I am very surprised to hear this.  This is not my perception, but perception is sometimes faulty when it comes to probability.

I will lab some results when I get a chance and present them here.

Take your example, 4 strength 7 knights attacking a unit with 16 defense, and your system as described.

The distribution of outcomes for a single knight can be seen in an 7*16 table.  Have the rows as the roll the knight gets, the columns as the roll the defender gets.  So the knight does no damage in element (1,1), does 1 damage in element (1,2), does 2 damage in element (1,3), does 1 damage in element (2,3), and so forth.

The probability that NONE of the knights hits is (1-0.1875)^4 = 43.58%.

The probability that at least one of the knights hits is 1-0.1875 = 56.42%.

The expected damage of a single knight is: (1*6+2*5+3*4+4*3+5*2+6*1)/(7*16) = 0.5

So the expected (ie average) damage of the squad of 4 knights is 2.

I do not believe that this is what I am observing in game.

I will try to lab some data to see whether it is my perception that is incorrect, or whether there is a bug.

*edit*

Table didn't paste well, removing it messed up formatting.  Sorry.

*edit2*

To help for labbing; does the game preserve a random seed?  That is, if I'm in a situation and I play a combat, if I reload a save right before and replicate will it give me new/random data or the same data?

He never said it would be 4 individual attacks. He just said it would be 4 individual rolls. He could very well be describing a system that adds all 4 knights damage together, and then gives a single defense roll against it for every figure in the enemy squad. That matches both Frogboy's description and what I have seen in battle. It also is entirely different from what we want, and is described in point 2, making the statement that parties already work like that false.

Because HIS armor deflects damage directed towards him. The way you're suggesting it should work, it's like the first guy has an armor, and all the others are naked. You're suggesting we make squads weaker than the same number of individuals...

I see what you mean.  The difference between:

i) Rand[1,28] - Rand[1,16]

ii) Rand[1,7]+Rand[1,7]+Rand[1,7]+Rand[1,7] - Rand[1,16]

iii) Rand[1,7]- Rand[1,16] + Rand[1,7]- Rand[1,16] + Rand[1,7]- Rand[1,16] + Rand[1,7]- Rand[1,16]

You're saying that Frogboy is saying that its ii)

While I'm interpreting it as Frogboy saying that its iii)

ii) is still not very interesting.  Its still 1-28, just with heavier probability density on the center (around 15 damage)

In case ii), the 4 knights would have expected damage of roughly 8 - the same as in i).  Which is very different from expected damage of 2 (which is what they get from iii)

I'm arguing for iii).

I want defense > attack to be very powerful.

Yeah, that's why a few of us asked for clarification on how defense works

it strikes me as weird that there are no employees at stardock who would notice these glaring faults in balancing and let Mr Wardell know about them.

No I'm not.  I'm saying, you're rolling a weapon with power 20 against armor of power 5.  It doesn't matter how many individual there are; they just pool their hitpoints.  But they all have the same armor.  It doesn't get stronger because there are more of them.

The only way in which I'm making them weaker than individuals is because in the case of individuals the splash damage is wasted; if I do 30 damage to a 10 hit points stack, the rest of the damage evaporates.

If you get extra armor checks for more guys, then a squad of 10 guys with 5 hit points each with defense 5 take less damage than a single guy with 50 hit points and defense 5.

I don't think this should be the case.  Whether a guy has 10 hit points or 50 hit points, he's still only wearing leather armor, vs an ogre.

But you have to understand that 3, as you describe it, means that a squad has identical defense in practice as an individual. The game displays a higher defense, therefore 3 is unlikely to be the case.

I also want option three to be the case as you described it, with the caveat that I also want the side system that gives an extra defense roll for every slain individual by a single attack. If a big dragon wants to kill a squad of 4 knights in a single blow, it should have enough damage left over after 4 defense rolls, like in system 2.

However, to kill only 1 knight of the 4 it should have to penetrate only that one knights defense, being system 3.

In other words, like master of magic does it.

Of course, point 1 about the distribution of individual rolls still stands, so I'd like that part to be like master of magic too:

(one random check for every point of attack/defense, the amount of successes determines the value of the "defense/attack roll".)

 If you'll read back you see that I am one of those few.

We are only arguing for extra armour checks for extra guys if a single attack kills/wounds multiple of those guys. In that case, multiple sets of armour are being penetrated, thus the extra rolls make sense.

Ye, unless it's a really big ogre, it will still be hitting one guy at a time, and it's against that guy's armor that the damage is counted. Even assuming abstracted multiple attacks (or ogre hitting multiple units at once with the big club) the armour shouldn't be equal to the combined armour of units.

Yes, if it's abstract multiple attacks (or even if it's not), then every time the ogre swings the club to kill a unit in the stack, it encounters a leather armor. Thus, Netriak is right: armour should be counted for every guy that takes damage in the stack, which is far lower than adding the armour value of all guys in the stack, but potentially higher than if the armor was counted only once.

For the record, those Crowns after the tactical battles ARE NOT experience.  Still not sure what they are.  Per FrogBoy in the #Elemental chat last evening, the experience gained for your army is equal to the combat rating of the defeated party.  Each member of the attacking army gets the full value of experience (i.e. it is not divided between them). 

This is true unless overridden by the game.  I assume he meant unless it's quest/boss related and defined elsewhere.  I tested this last evening and it appears to be correct.

Now if I could just figure out what those crowns mean...

Regarding tactical combat still, this is far smaller issue than any in the OP, but anyway: Weapon speeds should modify the cost to make an attack, not total tactical combat action point pool. Wielding some weapons grants more action points, which can also be used to cast spells. That feels weird. Also, in the current system weapon speeds aren't really relative to each other - warhammer is just as fast as other weapons for most units, as long as they don't drag the speed down to 0.

In lesser degree same goes for mounts too, they should modify the movement cost.

At least this is how I see it

Yes.  The advantage to being in a ground should be:

a. pooled hit points, so even if half the guys are killed they heal back up.

b. concentrated firepower, they only take up a single tile, and a single army slot.

So fix the display.

The game also currently displays the same attack figure for a squad of 4 guys with attack 10 vs a big monster with attack 40.

This doesn't make sense to me.  I don't understand why 4 guys with 10 hp and defense 5 should be better at defending than a single guy with 40 hp and defense 5.

But in reality we're not modeling a single strike.  We're modeling the performance of the weapon against that strength of armor.  It doesn't matter whether the armor is on one big guy or two small ones.

It is abstract multiple attacks.

In your model, a champion with defense 10 takes more damage than 4 guys with defense 10.  That seems wrong to me.  I think a strength X attack vs Defense Y should deal the same amount of damage, no matter how many models there are in the defender's unit.

Anyway, neither way is terrible, but personally I think your way is more confusing.

I think that the simplest thing is to display the attack and defense value of each member of the squad, and then display the number of members.

So 7 attack/2 defense soldiers will display 7/2, whether there are 2 of them or 4 of them.  So to measure the combat value, you look at both their stats and how many there are.

Huh.  Weird.  Who knows then.

Agreed on all points and I am glad to see that stack attacks are not for the combined atk of the squad. However, as other mentioned, this is confusing on stack VS stack defence. I think the way it works is like the 3rd way Netriak wrote

Which makes the most sense. However this is not what Frogboy said but then again, he was talking about squads VS individual units and not squad VS squad, which hopefully is setup as above.

Now however there's an issue with squad VS powerful individuals, where someone may have an atk of say 50 while you may have a group of 12 with a def of 5 each. It doesn't make sense that you roll a 50, while they roll a combined 47 easily and take almost no damage even if they so low armored. It makes far more sense that each of them rolls their defense and takes that and their HPs out of your atk. So  if there was a squad of 12 with 5 def and 5 hp each, against your atk of 50, it would be first rolls a def of 5. So 5 def + 5 hp is taken out of your atk. First guy dies. 40 dmg left. Next one rolls a 2. 40 - 2 -5 = 33 atk left and so on. So a powerful champion or monster can end up wiping a squal with a strong atk. Hopefully that's how it works.

Of course that too is a bit unrealistic as one guy might end up wiping a whole squad with one swing of his sword. Perhaps an individual's attack should alwys slay only one opponent, unless they have some kind of special trait from their weapon or from magic. Such as an ogre's sweep which should be able to kill up to 3. Thus one individual against a whole squal might be at a disadvantage, unless they've been explicitly prepared for it, which also makes sense.

On the other hand as well,the combined atk that frogboy mentioned can also get very powerful or not powerful at all against individuals. The change that he mentioned is that instead of a result of 1-28, you have 4-28. This is not such a huge difference in terms of balance and makes squad attacks still quite powerful. If you've got 12 soldiers with an atk of 5, against an Ogre with a defence of 30. Then at very few instancesthey will do no damage, while other times they will do obscene amounts (i.e. up to 59 dmg). This is because the Ogre's defence relies on one simply roll and if you're unlucky, you can lose a powerful unit just like that, to a squad of peasants. A better option would be to have each attack compare to the defence by itself, without first being summed up with all the others.

This on the other hand might make individuals with high def quite powerful, but this should be balanced by increasing the individual atk of units in a squad by how much they overwhelm their opponent. This would allow peasants to be able to damage semi-powerful opponents by sheer numbers, but not simply wipe them out with one lucky stroke.

Because if you kill 2 of the units in a stack, you have to go against 2 leather armors, not just one. That doesn't mean all armors should stack, but every time damage overflows to the next unit in the stack, then the armor of that next unit should be taken into account.

That's an awesome idea.

Yes, a coordination/overwhelming bonus. Like 10% for each unit in the attacking squad over the number of unit in the defending squad.

But here's the thing.  An ogre's "attack" is an abstract representing a big fight, with maybe 20+ blows.  Why should it matter if those 20 blows are against a single guy in leather armor, or two guys in leather armor?

Your method also ends up making stacks very strong, and makes defense incredibly strong, particularly with large stacks.

I think a very useful rule of thumb is that two equal units should need ~3-4 attacks on average to kill each other.  That is, they're taking up ~1/3 to 1/4 of the enemy's damage.

But with your system, if a 10-man squad is being attacked, and should be taking 3 men per combat, then you're effectively tripling the defensive value of the unit, because you're subtracting the defense value three times.

This gets very powerful, and very confusing; two units with the same defense value should take the same amount of total damage from the same attack.  But in your system, the more subdivided a unit is, the better it is defensively.  20 midgets with defense 4 and 5 hitpoints are much better than 10 normal guys with defense 4 and 10 hit points.  This seems wrong to me.

But anyway, I could live with either system.

This is an excellent post. I very much hope stardock take this seriously.

It's obvious (and not just from here) that serious strategy game players are expert tacticians, who understand and exploit the probability distributions underlying the systems they're interacting with. For a game to satisfy them it needs to be both complex and interesting, but also well balanced and impossible to dominate with a two dimensional strategy.

I've been eagerly anticipating this game and but have not participated in the lead up to realease, I just bought the game now. I was going to insist on my friends buying it (we often play strategy boardgames together) so we could play together, but having put a night's play in to it I can't do that with a good conscience anymore. The game is beautiful, the world is interesting, some of the ideas are exciting and new - clearly passionate artists, designers and programmers have put a lot into making it good. But strategicly and tactically it's almost entirely uninteresting - there is usually only one best way to do things, and it's quickly obvious what it is. It feels like the strategic balance has been thrown together by non-experts, who assumed it was simple and anyone could do it.

I'm still excited about the game and will try it again in a few months to see if things have changed. In the meantime I hope that stardock hire an expert game-theorits or strategy game designer to turn this into the strategic masterpiece it has the potential to become. Perhaps the OP or some of the excellent posters in this thread might offer their services? Alternatively, if they open enough of the design to modding I'm sure a community mod would quickly emerge that achieve a much better strategic balance, which stardock might then incorporate into the main game.

In either case I have my fingers crossed and just wanted to put in my 2c before I sign off and give things a few months to stew. Again, excellent suggestions. Stardock - please read this thread carefully and take it seriously. You might have made a classic, but you're at serious risk of having made a flop...

Maciek

This is true, but it's important to note that one doesn't need an understanding of probability distributions to notice that the balance is off, and neither are these recommendations intended merely to satisfy the serious strategy gamers. Any average player might say, "Hmm, it seems like my squad of peasants is a lot stronger than a handful of individual peasants, in fact they kill dragons easily, that doesn't seem right.." Our hypothetical average player might not understand why this unusual balance issue arises, the detailed numbers behind it - but nonetheless the problem exists for everyone, not just those who fully understand the math behind it. Numbers are just a more precise way to communicate exactly what the problem is and why a certain recommendation would be an improvement, one need not understand them to be affected by the problem.

That being said, it's good to hear that 4 knights get 4 separate rolls of 1-7 instead of one 1-28 roll; it weights attacks more towards the average, i.e. it makes a total damage of 14 more common than 28. This is great for making random results a little easier to predict and plan for, and as the OP says more attacks should work like this - i.e. spells doing 2d10 damage instead of 1d20. The problem is - and correct me if I'm wrong, but this the way the current system seems to me without exhaustive testing - the problem is that the defender only seems to get one defense roll against the total of those knights' 4 attack rolls, when he should get a separate defense roll for each attack. In short, it seems to be situation (ii) below as Scooter explained it, when it should be (iii).

That is if the knights each roll 1-7 and total up to, say, 17 damage, and are attacking a 16 defense ogre who rolls 8, they do 9 damage to him (ii). It should be more like, the first knight rolls 1-7 and gets a 4, this gets compared to the ogre's defense roll of 8 and he does no damage, then do the same for the other 3 knights, with a new defense roll for each (iii). Why should it be like this? This ensures that a group of 4 knights does (on average) the same damage as 4 knights attacking separately, which is about what the player would expect, whether or not they know the math behind it. If the group of knights only considers the ogre's defense once for 4 separate attacks, they'll hit much much harder than a sum of individual units, and this causes all sorts of balance problems. I'd be all for giving the group of knights some kind of group bonus, like 10-20% more attack or hp due to their "coordination" - but the current system (if I understand it correctly) is far more than 10-20%, stacking enough peasants with pointy sticks and leather armor together can give you a unit with stats equivalent to a dragon (exaggeration, perhaps, but not too far from the way it seems to be).

Which by itself isn't an issue, as surely enough peasants could take down even a dragon in a theoretical scenario. The issue occurs when the costs of the peasants a far less than the costs which the developers assumed would be required to take down a dragon, or an ogre or whatever. This throws balance out of the airlock.

You should have big individual units, and you should have groups of small units and those should have different gameplay mechanics. Even on a simple rock/paper/scissors scale such as: Unit Stack > Individual Super Unit (eg pimped champions) >  Individual Mass-Control unit (eg Firebreathing Dragon) > Unit Stack.

So your champions would be very good going against individual monsters and champions, especially those geared to handling squads (such as nuking wizards), but would have trouble going alone against an army.

Simply treating stacks of units as one big unit with four times the stats makes little sense realistically, plays weirdly as gameplay and is easily unbalanced.

The thing is that the rock/paper/scissor idea above doesn't have to be very complex in implementation either. Simply the way the mechanics work. By allowing squads to do individual attack and defense rolls and giving them "overwhelm" bonuses, you make them immediately more effective against individual champions with the same cost of equipment. By making AoE spells weaker in damage than currently but also do *n damage on stacks (where n is the number of units in a stack) you make mass-control units automatically better at handling such squad-heavy armies but  also weaker against individual units.

True, but there's another problem as well. A group of peasants being able to take down a dragon for less cost is a balance issue to be sure, but one that can be solved in many ways - lowering the cost of dragons, for example. The reason I support this specific solution (changing the way stats add up for groups of soldiers) is because a squad of 4 peasants, with cost similar to 4 individual peasants, is much more powerful than 4 individual peasants. Not only illogical but bad for balance - it forces us to prioritize researching larger stacks over anything else. ..Not to mention it makes it nearly impossible to balance units that cannot stack vs. stacks - if your dragon (or sovereign, or champion) is competitive with a large group of soldiers, individual soldiers are hopeless no matter how many you build, and if the dragon is balanced against individual soldiers, he quickly becomes obsolete when you can stack groups of 4 soldiers together.

Edit: What I mean, essentially, is that it's not all about the big individual unit vs. big stack of soldiers endgame, which certainly has its problems - there's another set of balance concerns that arise when you start comparing a group of 4 knights to 4 knights trained one by one.

I don't agree with this. I very much like that once a unit in a squad dies, it's dead. That's how it is at the moment, and that's how it should stay. The advantage of squads should only be that they let you take more men into combat than you could otherwise, nothing else. Each unit in a squad should be treated completely as its own separate unit with its own hp, damage, and defense and being able to die permanently.

It being abstract doesn't mean it has to be without common sense. An ogre's "attack" against a squad simulates a fight between the ogre and that squad over a certain amount of time. In other words, "The ogre does X damage in this amount of time. How many guys can he kill with this amount of damage." Obviously there's some degree of abstraction, but not to the point where only one guy in a squad ends up actually having armor. If the Ogre kills one guy and still has "damage" left, he's going to go attack another guy, who also has a set of armor. Just because the Ogre manages to kill one guy during the one-turn scuffle, doesn't mean the other guys stop trying to defend against his attack.

This is the most important issue here I think.

We need individual units and groups to scale in a similar way.

I think this is terrible without at least some means of replenishing the squad (by merging units into it).  Which then becomes MM busywork, so its easier to just let the squad heal back to full health.

This isn't really worth a tech all by itself, or the longer build time.

I agree, but what is common sense?  To me, it is common sense that a single unit with defense 5 should take the same amount of damage from an attack as a squad of units with defense 5.

But I don't think that's what this is modeling in my conception; what you're modeling is that all units have the same armor value.

Once you accept that a fight is really a bunch of blows abstracted, why should I inflict less damage if I hit three guys once each than if I hit a single guy three times, when all of the guys have the same armor?

And I would like a small "unit coordination" bonus, showing that the whole is slightly more than the sum of the parts. 

This is the natural progression of the game. There is literally no way to balance between 1 of "Guy A" and 10 of "Guy A". It can't be done, and it shouldn't be tried. Squads exist to be used and there should not be an expectation that a single trained unit can somehow remain competitive versus a squad of the same unit. All scaling (monsters, Sovereign, Heroes, etc) in the game should scale in accordance to growing number of total troops, which is accomplished partly through squads. There's absolutely nothing wrong with a late-game Sovereign/Hero being balanced against a late-game squad, because these units can only be single and therefore need to be able to compete with a squad, else there's never a reason to take them, especially since once they die they're dead. But the same expectation should not exist for individual trainable units. Sovereigns, Heroes, and Monsters have a level-up system which allows them to compete against squads with proper number tweaking.

The progression of the game needs a lot of rebalancing to make some choices more viable. And as someone pointed out, to make not-stackable units such as dragons and champions useable.