Where The Dials Are

As an example, imagine a platonically simple RPG system, where the maximum importance of things in the game is related to where they come from.

For simplicity's sake we can say it's resolved on a d20.

1. Anything on your character sheet--anything established from the beginning about your character or anything in the players' section of a book about how your class/race abilities are supposed to work (including a fighters' weapons or a wizard's spells)--is worth a maximum of +1 (or a minimum of -1). So it says on your sheet that your PC is strong? That's a +1 to do damage. It says the PC is strong and a fighter? Still only +1. Your PC is strong and a fighter and 10th level? Still only +1.

2. Anything the GM imposes because of the situation? That's worth a maximum/minimum of +/-1. So the GM says like you're fighting in tar: minus 1 to hit. You're fighting in tar and fighting multiple opponents? Still only minus 1.

3. Anything you, the player, think up to do that's a fairly non-situational and reusable tactic--that's worth a maximum of +/-1. So you go "Ok, this is a monster with a shield, so I'll use a flail instead of an axe" (this is, as I understand it, one of the points of using chain weapons--to get around shields). So you'd get a +1. Most new power stunts you'd invent in a superhero game would be included here.

4. Anything that is something the player thought up plus it uses something established that's situational, that's a maximum of +/-2. So like "I scoop up the tar and throw it in the enemy's eyes because that'll distract and maybe blind it" that's a +2. It's not only a player idea, it's a player idea building on the fiction that's set up at that particular moment.

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So the pie chart down here sums up the relative influence each factor could have in this scheme, assuming each factor is pushed to its maximum...

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What's the point of this?

Point is a lot of arguments about playstyles basically boil down to how different groups would want to weight these 4 factors.

You can talk about how an encounter-as-GMed by a certain person works (and, to a less accurate degree, how a given game is meant to work or usually works) in terms of how important each of these factors is.

In our imaginary game, things are at 1, 1, 1, 2, but imagine if we tweak the dials:

Some people want what's on their character sheet--that blue area--to be like reliably +6 compared to the other stuff, so no situation could overpower what is established about the PC and the way the PC is and s/he's "role-protected". Not only against the GM but against other players. This isn't necessarily about winning, it's about always performing like the character the player imagines. The thief's good at climbing even if the player's no good at thinking up extra reasons the thief should do to be good at climbing.

Some people would want factor 2 to be at +/-6 so that the onus is on the players to solve situations more or less on terms as they are presented by the GM. Yes, your clever plan will give you a bonus, but not so much of a bonus that it overpowers the overall logic of the situation. An only-one-solution puzzle essentially works this way. Trying to "beat a module" like Tomb of Horrors often works a lot like this, although a certain degree of Factor 4 comes into it (like under "crowning moment of awesome"here).

Some people would want to weight the player ideas (3) heavily, so that the game is largely about players shaping the setting creatively. Games where the players get to narrate a lot and the more they narrate the more of a mechanical bonus they get work like this.

Some people would want to weight 4 really heavily so that the game is about players solving scenarios by using resources provided in those scenarios (or previous linked ones, a whole campaign might be considered a "scenario" here). This would be weighted heavily if every encounter is supposed to force players to think outside the box.

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These aren't the only factors that affect the outcome of an encounter, of course:

-You could easily add a factor labelled "chance" to the chart--that would simply show swingy a game was. But I think most people already know about that idea. In the scheme above, since it assumes a d20 is being rolled, chance is way more powerful than any of the other stuff, even put together.

-You could also add a factor labelled "GM guidelines" to the chart. There's already a space for player guidelines ("Character Sheet")--the "GM Guidelines" are things like the Monster Manuals numbers or a module's description of how much damage a trap does. Between these two categories you have all the static numbers written into the rules. That factor would describe the maximum amount of influence over the situation the game's author's ideas (rules-as-written for the GM) would have over the situation. This kind of thing is rarely explicitly enforced in play except when players are trying to see if they can "beat" a module as-written. In practice, these factors (giant eagles have 26 hit points?) are basically a subset of the Situation--the GM has total discretion here.

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Some other observations here:

-In games where PC advancement is a big deal (like D&D), the game can easily slide from 3 or 4 being really powerful to 1 being really powerful at higher levels. Like once someone's at +13 to move silently, your clever idea to put sponges under your shoes that was giving you a +1 earlier doesn't seem like much of a big deal any more.

-In a wargame like Warhammer 40, where there's little to zero room to go outside the rules, your main tactical concern is to decide when and how to use which absolutely-defined troop type. Factor 1 is king. The enjoyment and complexity comes from having a very wide range of buttons to press and possible interactions you can activate on your turn. That is: if factor 1 is the most important, you'll want a lot of different options at your fingertips to keep things interesting.

-1 being really powerful and 3 being really powerful enforce player agency in two very different ways. The first enforces sort of the-right-to-play-who-you-wanna-play whereas the second enforces the right to reliably contribute new ideas as the game progresses.

-3 being really powerful and 4 being really powerful make the game about creative collaboration but in two different ways.

-This isn't meant to be an exhaustive description of the parts of games. See my answer to Semiprometheus below...