The Joys of Balancing (help, please?)

[doom3607]

Ok, so a friend and I are trying to make an MMO. Yes, it'll be crappy, we're still in high school, and so forth, but we're trying. And at least we've got Dad to help with the bits we just plain don't get.

Anyway, relevance:

This will be a fantasy game, just to avoid dealing with the joys of science. Thus, there will be magic. And mages will be able to group together and share power according to the equation:

[total mana of the group] = [sum of the mana of all the mages in the group independantly] * 2^([number of mages in the group - 1]/2)

This leads to certain inherent balancing problems, of course. While it does create the desired effect of making groups of mages working together better than a group of mages each working seperately, it also leads to fun situations like:

10,000 * 2^((100-1)/2) =~ 7961314590657215706
100,000 * 2^((1,000-1)/2) =~ 2.314636696315716974324347279212e+155

[sarcasm] This is... mildly problematic. [/sarcasm] This is assuming one hundred mana per mage, for those who don't want to have to work it out themselves. Anyway, this leads to the problem of: If one hundred mana is even remotely useful at doing damage, even a hundred mages are a nuclear weapon, and a thousand of them can toss around doomsday weapons like firecrackers.

Now, while insane firepower in warfare is all well and good, this goes from mere "insane" straight to "apocalyptic isn't a big enough word", jumping straight past "that's no moon".

So- does anyone have any idea how to balance that?

[HMS Sophia]

Have a maximum limit? Have the increase be a degrading curve?

[doom3607]

Maybe. Not quite sure what the equation would be for that... diminishing returns makes sense, though.

[salm]

Just set a threshold that, if reached keeps the power from increasing.

Or use exponential growth with a capacity limit which would look like the following curve:

[Simon_Jester]

Um, don't use exponential scaling because that's silly?

I mean, that N*(2^(N/2)) scaling for large N is the vast majority of your problem right there; it's far, far too overpowered for large N; it's almost as bad as making the power scale with N! As you've already seen, every time you increase the number of mages in the group by two (assuming constant average power), you increase the power of the group by a factor of two.

Adding two men to a group of 100 men should not make them twice as powerful.

What on earth possessed you guys to use exponential scaling? Geometric scaling would produce a less ridiculously overpowered result. Try:

M_collective = M_summed * (N-1)^2

For small groups, this scaling isn't very different. Under the two systems, assuming 100 mana for each mage, we get as rough mana levels, for your exponential versus my geometric progression:

1 mage: 100 vs 100
2 mages: 280 vs 200
3 mages: 600 vs 1200
4 mages: 1130 vs 3600
5 mages: 2000 vs 8000
10 mages: 22600 vs 81000
15 mages: 192000 vs 294000
21 mages: 2260000 vs 840000

Now, you can play around with this, but this way, the power of the group scales roughly with the cube of its size, not with 2^(size), which gets ridiculously large.

Of course, even this becomes quite overpowered: two mages outpower one mage by a factor of two, while twenty mages outpower ten by a factor of 100.

If all you want to do is create a moderate incentive to coordinate, without making it totally impossible for one master to stand against a handful of apprentices chanting in a circle, you should use a scaling like N^2. Simply have the power of the group equal to the "summed-up" power of the individual wizards, times the number of wizards in the group. Now scaling becomes easy, the power of the group is NX*N, where X is average power and N is the size of the group.

This at least makes things relatively manageable as long as you can't amass thousands of wizards who have real firepower: if one wizard can cast a death curse that kills one man, 100 wizards could cast a death curse that kills a small army, but you're going to have a hard time finding 100 wizards and this is not totally unbalanced with the difficulty of finding a small army.

Or you could have the multiplier factor go with the square root, or the cube root, of the size of the group.

Or even make it scale logarithmically- that's a great way to discourage people from trying to put together huge groups. If having 2 wizards increases the power of each by a factor of 1.3 (that is, 1 + log(2)), that sounds great and gives them an incentive to work together... but then to make the size of the group double the power of the individual wizards you need ten wizards. To triple the power of the individual wizard you need a hundred, to quadruple it you need a thousand, and so on. Thus, at some point it becomes cost-ineffective to keep that many wizards operating in unison, or at least more trouble than any normal person would want to go through.

For a logarithmic curve, you never really hit diminishing returns- adding one man to the group always increases the power of the group by a factor greater than what that man could achieve working alone. A group of 110 wizards is noticeably stronger than a group of 100 wizards. They're just not all that much more than 10% factor of strength you'd expect just from looking at the numbers on each side.

Yet another option is to make it take skill to work in large groups- to join a huge group, a wizard must be highly skilled in such operations, and wizards who can do that are rare.

[HeadCreeps]

It depends too much on exterior factors to give a correct result, too. How survivable are the mages? How dependent are they on MP recharges, healers, buffers, or tanks? Assuming they are ranged classes whose magic can be interrupted, how quickly can they get off a spell before their target is within damage range and canceling the spell? If the formula is based on current MP and not maximum MP, you'll see the mage groups losing power significantly as time goes on, unless they have sufficient MP being restored to cover the losses.

If this is every individual mage in the party getting a boost based on the number of mages in the group, you want to set your target cap before you even begin creating a formula for how it works. Depending on actual damage per second, you might want to set your cap somewhere in the 1.5-3x base damage range and build your formula around this.

A typical balance issue you may find in an MMO is the multiplicity of damage boosts. As time goes on, expect a multitude of buffs to exist which boost this damage even further, which renders defense useless. I've found mages have balance issues once there is both a way to increase magic damage and increase casting speed. If the mages can cast their spells almost instantly at their expected damage output (typically enough to kill something in 1 or 2 shots), they become extremely overpowered. However, without the casting speed element, a slow casting mage has many inherent weakness that can render even the most devasting damage per hit "balanced".

[doom3607]

All off this makes sense. The geometric method also makes sense. Or course, my friend had another solution to the problem- just make the world so big that they could throw around doomsday weapons all the time. but I'll probably go with one of yours.

[Stark]

When working backwards from the maximum you effect to want, don't forget there are plenty of hard limits you can throw in to prevent various behaviours like throwing in 1000 level 1 guys to buff the king wizard, magnifying the effects of individual mana pool boosts or increases, etc. The key issues - as mentioned - is to know what you want the mechanic to do before you put any numbers in there, and make sure at each stage that its doing what you want and nothing else.

[Aleva13]

I had something of a similar idea back in high school. Though with my idea, it was multiple mages casting a single spell and individual power was increased by the total amount of mana expended in the area recently.

[doom3607]

Hmm. I think I may just go with Simon's "summed-up power*number of wizards". Of course, if you can get enough good wizards you can still get apocalyptic warfare... Which works just fine.

[Mr Bean]

There's also the possibility of stealing an idea from the Wheel of Time series, Mage's don't add their full power to any links say only 75% with a link maxing out at some arbitrary number, like 13, or 42 or 69 or pick your own joke number here. Besides there is always the issue of how this linking works, when the mages are exchanging Mana pools is one leading and the other 41 just acting a Mana batteries? Or can they all chuck spells like hand grenades at random?

[Korto]

I've found using a sine curve useful for similar jobs (accelerating increase, inflexion, decelerating increase to maximum) or the equation ( x ) / ( x + constant ) where x is the increasing quantity, but for this purpose I admit I prefer Jester's solution with logs. Just thought I'd mention another couple of options. Have fun!

[Stormin]

How about instead of increasing base damage with more mages, you increase magic resist piercing? Makes it less overpowering vs smaller mobs (which have lower resists) and better vs the raid bosses and the like (which will have higher). Maybe even have every class give a stacking group buff, like having tanks increase all group member received heals by 5% per tank, melee dps increase accuracy and damage, healers get a group power regen, etc.