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Balance

Zero Sum Rule (Shadwolf)
Too Little is Better than Too Much
Why Nerfing is Good

Zero Sum Rule (Shadwolf)

There are several different genres of game today (sadly less than there use to be).  Each of them has its own peculularities, but all seem to have the consistent problem that imbalance develop in nearly every game designed.  Observation of these games has lead me to the conclusion that there are certain similarites in many of these games.  For these purposes, I will be dealing with any game that deals with combat.  This includes pen and paper RPGs, CRPGs, RTSs, FPSs, MMORPGs, turn based strategy games and a variety of others.

There are a few basic considerations for combat: how fast is the unit, how much damage does the unit do, how fast does it do damage, how hard is it to hurt, and how much damage can it take before it is disabled (not neccessarily killed).  In an RPG or FPS, the unit is the player character or their opponents; in a strategy game this refers to the combat units of all sides.

The first of these considerations, and possibly the most important, is how much damge the unit does.  This is closely linked with how fast the unit does damage.  The hardest part of solving this is picking a useful unit of time.  This unit should be based on how long it will take to kill another unit.  This unit of time can then be compared to the damage of a given attack to generate a damage over time ratio.  This should include the healing rate of the average unit.  If you do 5 points of damage in a given time, but the target heals 2, you only actaully did 3.  This damage should be expressed in terms of a percentage of the average health a unit has.  Thus, you should end up with something like a 5% per second or a 7% per round ratio.  A maximum and minimum value has to be set for this.  Many a game has been broken for lack of this.  Most games start with a maximum, but each new episode or suppliment wants to add a weapon or attack that is more powerful than anything that's been done before.  The values keep climbing and the game gets broken.  You need to ensure that this maximum is never exceeded, now matter how cool or unique the circumstances.  A good guideline is around the maximum health possible for any unit.  The minimum is a little harder to judge, but it should be at least higher than the minimum rate at which a unit can heal.

Once damage over time has been determined, a value should be assigned.  Remember that higher damage attacks have a better chance of killing the enemy in one shot and so should have proportionally higher values.  An example might be as follows:
 
D/T
5%/turn
10%/turn
20%/turn
30%/turn
50%/turn
etc.
Value
1
2
5
7
15
etc.

Next, how hard is this unit to hurt compared to other units?  This would then be expressed in terms of what percentage of damage it typically avoids.  This would then allow you to determine how many shots an average attack will take to disable the unit.  This number would then correspond to a value much as damage over time did.  This value would be added to the damage over time value.

The last positive value to add would concern how fast the unit is.  The value for this would depend on not only the speed, but whether or not there are ranged attacks and how this speed affects the use of thos attacks.  If the speed is high enough to constantly stay at range and avoid melee units, or to close with any ranged unit before it can fire, then this value should be inordinately high.  If it is fast enough to allow one melee unit to eventually close with another, it should be moderately high.  Again, this value is added to your total.

As a blance to all these values, cost must be determined.  Cost may have up to three factors, intitial cost, upkeep cost, and time to produce.  Intiatial cost should be the least of these.  The three should balance out to give a negative cost which reflects the potential usefullness of the attack or unit.  This cost, when added to the above values, should give you a zero sum.  The net effect is that all attacks, if you've done it right, should be balanced.

How this works:

For an RTS you might have infantry that would be slow, weak, but cheap.  Cavalry might be much faster and have a stronger attack, but be weak on hit points and cost more.  A dragon might be stronger, faster and harder to kill, but the cost and upkeep would be outrageous.

For a pen and paper RPG, a CRPG or an MMORPG a fighter might have a good fast attack with his sword that does moderate damge and costs him one stamina per round to use while a mage might have a fireball that does huge area effect damage at range, but takes 3 turns to fire and costs 10 mana to cast.

These values work best if stats are kept as low as possible.  If the weakest character has 3 health and the strongest has 10 and most attacks do 2 to 4 damage, there is a good spread and all characters will be fun to play.  If the weakest player has 10 health and the strongest has 250 and attacks do anywhere from 10 to 100 points a shot then any character with low hitpoints will be perpetually one-shotted whereas the high hit point players/units/monsters will completely invalidate the use of any but the most numbercrunched weapons.

Too Little is Better than Too Much

Once you have defined your baseline for your zero sum formulae, things get tricky, which is why there is a need for constant system adjustment via patches in a persistent world.  When these adjustments are made, you try to get as close as possible to the ideal balance, but in general, you're better off erring on the side of caution than excess.

The reason you want to err on the side of caution is to make sure that you don't invalidate most of your players' options.  Say for example you have a set of weapons available to players in an extremely simple middle ages-style RPG.  Barring weapons classified as ceremonial/gladiatoral/desperate, you have the following choices:  axe, sword, spear, mace, dagger.  This system is very simple, and the weapons behave pretty much like you'd expect them to.  However, you have a rogue developer on your team with a personal bias about the dagger, and it winds up being imbalanced.

First let's see what happens if he thinks the dagger should be better.  Maybe he was stabbed in a barfight or something, and attaches more importance to the dagger as a result.  Therefore, when your game is released, the sum of your factors for axe, sword, mace and spear even out nicely to zero, but your rogue developer has increased the damage and accuracy of the dagger disproportionately, and the dagger's new total is around +4.  How long do you think it will take for the players to pick up on this?  Now instead of having 5 viable weapons to choose from, you have one.  You have just lost 80% of your character type variety, not to mention the whining you will have to deal with when you nerf the dagger down to acceptable levels.

Now let's say the rogue developer thinks the dagger is excedingly silly, and thus lowers its speed and damage ratings.  The dagger now has a rating of -4.  It's still a problem, but now your viable weapon choices are limited to 4 good, balanced weapons, instead of the 1 they had in the other scenario.  It's still a problem, of course, unless you want to relegate the dagger to the ceremonial pile of substandard weapons nobody will ever use under normal circumstances, but when you fix this problem, it will be seen as a buff, and in the meantime your players aren't all running around carrying nothing but daggers.

Why Nerfing is Good

"Nerf!  Nerf!" is the eternal cry on dev boards whenever something is perceived as being weakened by the game's designers.  Let us suspend disbelief for a moment and assume that for once the implementors of patches are not making a horrible mistake based on skewed misinformation about the way the game works, and that this "nerf" is being used correctly:  as a balancing technique.  Something in the game has been identified as being too powerful, and a nerf is required to bring it in line.

Used in this way, the nerf is an excellent and vital method of maintaining a sense of balance.  If you choose to not nerf the offending object, a universal (and much misbegotten) policy in Asheron's Call, there are only two other options open to you:

Neither of these "solutions" works.  The first option, the common solution for power problems in Asheron's Call, leads to unstoppable and never-ending inflation of player power.  It also tends to lead to more problems than you initially had.  If element 4 of a weapon set including 1 through 9 is considered overpowered and you subsequently buff weapons 1, 2, 3, 5, 6, 7, 8, and 9 to compensate, you run a tremendous risk that one of these weapons is now overpowered, which leads to another cycle of buffing, etc. etc.  Compare this to the nerfing cycle:  element 4 is nerfed back down to a balanced level, and if you nerf too far, you can always nudge it back up slowly until it works.  This, coincidentally, was the "pendulum" method of fixes during Asheron's Call beta, and it worked considerably better than the "no nerfs" nonsense they use now.  (See the section above, "Too Little is Better than Too Much," for elucidation.)

The second method, leaving the game broken, is even worse, but it happens on a semiregular basis.  In games that are not persistent, like Age of Kings (early), the trebuchet was horribly unrealistic and therefore could be used to devastating effect.  Why bother building a mixed force if a trebuchet is as easy to maintain as a peasant levy, and far more devastating and hard to destroy?  (To their credit, the publisher did eventually patch this.)  In Heavy Gear, the bazooka was implemented as a guided weapon (which is incorrect from the standpoint of the original Heavy Gear tabletop system), and if you could get one, there was little reason to get anything else.  This was never changed.  Typically, such a game's publisher looks at a product like this as a product with built-in obsolescence, and so he leaves it broken rather than devoting company resources to fixing it, when that manpower could be steered into producing their next income-generating broken game.  The buying public is gullible and stupid as a rule, and although I might never again buy a product made by that team as a result of their shortsightedness, many others will.  It's easy to see where the profit lies.  (NOTE:  The only game to ever be successfully and persistently fixed for balance after publication is Starcraft.  End result:  Starcraft is one of the most popular computer games of its time, and the absolute best RTS game on the market even today.)

In a persistent subscriber-based game like an MMORPG, there is considerably more pressure on the development team to fix mistakes and address balance issues, but it doesn't always happen.  In Ultima Online, lord of all buggy cesspools, bugs that allowed cheaters to loot houses and instakill other players were not fixed for a very long time, explained away as "creative uses of magic," until subscribers began cancelling in droves, at which point this sort of bug abuse suddenly became their biggest concern.  In Everquest, there are character classes that have never been on par with other classes, and they have never been fixed despite subscribers leaving.  In Asheron's Call, foolish mistakes like tuskers being worth an inordinate amount of XP for the risk involved in killing them should be considered game-destroying snafus, but it has been publically stated that they will not be reworking these creatures, most likely due to this "no nerfs" bullshit.

Let me digress a little more about Asheron's Call and the value of nerfing for a moment, as I have some experience with this game system and its absurd policy of not nerfing.  One of the largest problems with Asheron's Call is the predominance of the 3-school archer/melee, particularly the melee.  The initial buffing of these classes was due to a perceived dominance of mages in killing effectiveness.  This was a correct observation, but the answer (buffing other character types) was absolutely the wrong one, and led to a nigh-infinite series of additional class problems that have only gotten worse through the game's history.  The correct solution was to look at why the mage was so powerful.  The answer was that the mage had an extremely powerful attack (war), but it was also nearly impervious to damage due to the overwhelming power of Life and Item protections.  The correct response would have been to nerf these protections and their associated vulnerabilities, most especially Imperil.  Had this been done right away, we would not be seeing the sorts of absurd class problems that fuel the fires of particularly vitriolic ranters.