The Basic Play Balance Process
With ground rules, and basic techniques aside, process is important. There are several steps in the play balance process, each of which have assorted techniques which can be used to enhance the balance of the game.
The first priority is always to get the game in a fun and playable state, and this requires macrocalibration, or getting the game in a state where most elements are at least vaguely balanced, and no element is egregiously imbalanced. Once this state is reached, it is possible to continue to hone the balance between specific instances of game elements, such as races or sides in an RTS.
Of course, since games are often macrocalibrated well before they reach alpha stage, it is possible that they may have to be recalibrated as new lumps of functionality are added to the game. Erin Daly, lead designer of Homeworld, suggests that adding groups of related functionality at the same time, and doing a macrocalibration when they are added, is generally the most effective way to keep the game playable throughout development.
Once the final macrocalibration has been achieved, hopefully in late alpha, the game can be microcalibrated, or "tweaked", to a perfectly balanced state.
Allowing for a balanceable game system is obviously only the first step towards a balanced game. Even the most immaculate design must be implemented, and just as error can seep into implementations, slight errors are often made in the initial design. In addition, many game values really can't even be effectively guessed until the game is implemented. In these situations, which generally occur during the pre-alpha and alpha stages, designers must use macrocalibration techniques or "get the balance values in the right ballpark".
Macrocalibration should always be completed before microcalibration is begun; small balance changes will be washed away and made into useless work if the foundation that the game rests on is still in transition. While macrocalibrating, the goal is to "find" the target gameplay that is described in the design document. Obviously, you can't polish the gameplay with small tweaks when you aren't even sure you've gotten the core gameplay to manifest!
In order to zero in on the core gameplay desired, it is important to explicitly define what the core gameplay is like and how it will manifest. Once this is done, it is possible to establish some sort of baseline, or "anchor" as Ensemble Studios calls it. For instance, for game pacing you might set a baseline of "roughtly ten minute-long games" or for the player character's toughness you might set a baseline of "three attacks from a dangerous monster should be deadly". Once you get an incarnation of each game element (ONE map, ONE character class, ONE dialogue, etc) that works satisfactorily well, it is easy to expand upon the game, using the baseline game element as a ballpark figure to start from.
Once you have a particular element macrocalibrated, balance math may be useful in some cases to "clone" the result to similar elements. Although balance math is of dubious usefulness in perfecting the balance of a system because it is hard for it to correctly take into account more subtle issues, it is still useful for applying a baseline to various game elements. One formula that is universally useful to almost every game is the cost effectiveness equation.
The cost effectiveness formula states that for a component, its:
Game Impact * Durability = Effectiveness
And it follows that:
Square root (Game Impact * Durability/Cost^2) = cost effectiveness
Game impact might be firepower (damage * Rate of Fire), or points. Durability might be number of uses, or hitpoints. Cost represents game resources, which are often gold, money or turns (e.g. the "actual" cost of a move in chess is a turn).
Another useful equation that is primarily suited towards strategy games and other "combat" situations is the fragmenation formula. Fragmentation simulates the fact that in a combat situation, swarms of small units with a sum effectiveness equal to a few larger units are not actually the same in effectiveness. The swarm of small units is always lower in effectiveness, assuming no other subtle factors (such as "overkill" when damage is lost to no useful means). This is because a swarm gradually loses power over time as individual units die, while a large unit or element lasts much longer, and hence, doesn't suffer from incremental loss of effectiveness. The formula for relative effectiveness due to this effect is:
Reduction in Effectiveness (to smaller units) = .5 + .5(Number of Large / Number of Small for the same cost).
The inverse of the resulting number is the effectiveness increase to the larger units.
These formulas and other "balance math" are typically best for ballpark balance. Attempts to reach perfect balance mathematically are best avoided, except with fairly simple game systems. For instance, balancing Risk isn't terribly difficult because the game rules are fairly simple, and player choices can be quantified very effectively. Balancing monopoly is doable, but trickier than risk, because the random element (dice rolling) can produce much more widespread effects than it does in risk, and also because monopoly has a much larger number of distinct game elements (chance cards, mortgage rules, jail, etc). More complexity, such as that in a modern RTS, creates a situation where a complete mathematical play balance solution is worth of a doctoral thesis.
Balance math is particularly potent when used in symmetrical games, such as games like Warcraft 2 or Homeworld, in which the opposing sides are more or less the same when it comes to game functionality. The more similarities two elements or groups of elements possess, the fewer hard-to-model variables exist to throw off balance math.