When running a game, I find it handy to figure out what the goal of it is so that I can figure out how to adjust the rules to fit my group’s needs, and also in order to better derive my own explanations for things that fall outside of the rules but which may come up in play (for instance, if a certain roll result normally fails, but defense is an active skill, and both parties come up with a, what happens?). These are the sort of things that understanding helps create a more consistent response to, and consistency in rules interpretation is important.
My three cores of any game that I look at when writing houserules are Simulation, Story, and Speed; these represent different things, but almost any game has all three (a few exclude simulation or story elements). The decision to look at speed as a core factor really stemmed out of experience; rather than creating house-rules more complicated than the original game’s rules, I try to make sure that I keep them the same “flavor” so that they don’t become a stumbling block.
Simulation is simply a measure of how realistic a game attempts to be; something like D&D falls about halfway on this scale, since although it attempts to be somewhat realistic it abstracts most of its components. Savage Worlds, on the other hand, falls much lower on this scale, as the mantra of “Fast, Furious, Fun!” doesn’t exactly coincide with attempting to model everything down to a small degree of realism. It’s rare to see a game go very high on simulation, since it can quickly turn into a spreadsheet with dice (look at any hard sci-fi game that seriously tackles space flight from a micro scale and begins to analyze stuff like fuel, mass, and flight-time; I’ve seen a game with trigonometry required). Typically players don’t like this sort of game, since the scope of a traditional roleplaying scenario extends beyond the sort of thing that people are really a fan of; they may enjoy the concept of realistically flying a spaceship or performing medical operations, but the massive rolls of paper used up by the GM hardly justify the ends. Understanding the simulationism or lack thereof in a game is useful, because having wacky, arbitrary results mixed in with heavily realistic systems throws out the best parts of both (for instance, integrating Savage Worlds with a three-part sniper shot system that accounts for weather, lighting, relative position, and movement using a large table full of modifiers at each stage).
Story is another core element of gaming; it tends to, but does not always, contradict the simulation parts of gaming, or supplant it-for instance, Vampire the Masquerade may make an attempt to measure how fast characters can move, but it doesn’t care whether they move 20 meters or 21 in a combat turn. On a more practical level, however, the amount of storytelling that a game focuses on is really related to the role of the player’s characters; Only War, for instance, cares about the players’ characters but throws in meaningless “backup” characters to send out on missions best left to the expendable. On the other hand, something like Eclipse Phase allows an out for characters dying, but this exists for everyone (except the unlucky people who don’t have access to it) in the setting. Call of Cthulhu is heavily apathetic to the player’s characters, with the results sharing Lovecraft’s disregard for his protagonists and likely murdering them pretty quickly on their first encounter with anything truly grisly. This is one of those things where adding or removing stuff will change the feel of the game if done improperly; adding a rip-off of Shadowrun’s Edge to Call of Cthulhu will allow investigators a better chance at surviving an encounter with something that should kill them, immediately changing the game from one of horror and careful action to one in which recklessness is not inherently fatal.
Speed is another thing to consider-it usually ties in with simulation elements, since attempting realism usually means achieving more granularity through more complex mechanics, but everything matters. D&D, for instance, usually winds up with a two or three stage attack; if necessary the roll is made for accuracy and then the roll is made for damage, and depending on the attack there may be a save involved. Occasionally this will rise up to a four or five stage process, but only rarely and usually with the assistance of magic or less-readily available interventions. On the other hand, Shadowrun has a three-stage minimum for attacks in Fourth and Fifth edition; an attack is made, a defense is made, and damage reduction is attempted, and combat spellcasters can worry about more. This is pretty common, but BattleTech: Alpha Strike still has a seven-stage attack flow to keep track of, not all of which always matter, but still enough to be a little intimidating to a rookie. Houseruling Shadowrun to use BattleTech’s location-based damage would be pretty much impossible, since it would add another couple steps to the whole process and slow down play pretty heavily.