In the 6th century B.C., the philosopher-mathematician Pythagoras declared "The World is Made of Numbers". Ever since, and until 4e, developers have been trying to convert his statement into RPG form. One of the ways in which 4e is different from pretty much any prior version of the game is that it has dislodged numbers from the center of the game. Like Copernicus declaring that the Earth is not the center of the universe, this has caused some consternation, often because most people (and at times, I think, even the developers) have not realized how the game has changed at a fundamental level.
I think dice-based role-playing games can be divided into two categories, which I have labeled (in my most unweildy manner), numerocentric and protagonocentric.
Most games are numerocentric. In such games, the game revolves around the numbers primarily, and the PCs must fit the numbers. The numbers, in fact, become a sort of set of physical laws for the world. They are objective, and unchanging and anything that has an impact on the world must have some sort of number or mechanic associated with it.
Protagonocentric games, in contrast, revolve around the player characters. The numbers do not reflect objective reality, but rather a subjective reality that simply defines how the world interacts with the characters in the specific moment of time in which that slice f the world is relevant to the characters' ongoing shared story. In a protagonocentric world, the numbers are malleable.
A solo creature that escapes the PCs at level 5 might be encountered as an elite creature at level 10, a standard creature at level 14, and a mere minion at level 22. The creature's powers might be altered at each encounter to reflect the relative threat level that creature poses to the PCs at the specific encounter. Does this mean the creature has changed? No. It only means the way the characters interacts with the creature has changed because the characters themselves have developed over the course of the game.
Adjusting to a Protagonocentric World
The shift in 4e from numerocentricity to protagonocentricity is sometimes subtle and often jarring, particularly for players accustomed to numbers as king. Here are just a few of the many ways in which the shift has manifested:
½ level bonus: Many players are troubled by the fact that every adventurer gets good at all adventuring abilities with XP, even if their character is utterly disinterested in the endeavor. (My wizard could care less about Athletics -- why should he get a bonus to it?) But the bonus need not represent your character getting better. It measures your ability relative to the other PCs; there's no cause to compare a character's bonus at level 20 to the character's bonus at level 10 -- the two characters don't interact and do not exist in the same encounter.
Minions: Some players are confused by the existence of minions. How do they survive in the world with only one hp? Do they understand that they cannot be damaged on a miss? But minions are fragile only in relation to the PCs in the encounter in which they meet. They don't die when they nick themselves shaving. To the extent the PCs understand the enemy to be a minion, it only means they have observed the enemy and realize that the enemy is dangerous, but easily dispatched.
Statless NPCs: In prior editions, all NPCs received the same stats -- AC, hp, attacks, etc. In 4e, you are encouraged to give an NPC the stats that are needed in the encounter. If the NPC is a village healer, it only needs to be given a Heal Skill bonus and the rituals the PCs might hire the healer to cast -- everything else can be described narratively. The NPC is now primarily defined by her place in the story, not the numbers on her sheet.
Artisanship: Prior editions had numerical representations for skills like blacksmithing and baking -- skills that were improved by garnering XP to be used on non-weapon proficiency slots and skill points by slaying creatures. Now, such artisanship is to be described narratively, without numbers. To the extent that a character's background involves an artistic ability, that too is to be handled narratively between the PC and DM, based on the background written by the player and approved by the DM. To the extent that NPCs and PCs must compare relative skill, it will be handled by its relative importance to the story. How does the NPC's background stack up against the PC's background?
The Ongoing Gravity of Numbers
While 4e has traveled a long way from pure numerocentrism to protagonocentrism, it has not utterly eliminated the objective nature of numbers. Here are a few of the many ways in which numerocentricity still pervades 4e:
The Effect of Altitude: Damage from a fall is still objectively based on the height fallen, even though hit points are the most subjective mechanic ever developed. Also, the length and height of a jump is objectively determined from an Athletics check. I believe that these should be tailored to the game. If the DM does not want epic characters confidently jumping off earthmotes knowing the fall will not even bloody them, he should be able to determine falling damage by the threat level the fall represents to the characters.
The Hardness of Objects: While monsters are malleable based on the threat they pose to the PCs, objects remain universal. A fomorian might be an elite, solo, or minion, but an iron door will always have the same hit points. Traps are given mechanical representations based on the party's experience at the moment the trap is encountered -- other physical objects should as well.
Living in a Relative World
The purpose of this article is to encourage DMs and players to embrace the protagonocentric nature of 4e. When designing an encounter, the question should not be "how many hit points does a heffalump possess", but rather "how difficult should this heffalump be to the PC?" When a PC is interacting with the world, do not use the math to conclude objective facts about that object or creature; understand that the numbers only reflect the object or creature's qualities subjective to your character.
I think protagonocentrism is a great development in RPGs. It places story over the numbers. I understand why some people prefer to imagine the rules of RPGs operating like physical laws. But for me, the narrative benefits that come from a game built for the characters outweighs the universality that comes from a world made of numbers.