal Distribution

Hey guys,

This is my first post, be nice.

I've read quite a few suggestions to tweak combat, adding options or changing the rules and I decided I'd spam the forum with my own little idea. The objective of the post would be to suggest a change in the balance to improve the use of defence.

So, what wrong with the balance?

Well, as I played the game and read posts on the forum, there seems to be a penchant for focussing on the attack and first strike. As I heard, the combat system will undergo a change in the 1.2 Patch with the defender receiving a 'parting shot' meaning that destroyed ships will be able to fire back. Some claim this will shift the focus a bit more to defense, but I believe this change will make the attack even more important. I will try to keep this instinctive and brief but there quite a bit of math behind it.

As things stand now, the randomizers used in the game to determine the result of attacks and defences are equally distributed (ie. every number has the same chance of coming up). No problem, right? We just take the mean to determine the effectiveness of our design.

Well, that works...in large samples. Let's take the example of a single six-sided die. If I asked you what I would roll, would you answer 3.5 (the mean of a single die), or would you say any number is just as likely to pop up and therefore, it's a completely wild guess?

Hint: you can't roll a 3.5.

Now, what if I said I'd roll 2 dice and add the results together? What would you say? 7?
7 is the most likely number to turn up. Let's compare the odds of 7 turning up compared to say, 2.

2's easy, it just has one chance: 1, 1.
7 has more chances: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1.

Wait a minute. With one die, every result is just as likely to pop up, but when I roll two dice, that isn't the case anymore. Congratulations, you have discovered the 'Central Limit Theorem'. I will spare you the details but it means that most probability distributions will change to a normal (bell-curve or Gauss distribution) distribution if you take repeated samples (such as throwing more than one die).

This is what those people who play theoretic battles do. They're assuming they have a large sample and will therefore roll an average result. However, I found that battles are small samples and therefore, the mean is not nearly as useful a guideline as one would believe it was.

The main snag here is called 'variance'. People know means but few know variance. It boils down to how predictable/stable your results are. Variance is also a(n important) measure of risk and I believe this is what's keeping the defensive systems from being as useful as they should be at face value.

You see, defences are all about limiting risk, blocking an attack and ultimately, trying to keep your ship and crew in one piece. Once the variance becomes too big, the use of defenses drops to zero. The variance increases as the potence of your tech increases and as such, defences become less usefull. I'll try to explain this but it's a little abstract.

Suppose you have a Frigate 16 HP, 4 attack, 4 defence and you're fighting an identical vessel. Now, half the time, you should penetrate your opponent's defences and damage him. Given the low yield of the equipment, you can do at most 4 damage (and so can he). Anyway, this means you will both need a few rounds (at least 4) to determine the last man standing. So, many rolls are taken and the results will lie closer to the mean.

Now, image the same Frigate but this time tricked out with 40 attack and 40 defence. Suddenly, a fluke roll will end the fight. In fact, it doesn't even has to be a fluke roll, just a lesser roll (say, 10) compared the a better roll (say 30) will kill off the ship. So, odds are that fights become plagued by a greater variance.

But what if it is so likely you'll lose your ship? I mean, sure, you can't block everything but if the result is a total loss, why bother? Just stack op on weapons and beat the snot out of him! And by stacking on weapons, your chances of taking the enemy out of the game improve drastically. The best defence is a good offence, right?

The Cure

So, how do we fix it? Introduce the normal distribution (which has a lower distribution than an equal distribution over a similar range). How? Well, that's the easy part actually.

Here are some options which should also be fairly easy to implement:

1) Roll a die for every weapon/defence on the ship and add them together. So a ship with ten plasma beams get ten rolls and has them added together. This makes use of the Central Limit Theorem. Thing is, as you stack of equipment, you will encounter less variance (more rolls) compared to more variance (higher ranges) as the game progresses. You dampen the variance increase you would otherwise find.

2) Introduce a normally distributed variable and use that one instead of the one being used now. This one is trickier. You see, you have to dictacte a mean and a variance to the computer, but you can't really set clear boundaries (unless you're using cut-offs), so if you're not careful, crazy rolls are possible although they are very unlikely (in the order of 0.01% or less).

3) Just keep on rolling as you are used to but roll X times for the same ship and take the mean. This is the Central Limit Theorem yet again. This gives designers the greatest control over the variance. The more rolls they allow, the smaller the variance.

4) Beef up the hit points of the hulls. This is a fairly simple thing to do (players can do it just the same). The drawback is that you would need a large increase to make sure defences are useful in the end-game since the ranges are so high.

Word of caution:

Although variance is a measurement of risk, I feel that some variance is needed to keep things interesting. Many tactical games (PC and boardgames) make use of dice just to introduce something of a random element (and tension) in the game. There's a balance to strive for. To little variance creates a boring game, too much creates a dibillitating effect where gambling is encouraged.

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Let it ride on the passline, come on lucky 7!!!

PS: Math looks sound, but all I know I learned in one Econ Stats course at University, if you increase the hp and force fights to go a few rounds defense will automattically become more important, it's the one shot kills that make defense useless.

But reducing the variance would also help reduce one shot kills (Unless your weapons far outclass the opponent)

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So it all boils down to safety in numbers.

Come on, daddy needs a new pair of shoes! (And some fake ID, while you're at it.)

I like the idea in general, and like it a lot, especially since it would sort out some of the criticism that has been given on the combat system, including that ships are too easily destroyed and that defenses are "useless"; both related but altogether different topics.

"Okay, this here gun has a damage range from 0 to 20, and all of 'em numbers are created equally, that's the law," is not something I like hearing when you're trying to figure out what to buy for your ships. Sure, like Sleek pointed out, if the ships keep slugging it out on eachother long enough, the odds'll even out eventually. But we're talking big numbers here. No, ten shots each won't cut it. And most battles don't even last five (except if you count bumping into space debris).

Cue Gaussian distribution--get rid of that old uniform distribution, man, that's junk! Gaussian's the future: it's like slapping insurance onto your vessel! No, it doesn't eliminate those times when your shields feel powered by the battery from the captain's '70 Buick, but it tones down on them. And when the shields even work more predictably than said Buick, there's less incentive towards leaving drydock without them. Seriously, shield theory is obviously not an exact science. The button to raise shields on my cap ship is labelled "I'm feeling lucky".

Players artificially dampen this risk on the offense by using a platoon of smaller vessels. They fire a lot of rounds and chances are good that the sum of them will be about average. Besides, it helps soak the one-shot, one-kill mentality. Sleek's idea of rolling for each weapon sounds good (and kind of emulates this), but there may be a catch with Death Star helping out with beam assists (careful with that Planet Buster, fellas).

On the downside, it would require retweaking of weapons and shields. For instance, Plasma now has maximum damage of 2. A possible tweak could be to set the mean value to 2, and variance to accomodate down to 1 or zero, then mirror to the other side, so 3 or 4. The chances of getting 2 could be, say 50-60%, the chances of getting 1 or 3 (deviating 1) could be along the lines of 20-30%, and the leftovers for 0 and 4. Just an example.

Basically, remodelling in this sense could bring back the capital ships while not getting rid of the smaller ones. Size matters. Either way.

Tarbo like.

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Yes, age of wonders has the same uniform distribution and some of the same arguments against it was made.

But at least AOW allowed defenders to strike back (unless you had the special first strike ability), something Galciv2 does not YET which makes defense even less useful.

That alone helps a lot i think

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The basic idea of a parting shot is to allow ships that have been destroyed to return fire one time before being destroyed. Now, I agree this will reduce the effect of the first strike but it will worsen the balance on off/def. The reason I believe this will happen is based on the MAD-principle.

MAD stands for Mutually Assured Destruction.
So, what happens with the new combat is that you are essentially guaranteed a return shot, whether your defences worked or not. This means they become even less important since survival is not a prerequisite to do damage.

What is the best tactic then?
Well, if your defences are solid and reliable, you can install them on your vessel. They will survive the attack and fire back (no need for a parting shot). As it is, defences aren't really reliable and become less so as the game progresses so ships become more and more likely to get blasted in one shot anyway. The problem is that the off/def values become too large with respect with your HP so a slight deviation from the mean results in a total loss and a pricey insurance claim.

So, if defences become less important and you are guaranteed a retaliation anyway, why bother with them? Just churn out as many offence-oriented ships you can get your hands on and make sure that your parting shot makes an everlasting impression.

If this is correct, the parting shot will not shift the balance in favour of defences (since survival becomes less important) but will turn battles into bloodier affairs and possibly create a race for the cheapest fighter with credible offensive powers; a kamikaze if you will.

PS: I'm having a lot of difficulties to access this thread (all the others are just fine). Anyone else having this issue? Did I do something that ticks off this forum/server?

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Interesting post.

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Brings to mind a certain famous saying... "There's lies, damn lies, and statistics".

The possibility of unexpected results due to variance is what keeps the game interesting. Besides, your analysis completely ignores the concept of fleet battles - my experience with the new combat rules is that if you do not fit your ships with appropriate defenses, you lose many more than if you do. The change is designed to make the attacker rethink their ship design and redress the existing total imbalance in favour of the attacker.

When you've got a fleet of dreadnoughts with 100 beam attack and no defenses attacking a fleet of 10 beam attack chaff, those combined parting shots will destroy some of your expensive ships. Change it to 60 beam attack, 40 beam defense and you'll get a few damage points at worst while still killing all the chaff, but when that fleet comes up against one of similar power, the battle will be much more interesting under the new rules.

I've played 1.5 games with these rules at suicidal difficulty so far, and when 2 fleets of equal size (i.e. HP) and power meet, then the one with the most appropriate defenses usually comes out on top. Just proves the saying at the start of this post.

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I believe the issue lies with the discrepancy between attack and defense, and the proportions towards hit points. You see, when a Drengin fighter carries 100 mass driver attack --and I've had it happen-- then I lose all incentive to add any defenses to my ships. I could never match 100 defense, and even if I could, the variance would be so high compared to the hit points of my ship that a small mishap would see it blown to pieces. Since defenses are quite expensive, you're better off building a horde of small 100-attack fighters than bother with defense.

This is a mid-late game problem, not a general problem. Part of the solution could be in applying a normal distribution so that the values are more predictable, which makes it acceptable to match attack with defense.

I believe that, unfortunately, returning shots won't readily resolve this issue. It will give the defender better chances of inflicting damage, ridding us of the "I'll be fine as long as I strike first"-mentality. If return shots are fired no matter what, attacking or defending will make no difference, and this resolves the issue with defenses in the early-to-middle game.

However, with these 100-attack fighters, you'd simply have a MAD-principle (like SleekDD explained elsewhere): unless I can reliably match this massive attack value with equally massive defenses, the result of combat will be space debris.

But this is nothing new.

I like putting shields and armour on my ships, even if it makes them expensive, simply because they tend to live longer, and I agree that defense is often a decisive victory in battle, as I have had the pleasure of finding out. However, I share SleekDD's sentiments on the returning shot and the deviation from the expected value.

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An alternative solution to the whole first strike problem would have been to simply increase the HP of all ships and starbases. With longer battles, it would make less difference who struck first, since if all ships had, say, 10 times as many HP, even ships loaded up with top level weapons would have trouble wiping an entire fleet in a single shot.

I hadn't thought of the whole MAD thing, but now you mention it, I could imagine it being a big problem... I don't want all my battles to end in draws!

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I like the idea of roll per weapon and roll per defense module. Then small ship battles using tiny fighters with high calibur guns stay variant, but as ship size increases, the repeated rolling makes layered defenses formidable to beat.

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Very nice analysis and spot on I think.

All your solutions can work.

I like the IDEA of 1) but I think there's a problem...defences are smaller than weapons so you can turn out ships with much higher defence than offence. If you know what level of attack is coming at you, it shouldn't be too hard to design attack ships which are virtually impregnable to that level of attack whilst still having just enough offence to (perhaps slowly) win the day. This hands too much of an advantage to the human player who can redesign their ships whenever they like and are better at it than the AI. There's another problem...hull size becomes too important. Swarms of small fighters won't be able to put a dent in a well defended dreadnought. Even the difference between large and huge could be...well...huge.

4) might be OK but could be a nightmare to implement. The hitpoints would have to change throughout the game to reflect the increasing potency of offence. One interesting possibility...have defences not just reduce the amount of damage taken, but also increase the ships hitpoints. I think this could work, but it would take an awful lot of balancing.

So my favourite would be for 2 or 3. Probably 3) is sufficient (and I assume very easy to code)

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It is true that vessels with less room for equipment could begin to suffer when variance becomes limited. After all, the lucky shot they're depending on is removed for the most part. Large ships will become more predictable by stacking on more and more, leaving the little guys unable to scratch them. This is taking reliability to the extreme and will be just as 'game-breaking'. Balancing the system would require some thought and probably a lot of testing.

Increasing the HP works but draws out battles. A huge ship has 50 HP. Multiply that by 10 and you're exchanging fire until Saint-Patrick's Day. It'll work, but viewing the battles will become boring. A modest boost would alleviate the worst cases so perhaps 2 or 2.5 are acceptable?

Replacing the uniformly distributed variable with a normally disributed one is simpler than I had first thought. Most programming languages and some worksheets actually have a command to generate one, including Excell. All that would have to be done is to replace the command to generate a random variable with another one.

The idea of having defences contribute to the battle in other ways than simply blocking damage is one I've been playing with for a little while now, so you'll understand I like it a lot

. This would certain make things a little more interesting than a simple match of Offence-Defence but it would also make the system more involved. If I understand correctly, Stardock strives to have a simple system rather than an involved one. It means it's fairly easy to learn but, on the other hand, nuances will be lacking as well.

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Yes, but the flaw with this logic is that the aim is to do as much damage as possible attriton be damned.

With attacker first strike advantage, as long as you strike first, overwhelming attack is as good as if not more so then equipping your attacking vessels with invulnerability shields to avoid damage. So defense is truly useless, if you have superior speed.

I agree that in simultaneous combat, you can still go for extreme attack, but you must be ready to accept losses, even if you are the one who engages the enemy most of the time. If you value your ships, you will add defense.

What is the best tactic then?
Well, if your defences are solid and reliable, you can install them on your vessel. They will survive the attack and fire back (no need for a parting shot). As it is, defences aren't really reliable

I think the reliability of defense is a separate issue from simultaneous combat. The point is simultaneous defense ensures that you need defense to avoid attriction, compared to the past, where superior speed + attack means defense is pointless.

Your variance theory shows that defense is less useful then expected true. But the point is defense still helps attacking fleets, even if they go for the "MAD" system, because once they get pass the point where they can destory defenders with one shot (easily reached most of the time) , it is pointless to strap on attack systems but rather defense becomes useful. In the old system, there is no reason for defense at all once this point is reached.

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I think the reliability of defense is a separate issue from simultaneous combat.

True enough. This thread was more intended to advocate a different random variable to reduce the variability of battles. After all, many battles are settled in a few rounds, leaving the mean a nice statistical but ultimately hypothetical method of thinking.

In oder to advocate this, I claim that defences start losing their use when the weapons and defences begin to dwarf the ship's HP they're mounted on simply because the variance (luck) begins to play an ever increasing part.

As an example:
Suppose you're pitting small hulls against each other with the attack and defence evenly matched (ignoring manufacturing and researching costs). What are the odds of delivering a one-shot-one-kill?

10 Attack/ 10 Defence: 1%
20 Attack/ 20 Defence: 16,5 %
...
50 Attack/ 50 Defence: 34,44%

As you can see, chance starts to play an ever increasing hand simply because a fluke roll can't be compensated by HP.

Of course, you're right that single-minded attack vessels will have the life expectancy of a credit card in a shopaholic's care but the question is whether they cause the enemy more harm than they cost. After all, it does cost more manufacturing effort to build a balanced ship. I just think it blows to have your expensive ship blown out of the sky because luck decided to give it a little nudge. A normally distributed variable would reduce the occurance of such outliers and hence improve the worth of defences without actually making them more potent.

I won't claim that defences are utterly useless but after seeing several large ships with ample defences being...forcefully retired by a kamikaze frigate just because my crew couldn't find the ON-button for my shields, I found myself wondering if I actually wouldn't be playing it safer by not installing defences at all and simply assume I'll suffer losses.

Lastly, weapons are larger in size but also noticeably cheaper. So maybe we shouldn't be looking at single battles but rather at a string of battles were cheaper, attack vessels are pitted against more expensive and survivable ships. Veblen's experiments seem to indicate that (if I understood correctly), although attack-oriented ships lose battles, they cause more damage in manufacturing points than they cost. The victories would be Pyrrus Victories and would drive the balanced player towards defeat one victory at a time. Of course, this assumes that the attack vessels can keep the pressure on and that manufacturing capacity is comparable.

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Remember, I'm on the side which says defense is worthless. I maintain that defenses will be more useful after simultaneous, but I still won't use it.

Lastly, weapons are larger in size but also noticeably cheaper.

To be honest, I seldom use defenses, so I was surprised tto read that defenses were more expensive. Given that defenses are a lot cheaper to research than weapons and smaller to boot, i thought production costs would be less as well or equal.

But i went back to look at the spreadsheet i made and indeed defenses are more expensive.

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ships packed with nothing but offensive power are fine so long as they hold a numerical advantage and strike first. Otherwise the casualties will add up and take em out of action. That's assuming the economic and industrial clout to maintain that type of a war effort. Packing on firepower at the expense of all else is a common mistake in new, small, or developing navies.

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But how often should the little guys be able to destroy huge ships? It should definitely be possible but throwing a bunch of small, lightly armed ships up against an enormous dreadnought should really be a desperate gamble with a slim chance of success, shouldn't it?

I'm reminded of the original version of Civilization where a defending spearmen unit who got lucky could take out an bombarding battleship or an attacking tank. Civilization II fixed the problem by shifting the balance and making this occurrence much rarer, but still keeping the possibility that those spearmen might win out. The result hugely improved the game combat.

I completely agree that any change like this would require a lot of thought and testing but it seems right now as if the combat system is perhaps a bit too simple. Using a normal distribution for damage and defense appears like too good an idea to ignore.

I do wonder what the developers think about this, though. Surely they must have considered various options when they were designing the game. They must have had their reasons for doing what they did (they've done too good a job just to have thrown this part together without thinking about it).

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How about scrapping the defence roll altogether and instead letting defences act more like hit points? ("Shields at 60% captain"!)

That way you could reduce the variance substantially and defence would actually be useful, but swarms of fighters would still have a chance against huge ships if they had enough combined firepower.

You could either give defences a "recharge rate", or make the current ratings the "damage per round" they can absorb before the ship starts taking damage.

Edit: this system would need a little refinement, otherwise you will get caught in never ending battle loops with ships unable to penetrate each others defences. Although having said that, I don't see why battles should HAVE to end with complete annihilation of one side or the other! For example, should a tiny scout ship with 1 attack be able to take down a massively armored troop transport with 100+ defence but no weapons?

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You could also keep the system that certain weapons ignore certain defenses (i.e., beam weapons bypass point defense and armour), though this whole thing might be changing the system too much. I would imagine that any adjustment really needs to be as subtle as possible to avoid completely changing game balance.

I'd still be really interested to know what Stardock's rationale was behind the existing system.

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Cheesy AI tactics?

I ran into a Drengin fleet with each ship called a "defender". It looks like what they did was put weapons on a cargo hull to boost their military rating and then kept upgrading. This was near the end of the game and they gave me a hard time since most of my fleets were larger ships. Even though I could put 4 ships with 60+ attack each, these defender fleets were wearing me down because I could only kill 4 ships each turn. I'd attack, kill 4, the remaining 4 would attack and kill 1 and sometimes 2 large hull ships, then I would kill the rest. I shudder to think what will happen in 1.2. Those cargo hulled ships with 1 hp and 30+ attack will eat through my battleships. I'll attack, kill 4, then all 8 will counterattack, kill 3-4 of my ships, my 1 ship will fire back, kill one then get destroyed.

I fear without some kind of change in the combat rules with 1.2 it will become a game of suicide ships.

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The computer puts weapons on cargo hulls? Then why is it so wide open to the tactic when you use it yourself?

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I've been toying with the idea of giving each type of defence a certain effect, instead of using the mix-match style that's in use now.

Shield would absord a percentage of the incoming damage. The damage it absord recovers slowly over time and when a generator falls down to zero points, it shuts down for the battle.
Armour would increase the HP of the vessel at the expense of slot-space. Instead of mounting a powergrid for that cool laser, it gets layers with some extra titanium.
Point Defence would become something like stealth. Instead of blocking missiles, it would hamper the enemies from getting a lock, increasing the odds of an attack altogether.

In order to balance those effects, one could introduce a degressively increasing effect. 2 shield generators would not be double the effect of a single generator but a little less. In this case, even if defences are overpowered (because this system is harder to balance), it should even out because of the reduced efficiency. But that probably belongs to another thread.

I've seen those weapon cargo ships and they can be pretty nasty. Actually, I had considered those models a freak occurrance but it appears I'm wrong. If it is possible to build these kind of ships en masse and with a reasonable price, this is taking MAD to the next level. I hadn't even considered this as a tactic.

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Yeah seen the Terrans do that last night, they had an entire fleets (plural) full of 1 HP ships with fantastic weapons. I had a fleet of 7 Heavy Fighters, 2 Frigates, 1 Battleship and 1 Dreadnaught. Whacked as many as I could for as long as I could, than it was their turn. Even though I hadn't sustained much damage till that point it was all over but the kat hitting the frying pan.

Lesson learned for me was. Even if you think its cheesy and don't do it yourself, when your opponent is, be like a sheep and follow the herd.

W/R
Suralle Straykat
Kat Lord @ Large

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