Buried deep within every game system, whether paper & pencil, console, or MMORPG is the engine that drives combat. Hardcore mathematicians spend countless hours discussion these core mechanics. Testers spend even more time helping to perfect the exact details and values of the base line numbers. But, when you strip away all the superfluous additions, addendums, discussion, and even testing, what remains are 4 core concepts; Avoidance, Mitigation, Chance, Damage. While their names are subject to the whims of game designers, these four fundamental attributes form the utmost basis of good game design. Each one is juxtaposed by another, and it takes a great deal of work to have all four in perfect balance.
In any given combat, it all starts with an act . . . something, somebody desires to do. Whether that somebody is a computer controlled object or a player, all combat starts something initiating a combat maneuver. Regardless of the genre, game system, graphics, professions or any other details, every single game uses something to represent a degree of success in that act. For lack of a better term, that is the Chance. Depending on the game mechanics, this could involve hundreds of variables, but when all is said and done, a random number generator fires off and the result checked against that Chance.
Avoidance is the counter to Chance and is perhaps the easiest to understand. Like all four attributes, numerous mathematical computations can take into account the ability of the object (object being any given person or entity within a game) to deflect, dodge, duck, parry, weave, jump, and other such verbiage to describe an objects desire to just not be hit. Depending on the desire of the core team, this could represent either a reduction in the chance to hit, or even another randomized chance representing a complete negation in the successfully determined hit.
After determining if a combat action has indeed connected with its target, how much damage the initiator inflicts on the target must be calculated. Damage is the simplest of the four. It is the raw amount of damage being inflicted and can be affected by several factions including, but not limited to skill, weapon type, weapon size, weapon construction, training, hit location, or any thing game designers can imagine. Here to, a balance must be achieved in determining the overall damage by taking into account the rate of damage attempts versus the potential value range. Large possible damage values have a lower frequency rates. The massive, but slow two handed sword as apposed to the small but quick dagger.
Having determined if the combat action succeeds and how much potential damage is, the last stage is to determine the amount, if any, of mitigation occurs. This fourth statistic reduces to incoming damage to reflect the ability of the target to absorb the incoming blow rather than deflecting it. Mitigation is to Damage what Avoidance is to Chance to hit. Some games use a general damage allocation system and bundle Avoidance and Mitigation in a single statistic. Some even adjust the mitigation factor by damage type to achieve combat harmony. In game design, good game design, the lower the Mitigation the higher the Avoidance.
In any given game system, there are far more factors that those listed above; however, these attributes form the core of the mathematical combat engine. Balancing these attributes is among the hardest to perfect and consume large amounts of test and design time. If not perfectly in tune, a game system can collapse. In practice, perfection is never fully achieved, but it is a goal the designers strive for nonetheless.